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5.02:_The_First_Law_of_Thermodynamics
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<div class="box-objectives"> <span id="Learning_Objectives"></span><span id="Learning_Objectives"></span><h5 class="box-legend"><span class="lt-icon-default"><span style="display:none;"> </span>Learning Objectives</span></h5> <ul> <li class="lt-chem-21721" style="background-color: unset;">To calculate changes in internal energy</li> </ul> </div> <p class="lt-chem-21721" style="background-color: unset;">To study the flow of energy during a chemical reaction, we need to distinguish between a system, the small, well-defined part of the universe in which we are interested (such as a chemical reaction), and its surroundings, the rest of the universe, including the container in which the reaction is carried out (Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="98" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" 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In the discussion that follows, the mixture of chemical substances that undergoes a reaction is always the system, and the flow of heat can be from the system to the surroundings or vice versa.</p> <figure><img alt="Diagram showing three boxes labeled 'System,' 'Surroundings,' and 'Universe,' each containing a laboratory flask with blue liquid." style="width: 401px; height: 165px;" class="internal" loading="lazy" width="550" height="227" src="https://chem.libretexts.org/@api/deki/files/58270/ddfd5dc289640638921ad7e80db57152.jpg?revision=1&size=bestfit&width=401&height=165" /> <figcaption><span class="title-prefix">Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="99" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-100-NCM-N-35" d="M118 315C123 315 129 319 134 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331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-100-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 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data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-100-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" 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data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container></span>: A System and Its Surroundings. The system is that part of the universe we are interested in studying, such as a chemical reaction inside a flask. The surroundings are the rest of the universe, including the container in which the reaction is carried out.</figcaption> </figure> <p class="lt-chem-21721" style="background-color: unset;">Three kinds of systems are important in chemistry. An <strong>open system</strong> can exchange both matter and energy with its surroundings. A pot of boiling water is an open system because a burner supplies energy in the form of heat, and matter in the form of water vapor is lost as the water boils. A <strong>closed system</strong> can exchange energy but not matter with its surroundings. The sealed pouch of a ready-made dinner that is dropped into a pot of boiling water is a closed system because thermal energy is transferred to the system from the boiling water but no matter is exchanged (unless the pouch leaks, in which case it is no longer a closed system). An<strong> isolated system</strong> exchanges neither energy nor matter with the surroundings. Energy is always exchanged between a system and its surroundings, although this process may take place very slowly. A truly isolated system does not actually exist. An insulated thermos containing hot coffee approximates an isolated system, but eventually the coffee cools as heat is transferred to the surroundings. In all cases, the amount of heat lost by a system is equal to the amount of heat gained by its surroundings and vice versa. That is, <em>the total energy of a system plus its surroundings is constant</em>, which must be true if <em>energy is conserved</em>.</p> <p class="lt-chem-21721" style="background-color: unset;">The state of a system is a complete description of a system at a given time, including its temperature and pressure, the amount of matter it contains, its chemical composition, and the physical state of the matter. A state function is a property of a system whose magnitude depends on only the present state of the system, not its previous history. Temperature, pressure, volume, and potential energy are all state functions. The temperature of an oven, for example, is independent of however many steps it may have taken for it to reach that temperature. Similarly, the pressure in a tire is independent of how often air is pumped into the tire for it to reach that pressure, as is the final volume of air in the tire. Heat and work, on the other hand, are not state functions because they are <em>path dependent</em>. For example, a car sitting on the top level of a parking garage has the same potential energy whether it was lifted by a crane, set there by a helicopter, driven up, or pushed up by a group of students (Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="100" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-101-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 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data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container>). The amount of work expended to get it there, however, can differ greatly depending on the path chosen. If the students decided to carry the car to the top of the ramp, they would perform a great deal more work than if they simply pushed the car up the ramp (unless, of course, they neglected to release the parking brake, in which case the work expended would increase substantially!). The potential energy of the car is the same, however, no matter which path they choose.</p> <figure><img style="width: 362px; height: 290px;" class="internal" alt="Illustration of a multi-story parking garage with cars on different levels and ramps connecting them." loading="lazy" width="550" height="441" src="https://chem.libretexts.org/@api/deki/files/58271/c4edc2133cba844994fa308c6866479e.jpg?revision=1&size=bestfit&width=362&height=290" /> <figcaption><span class="title-prefix">Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="101" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-102-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 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transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-102-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="32" href="#MJX-102-NCM-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container>:</span> Elevation as an Example of a State Function. The change in elevation between state 1 (at the bottom of the parking garage) and state 2 (at the top level of the parking garage) is the same for both paths A and B; it does not depend on which path is taken from the bottom to the top. In contrast, the distance traveled and the work needed to reach the top do depend on which path is taken. Elevation is a state function, but distance and work are <em>not</em> state functions.</figcaption> </figure> <span id="Direction_of_Heat_Flow"></span><span id="Direction_of_Heat_Flow"></span><h2 style="background-color: unset;" class="lt-chem-21721">Direction of Heat Flow</h2> <p class="lt-chem-21721" style="background-color: unset;">The reaction of powdered aluminum with iron(III) oxide, known as the thermite reaction, generates an enormous amount of heat—enough, in fact, to melt steel (Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="102" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-103-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 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data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-103-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="32" href="#MJX-103-NCM-N-32"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-103-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:3" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="33" href="#MJX-103-NCM-N-33"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{3}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="3}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{3};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:3" data-semantic-level-number="1" data-speech-node="true">3</mn></mrow></math></mjx-assistive-mml></mjx-container>). The balanced chemical equation for the reaction is as follows:</p> <p class="mt-align-center lt-chem-21721" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="103" style="font-size: 85%; min-width: 58.257ex; position: relative;"><svg width="100%" height="2.262ex" role="img" focusable="false" data-mjx-viewbox="0 -750 25749.7 1000" aria-hidden="true" style="vertical-align: -0.566ex; min-width: 58.257ex;"><defs><path id="MJX-104-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-104-NCM-N-2062" 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data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:3" data-semantic-level-number="1" data-speech-node="true">3</mn></mrow></math></mjx-assistive-mml></mjx-container>: The thermite reaction produces so much heat that the iron it produces comes out molten, a property that makes this reaction useful in welding. 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data-semantic-role="unknown" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="71" data-semantic-attributes="latex:\mhchemrightarrow;texclass:REL" data-semantic-operator="infixop," data-semantic-level-number="4" data-speech-node="true"></mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="27,57" data-semantic-content="69" data-semantic-parent="71" data-semantic-owns="27 69 57" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="70" data-semantic-attributes="latex:2" data-semantic-level-number="5" data-speech-node="true">2</mn><mspace width="0.167em" data-latex="\,"></mspace><mo data-semantic-type="operator" 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data-semantic-level-number="6" data-speech-node="true">Fe</mi></mrow><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="57" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:7" data-semantic-="" data-semantic-children="32" data-semantic-content="31,33" data-semantic-parent="57" data-semantic-owns="31 32 33" data-semantic-level-number="6" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="72" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="3" data-speech-node="true">+</mo><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="35,53" data-semantic-content="54,35" data-semantic-parent="72" data-semantic-owns="35 54 53" data-semantic-level-number="3" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Al}"><mi data-mjx-auto-op="false" data-latex="Al" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="55" data-semantic-attributes="latex:\mathrm{Al};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="4" data-speech-node="true">Al</mi></mrow><mo 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data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="38" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="38" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="53" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:6" data-semantic-="" data-semantic-children="39,41" data-semantic-parent="53" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="39 41" data-semantic-level-number="5" data-speech-node="true"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="42" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">O</mi></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{3}"><mpadded height="0"><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="42" data-semantic-attributes="latex:{\smash[t]{3}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">3</mn></mpadded></mrow></mrow></msub><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="53" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="45" data-semantic-content="44,46" data-semantic-parent="53" data-semantic-owns="44 45 46" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="72" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="3" data-speech-node="true">+</mo><mtext data-latex="\label{5.2.2}" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-parent="72" data-semantic-attributes="latex:\label{5.2.2}" data-semantic-level-number="3" data-speech-node="true">heat</mtext></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21721" style="background-color: unset;">to indicate that heat is one of the products. Chemical equations in which heat is shown as either a reactant or a product are called <em>thermochemical equations</em>. In this reaction, the system consists of aluminum, iron, and oxygen atoms; everything else, including the container, makes up the surroundings. During the reaction, so much heat is produced that the iron liquefies. Eventually, the system cools; the iron solidifies as heat is transferred to the surroundings. A process in which heat (<em>q</em>) is transferred <em>from</em> a system <em>to</em> its surroundings is described as exothermic. 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display="inline"><math data-latex="q < 0" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,2" data-semantic-content="1" data-semantic-attributes="latex:q < 0" data-semantic-owns="0 1 2" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 1 2)"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:q" data-semantic-level-number="1" data-speech-node="true">q</mi><mo data-latex="<" data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:<" data-semantic-operator="relseq,<" data-semantic-level-number="1" data-speech-node="true"><</mo><mn 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data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:8" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="7" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="39" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-children="11,27" data-semantic-content="33,11" data-semantic-parent="39" data-semantic-owns="11 33 27" data-semantic-level-number="5" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="34" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">O</mi></mrow><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="34" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:7" data-semantic-="" data-semantic-children="14" data-semantic-content="13,15" data-semantic-parent="34" data-semantic-owns="13 14 15" data-semantic-level-number="6" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="27" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="27" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="27" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></mrow></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="39" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mtext data-latex="~" data-semantic-type="text" data-semantic-role="space" data-semantic-annotation="factor:operator;clearspeak:unit;depth:6" data-semantic-="" data-semantic-parent="39" data-semantic-attributes="latex:~" data-semantic-level-number="5" data-speech-node="true"> </mtext></mrow></mrow><mo data-mjx-variant="-mhchem" data-mjx-texclass="REL" stretchy="true" data-latex="\mhchemrightarrow" data-semantic-type="operator" data-semantic-role="unknown" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="43" data-semantic-attributes="latex:\mhchemrightarrow;texclass:REL" data-semantic-operator="infixop," data-semantic-level-number="3" data-speech-node="true"></mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="32,30" data-semantic-content="41" data-semantic-parent="43" data-semantic-owns="32 41 30" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="18,21" data-semantic-content="31,18" data-semantic-parent="42" data-semantic-owns="18 31 21" data-semantic-level-number="4" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{H}"><mi mathvariant="normal" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:\mathrm{H};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">H</mi></mrow><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="32" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">⁡</mo><msub data-latex="{\vphantom{A}}_{\smash[t]{2}}" data-semantic-type="subscript" data-semantic-role="unknown" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="19,20" data-semantic-parent="32" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="19 20" data-semantic-level-number="5" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="42" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-children="22,28" data-semantic-content="29,22" data-semantic-parent="42" data-semantic-owns="22 29 28" data-semantic-level-number="4" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">O</mi></mrow><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="30" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="25" data-semantic-content="24,26" data-semantic-parent="30" data-semantic-owns="24 25 26" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{l}"><mi mathvariant="normal" data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:\mathrm{l};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">l</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21721" style="background-color: unset;">When heat is transferred <em>to</em> a system <em>from</em> its surroundings, the process is endothermic. By convention, <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="108" style="font-size: 85%; position: relative;"><svg width="1.023ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 452 1000" aria-hidden="true" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="q > 0" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-annotation="depth:1" data-semantic-id="3" data-semantic-children="0,2" data-semantic-content="1" data-semantic-attributes="latex:q > 0" data-semantic-owns="0 1 2" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 1 2)"><g data-mml-node="mi" data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:q" data-semantic-level-number="1" data-speech-node="true"><use data-c="1D45E" href="#MJX-109-NCM-I-1D45E"></use></g></g></g><defs><path id="MJX-109-NCM-I-1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 280 412C307 412 327 399 340 373Z"></path><path id="MJX-109-NCM-N-3E" d="M686 227C696 232 701 239 701 250C701 261 696 268 686 273L112 545C109 546 105 547 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data-semantic-content="1" data-semantic-attributes="latex:q > 0" data-semantic-owns="0 1 2" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 1 2)"><g data-mml-node="mo" data-latex=">" data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:>" data-semantic-operator="relseq,>" data-semantic-level-number="1" data-speech-node="true"><use data-c="3E" href="#MJX-109-NCM-N-3E"></use></g><g data-mml-node="mn" data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:0" data-semantic-level-number="1" data-speech-node="true" transform="translate(1055.8,0)"><use data-c="30" href="#MJX-109-NCM-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="q > 0" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,2" data-semantic-content="1" data-semantic-attributes="latex:q > 0" data-semantic-owns="0 1 2" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 1 2)"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:q" data-semantic-level-number="1" data-speech-node="true">q</mi><mo data-latex=">" data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:>" data-semantic-operator="relseq,>" data-semantic-level-number="1" data-speech-node="true">></mo><mn data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:0" data-semantic-level-number="1" data-speech-node="true">0</mn></math></mjx-assistive-mml></mjx-container> for an endothermic reaction.</p> <div class="box-note"> <span id="Heat_is_technically_not_a_component_in_Chemical_Reactions"></span><span id="Heat_is_technically_not_a_component_in_Chemical_Reactions"></span><h5 class="box-legend"><span class="lt-icon-default">Heat is technically not a component in Chemical Reactions</span></h5> <p class="lt-chem-21721" style="background-color: unset;">Technically, it is poor form to have a <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="109" style="font-size: 85%; position: relative;"><svg width="4.371ex" height="1.595ex" role="img" focusable="false" viewbox="0 -694 1932 705" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-110-NCM-I-210E" d="M512 138C489 59 457 19 415 19C402 19 395 28 395 47C395 62 401 85 413 116C453 223 473 296 473 335C473 406 427 445 356 445C303 445 257 423 218 380L291 679C289 688 287 694 274 694C241 694 168 685 155 684C140 682 132 675 132 660C132 650 141 645 159 645C180 645 203 646 205 632L59 43C56 32 55 25 55 21C55 0 66-11 87-11C107-11 121-1 128 18L168 182C180 231 189 268 196 293C199 300 207 314 220 334C256 388 300 415 353 415C386 415 402 393 402 350C402 309 382 236 342 130C333 107 329 89 329 74C329 26 365-11 413-11C457-11 492 14 517 65C536 105 546 132 546 145C546 154 541 159 530 159C527 159 512 150 512 138Z"></path><path id="MJX-110-NCM-N-2061" d=""></path><path id="MJX-110-NCM-I-1D452" d="M124 129C124 153 129 186 139 227L188 227C253 227 303 235 339 250C372 264 394 284 405 309C412 326 415 342 415 355C415 410 363 442 307 442C268 442 229 432 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374Z"></path><path id="MJX-110-NCM-I-1D461" d="M330 419C330 428 320 433 299 433L218 433C244 537 257 591 257 595C257 616 246 626 225 626C202 626 188 613 182 587L145 433L56 433C34 433 23 432 23 411C23 400 33 395 54 395L135 395C86 200 62 97 62 84C62 28 100-11 156-11C194-11 227 6 256 41C280 70 297 98 308 125C312 136 314 142 314 145C314 154 309 159 299 159C291 159 285 154 281 143C247 60 206 19 157 19C140 19 131 33 131 60C131 75 133 91 137 107L208 395L297 395C323 395 330 397 330 419Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="heat" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:1" data-semantic-id="8" data-semantic-children="0,6" data-semantic-content="7,0" data-semantic-attributes="latex:heat" data-semantic-owns="0 7 6" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(8 0 7 (6 1 4 2 5 3))"><g data-mml-node="mi" data-latex="h" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="8" data-semantic-attributes="latex:h" data-semantic-operator="appl" data-semantic-level-number="1" data-speech-node="true"><use data-c="210E" href="#MJX-110-NCM-I-210E"></use></g><g data-mml-node="mo" data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="7" data-semantic-parent="8" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="1" data-speech-node="true" transform="translate(576,0)"><use data-c="2061" href="#MJX-110-NCM-N-2061"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:2" data-semantic-id="6" data-semantic-children="1,2,3" 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data-speech-node="true">t</mi></mrow></math></mjx-assistive-mml></mjx-container> term in the chemical reaction like in Equations <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="110" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-111-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 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However, this is a convenient approach to represent exothermic and endothermic behavior and is commonly used by chemists.</p> </div> <span id="The_First_Law"></span><span id="The_First_Law"></span><h2 style="background-color: unset;" class="lt-chem-21721">The First Law</h2> <p class="lt-chem-21721" style="background-color: unset;">The relationship between the energy change of a system and that of its surroundings is given by the <strong>first law of thermodynamics</strong>, which states that the energy of the universe is constant. 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href="#MJX-113-NCM-N-29"></use></g></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="U_{univ}=ΔU_{sys}+ΔU_{surr}=0 \label{5.2.4a} " display="block" data-semantic-structure="(47 (46 (44 (14 5 (13 6 10 7 11 8 12 9)) 15 (43 (40 16 39 (24 17 (23 18 21 19 22 20))) 25 (42 26 41 (36 27 (35 28 32 29 33 30 34 31)))) 37 38) (4 (3 0 1 2))))"><mtable displaystyle="true" data-latex="U_{univ}=ΔU_{sys}+ΔU_{surr}=0 \label{5.2.4a}" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="46" data-semantic-attributes="latex:U_{univ}=ΔU_{sys}+ΔU_{surr}=0 \label{5.2.4a} " data-semantic-owns="46" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="44" data-semantic-content="4" data-semantic-parent="47" 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data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:\Delta" data-semantic-level-number="4" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="28" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="{U_{s y s}}"><msub data-latex="U_{s y s}" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="6,12" data-semantic-parent="28" data-semantic-attributes="latex:{U_{s y s}};texclass:ORD" data-semantic-owns="6 12" data-semantic-level-number="4" data-speech-node="true"><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:U" data-semantic-level-number="5" data-speech-node="true">U</mi><mrow data-mjx-texclass="ORD" data-latex="{s y s}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="7,8,9" data-semantic-content="10,11" data-semantic-parent="13" data-semantic-attributes="latex:{s y s};texclass:ORD" data-semantic-owns="7 10 8 11 9" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:s" data-semantic-level-number="6" data-speech-node="true">s</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="y" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:y" data-semantic-level-number="6" data-speech-node="true">y</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:s" data-semantic-level-number="6" data-speech-node="true">s</mi></mrow></msub></mrow></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="30" data-semantic-content="15" data-semantic-parent="32" data-semantic-owns="15 30" data-semantic-level-number="3" data-speech-node="true"><mo data-latex="−" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:−" data-semantic-operator="prefixop,−" data-semantic-level-number="4" data-speech-node="true">−</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="16,26" data-semantic-content="29" data-semantic-parent="31" data-semantic-owns="16 29 26" data-semantic-level-number="4" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:Δ" data-semantic-level-number="5" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="30" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><msub data-latex="U_{s u r r}" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="17,25" data-semantic-parent="30" data-semantic-attributes="latex:U_{s u r r}" data-semantic-owns="17 25" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:U" data-semantic-level-number="6" data-speech-node="true">U</mi><mrow data-mjx-texclass="ORD" data-latex="{s u r r}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="18,19,20,21" data-semantic-content="22,23,24" data-semantic-parent="26" data-semantic-attributes="latex:{s u r r};texclass:ORD" data-semantic-owns="18 22 19 23 20 24 21" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:s" data-semantic-level-number="7" data-speech-node="true">s</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="25" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="u" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:u" data-semantic-level-number="7" data-speech-node="true">u</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="25" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:r" data-semantic-level-number="7" data-speech-node="true">r</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="25" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:r" data-semantic-level-number="7" data-speech-node="true">r</mi></mrow></msub></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21721" style="background-color: unset;">where the subscripts univ, sys, and surr refer to the universe, the system, and the surroundings, respectively. Thus the change in energy of a system is identical in magnitude but opposite in sign to the change in energy of its surroundings.</p> <div class="box-note"> <p class="lt-chem-21721" style="background-color: unset;">The tendency of all systems, chemical or otherwise, is to move toward the state with the lowest possible energy.</p> </div> <p class="lt-chem-21721" style="background-color: unset;">An important factor that determines the outcome of a chemical reaction is the tendency of all systems, chemical or otherwise, to move toward the lowest possible overall energy state. As a brick dropped from a rooftop falls, its potential energy is converted to kinetic energy; when it reaches ground level, it has achieved a state of lower potential energy. Anyone nearby will notice that energy is transferred to the surroundings as the noise of the impact reverberates and the dust rises when the brick hits the ground. Similarly, if a spark ignites a mixture of isooctane and oxygen in an internal combustion engine, carbon dioxide and water form spontaneously, while potential energy (in the form of the relative positions of atoms in the molecules) is released to the surroundings as heat and work. 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data-semantic-level-number="3" data-speech-node="true">2</mn></msub></mrow><mo data-latex="/" data-semantic-type="operator" data-semantic-role="division" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:/" data-semantic-operator="infixop,/" data-semantic-level-number="1" data-speech-node="true">/</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-children="7,8" data-semantic-content="9,5" data-semantic-parent="13" data-semantic-owns="7 9 8" data-semantic-level-number="1" data-speech-node="true"><msub data-latex="H_2" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="5,6" data-semantic-parent="10" data-semantic-attributes="latex:H_2" data-semantic-owns="5 6" data-semantic-level-number="2" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:H" data-semantic-operator="appl" data-semantic-level-number="3" data-speech-node="true">H</mi><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:2" data-semantic-level-number="3" data-speech-node="true">2</mn></msub><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="10" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="2" data-speech-node="true">⁡</mo><mi data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:O" data-semantic-level-number="2" data-speech-node="true">O</mi></mrow></math></mjx-assistive-mml></mjx-container> product mixture is less than that of the isooctane/ <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="115" style="font-size: 85%; position: relative;"><svg width="2.714ex" height="1.934ex" role="img" focusable="false" viewbox="0 -705 1199.6 855" aria-hidden="true" style="vertical-align: -0.339ex;"><defs><path id="MJX-116-NCM-I-1D442" d="M702 263C727 320 740 377 740 435C740 513 717 577 670 628C623 679 561 705 484 705C431 705 378 692 325 666C217 613 138 529 87 415C62 359 49 303 49 246C49 167 72 103 119 53C166 3 228-22 306-22C358-22 410-9 463 16C572 69 651 152 702 263M644 474C644 341 584 208 520 129C476 74 400 12 312 12C205 12 149 105 149 218C149 253 156 300 169 357C196 475 264 579 353 633C396 659 438 672 478 672C586 672 644 586 644 474Z"></path><path id="MJX-116-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="O_2" data-semantic-structure="(2 0 1)"><g data-mml-node="msub" data-latex="O_2" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:1" data-semantic-id="2" data-semantic-children="0,1" data-semantic-attributes="latex:O_2" data-semantic-owns="0 1" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mi" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="2" data-semantic-attributes="latex:O" data-semantic-level-number="1" data-speech-node="true"><use data-c="1D442" href="#MJX-116-NCM-I-1D442"></use></g><g data-mml-node="mn" transform="translate(796,-150) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="2" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true"><use data-c="32" href="#MJX-116-NCM-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="O_2" data-semantic-structure="(2 0 1)"><msub data-latex="O_2" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-attributes="latex:O_2" data-semantic-owns="0 1" data-semantic-level-number="0" data-speech-node="true"><mi data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:O" data-semantic-level-number="1" data-speech-node="true">O</mi><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></msub></math></mjx-assistive-mml></mjx-container> reactant mixture. The two cases differ, however, in the form in which the energy is released to the surroundings. In the case of the falling brick, the energy is transferred as work done on whatever happens to be in the path of the brick; in the case of burning isooctane, the energy can be released as solely heat (if the reaction is carried out in an open container) or as a mixture of heat and work (if the reaction is carried out in the cylinder of an internal combustion engine). Because heat and work are the only two ways in which energy can be transferred between a system and its surroundings, any change in the internal energy of the system is the sum of the heat transferred (q) and the work done (w):</p> <p class="mt-align-center lt-chem-21721" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="116" style="font-size: 85%; min-width: 30.771ex; position: relative;"><svg width="100%" height="2.364ex" role="img" focusable="false" data-mjx-viewbox="0 -772.5 13600.7 1045" aria-hidden="true" style="vertical-align: -0.616ex; min-width: 30.771ex;"><defs><path id="MJX-117-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-117-NCM-N-2062" d=""></path><path id="MJX-117-NCM-I-1D448" d="M642 680C623 680 559 683 540 683C525 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data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.2.6}" data-semantic-level-number="4" data-speech-node="true" transform="translate(389,0)"><use data-c="35" href="#MJX-117-NCM-N-35"></use><use data-c="2E" href="#MJX-117-NCM-N-2E" transform="translate(500,0)"></use><use data-c="32" href="#MJX-117-NCM-N-32" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-117-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="36" href="#MJX-117-NCM-N-36" transform="translate(1556,0)"></use></g><g data-mml-node="mtext" data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" 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data-speech-node="true">w</mi></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21721" style="background-color: unset;">Although <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="117" style="font-size: 85%; position: relative;"><svg width="1.023ex" height="1.439ex" role="img" focusable="false" viewbox="0 -442 452 636" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-118-NCM-I-1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 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data-semantic-attributes="latex:s" data-semantic-level-number="3" data-speech-node="true">s</mi></mrow></msub></math></mjx-assistive-mml></mjx-container>) is independent of the path taken and is therefore a state function. A major task for the designers of any machine that converts energy to work is to maximize the amount of work obtained and minimize the amount of energy released to the environment as heat. An example is the combustion of coal to produce electricity. Although the maximum amount of energy available from the process is fixed by the energy content of the reactants and the products, the fraction of that energy that can be used to perform useful work is not fixed.</p> <p class="lt-chem-21721" style="background-color: unset;">Because we focus almost exclusively on the changes in the energy of a system, we will not use “sys” as a subscript unless we need to distinguish explicitly between a system and its surroundings.</p> <div class="box-note"> <p class="lt-chem-21721" style="background-color: unset;">Although <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="120" style="font-size: 85%; position: relative;"><svg width="1.023ex" height="1.439ex" role="img" focusable="false" viewbox="0 -442 452 636" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-121-NCM-I-1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 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data-semantic-children="1,7" data-semantic-parent="10" data-semantic-attributes="latex:U_{s y s}" data-semantic-owns="1 7" data-semantic-level-number="1" data-speech-node="true"><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:U" data-semantic-level-number="2" data-speech-node="true">U</mi><mrow data-mjx-texclass="ORD" data-latex="{s y s}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-="" data-semantic-children="2,3,4" data-semantic-content="5,6" data-semantic-parent="8" data-semantic-attributes="latex:{s y s};texclass:ORD" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="2" data-speech-node="true"><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:s" data-semantic-level-number="3" data-speech-node="true">s</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="y" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:y" data-semantic-level-number="3" data-speech-node="true">y</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:s" data-semantic-level-number="3" data-speech-node="true">s</mi></mrow></msub></math></mjx-assistive-mml></mjx-container>) is independent of the path taken and therefore is a state function.</p> </div> <p class="lt-chem-21721" style="background-color: unset;">Thus, because of the first law, we can determine <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="123" style="font-size: 85%; position: relative;"><svg width="3.604ex" height="1.67ex" role="img" focusable="false" viewbox="0 -716 1593 738" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-124-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-124-NCM-N-2062" d=""></path><path id="MJX-124-NCM-I-1D448" d="M642 680C623 680 559 683 540 683C525 683 518 675 518 659C518 650 525 645 539 644C582 644 603 631 603 605C603 599 602 592 600 585L511 232C496 175 467 126 424 84C377 39 325 17 269 17C195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641C292 643 309 644 338 644C364 644 375 644 375 668C375 678 369 683 358 683L231 680L104 683C88 683 81 674 81 659C81 652 84 647 89 646C99 645 107 644 112 644C143 643 161 641 166 640C171 639 173 636 173 631C173 629 172 622 169 611L74 230C69 211 67 192 67 172C67 57 150-22 265-22C330-22 390 3 445 54C498 102 532 158 548 223L636 574C649 625 677 643 739 644C753 645 760 653 760 668L760 672C757 679 752 683 743 683C724 683 661 680 642 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔU" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔU" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-124-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-124-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:U" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D448" href="#MJX-124-NCM-I-1D448"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔU" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔU" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:U" data-semantic-level-number="1" data-speech-node="true">U</mi></math></mjx-assistive-mml></mjx-container> for any process if we can measure both <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="124" style="font-size: 85%; position: relative;"><svg width="1.023ex" height="1.439ex" role="img" focusable="false" viewbox="0 -442 452 636" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-125-NCM-I-1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 280 412C307 412 327 399 340 373Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="q" data-semantic-structure="0"><g data-mml-node="mi" data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:q" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D45E" href="#MJX-125-NCM-I-1D45E"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="q" data-semantic-structure="0"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:q" data-semantic-level-number="0" data-speech-node="true">q</mi></math></mjx-assistive-mml></mjx-container> and <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="125" style="font-size: 85%; position: relative;"><svg width="1.62ex" height="1.025ex" role="img" focusable="false" viewbox="0 -442 716 453" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-126-NCM-I-1D464" d="M590 391C590 382 595 372 606 362C629 340 641 313 641 281C641 264 635 237 623 198C586 78 539 18 482 18C435 18 412 45 412 100C412 119 416 142 423 171C441 243 460 314 477 387C479 394 480 398 480 401C480 421 469 431 447 431C427 431 414 421 407 401L367 245C352 187 341 167 341 115C341 107 341 101 342 98C319 45 290 18 255 18C205 18 180 47 180 104C180 141 197 204 231 293C242 323 248 344 248 357C248 406 212 442 163 442C118 442 84 417 59 367C39 328 29 301 29 287C29 278 34 273 45 273C58 273 60 279 64 293C88 373 120 413 160 413C174 413 181 403 181 384C181 369 175 347 164 317C127 220 108 154 108 117C108 32 165-11 252-11C294-11 328 10 355 53C375 10 416-11 479-11C541-11 590 30 625 112C648 164 691 302 691 369C691 384 690 394 689 399C685 418 666 442 644 442C618 442 590 417 590 391Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="w" data-semantic-structure="0"><g data-mml-node="mi" data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:w" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D464" href="#MJX-126-NCM-I-1D464"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="w" data-semantic-structure="0"><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:w" data-semantic-level-number="0" data-speech-node="true">w</mi></math></mjx-assistive-mml></mjx-container>. Heat, <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="126" style="font-size: 85%; position: relative;"><svg width="1.023ex" height="1.439ex" role="img" focusable="false" viewbox="0 -442 452 636" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-127-NCM-I-1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 280 412C307 412 327 399 340 373Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="q" data-semantic-structure="0"><g data-mml-node="mi" data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:q" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D45E" href="#MJX-127-NCM-I-1D45E"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="q" data-semantic-structure="0"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:q" data-semantic-level-number="0" data-speech-node="true">q</mi></math></mjx-assistive-mml></mjx-container>, may be calculated by measuring a change in temperature of the surroundings. Work, <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="127" style="font-size: 85%; position: relative;"><svg width="1.62ex" height="1.025ex" role="img" focusable="false" viewbox="0 -442 716 453" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-128-NCM-I-1D464" d="M590 391C590 382 595 372 606 362C629 340 641 313 641 281C641 264 635 237 623 198C586 78 539 18 482 18C435 18 412 45 412 100C412 119 416 142 423 171C441 243 460 314 477 387C479 394 480 398 480 401C480 421 469 431 447 431C427 431 414 421 407 401L367 245C352 187 341 167 341 115C341 107 341 101 342 98C319 45 290 18 255 18C205 18 180 47 180 104C180 141 197 204 231 293C242 323 248 344 248 357C248 406 212 442 163 442C118 442 84 417 59 367C39 328 29 301 29 287C29 278 34 273 45 273C58 273 60 279 64 293C88 373 120 413 160 413C174 413 181 403 181 384C181 369 175 347 164 317C127 220 108 154 108 117C108 32 165-11 252-11C294-11 328 10 355 53C375 10 416-11 479-11C541-11 590 30 625 112C648 164 691 302 691 369C691 384 690 394 689 399C685 418 666 442 644 442C618 442 590 417 590 391Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="w" data-semantic-structure="0"><g data-mml-node="mi" data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:w" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D464" href="#MJX-128-NCM-I-1D464"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="w" data-semantic-structure="0"><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:w" data-semantic-level-number="0" data-speech-node="true">w</mi></math></mjx-assistive-mml></mjx-container>, may come in different forms, but it too can be measured. One important form of work for chemistry is <em>pressure-volume work</em> done by an expanding gas. At a constant external pressure (for example, atmospheric pressure)</p> <p class="mt-align-center lt-chem-21721" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="128" style="font-size: 85%; min-width: 28.173ex; position: relative;"><svg width="100%" height="2.262ex" role="img" focusable="false" data-mjx-viewbox="0 -750 12452.6 1000" aria-hidden="true" style="vertical-align: -0.566ex; min-width: 28.173ex;"><defs><path id="MJX-129-NCM-I-1D464" d="M590 391C590 382 595 372 606 362C629 340 641 313 641 281C641 264 635 237 623 198C586 78 539 18 482 18C435 18 412 45 412 100C412 119 416 142 423 171C441 243 460 314 477 387C479 394 480 398 480 401C480 421 469 431 447 431C427 431 414 421 407 401L367 245C352 187 341 167 341 115C341 107 341 101 342 98C319 45 290 18 255 18C205 18 180 47 180 104C180 141 197 204 231 293C242 323 248 344 248 357C248 406 212 442 163 442C118 442 84 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viewbox="2834 -750 1 1000"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:5.2.6" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="17" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-id="3" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mtext" data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true"><use data-c="28" href="#MJX-129-NCM-N-28"></use></g><g data-mml-node="mtext" data-latex="\text{5.2.7}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.2.7}" data-semantic-level-number="4" data-speech-node="true" transform="translate(389,0)"><use data-c="35" href="#MJX-129-NCM-N-35"></use><use data-c="2E" href="#MJX-129-NCM-N-2E" transform="translate(500,0)"></use><use data-c="32" href="#MJX-129-NCM-N-32" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-129-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="37" href="#MJX-129-NCM-N-37" transform="translate(1556,0)"></use></g><g data-mml-node="mtext" data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" transform="translate(2445,0)"><use data-c="29" href="#MJX-129-NCM-N-29"></use></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="w = −PΔV \label{5.2.6} " display="block" data-semantic-structure="(18 (17 (15 5 6 (14 7 (13 8 11 9 12 10))) (4 (3 0 1 2))))"><mtable displaystyle="true" data-latex="w = −PΔV \label{5.2.6}" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="17" data-semantic-attributes="latex:w = −PΔV \label{5.2.6} " data-semantic-owns="17" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="15" data-semantic-content="4" data-semantic-parent="18" data-semantic-owns="15 4" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="17" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.2.7}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.2.7}" data-semantic-level-number="4" data-speech-node="true">5.2.7</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="5,14" data-semantic-content="6" data-semantic-parent="17" data-semantic-owns="5 6 14" data-semantic-level-number="2" data-speech-node="true"><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:w" data-semantic-level-number="3" data-speech-node="true">w</mi><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="13" data-semantic-content="7" data-semantic-parent="15" data-semantic-owns="7 13" data-semantic-level-number="3" data-speech-node="true"><mo data-latex="−" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="14" data-semantic-attributes="latex:−" data-semantic-operator="prefixop,−" data-semantic-level-number="4" data-speech-node="true">−</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="8,9,10" data-semantic-content="11,12" data-semantic-parent="14" data-semantic-owns="8 11 9 12 10" data-semantic-level-number="4" data-speech-node="true"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:P" data-semantic-level-number="5" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:Δ" data-semantic-level-number="5" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi data-latex="\label{5.2.6}" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:\label{5.2.6}" data-semantic-level-number="5" data-speech-node="true">V</mi></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21721" style="background-color: unset;">The negative sign associated with <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="129" style="font-size: 85%; position: relative;"><svg width="3.448ex" height="1.595ex" role="img" focusable="false" viewbox="0 -683 1524 705" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-130-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path><path id="MJX-130-NCM-N-2062" d=""></path><path id="MJX-130-NCM-I-1D449" d="M671 680C652 680 592 683 573 683C558 683 550 675 550 660C550 650 557 645 570 644C598 643 612 633 612 616C612 607 607 595 598 580L300 107L234 619C234 636 255 644 298 644C318 644 327 651 327 668C327 678 321 683 309 683C287 683 209 680 187 680C167 680 99 683 79 683C64 683 56 675 56 660C56 649 66 644 85 644C102 644 114 642 122 640C138 635 137 633 140 614L218 4C221-13 229-22 242-22C255-22 265-15 273-2L629 564C652 600 674 623 696 632C711 639 730 643 752 644C763 645 768 652 769 667C770 678 764 683 752 683C737 683 686 680 671 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="PV" data-semantic-type="infixop" data-semantic-role="implicit" 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transform="translate(754,0)"><use data-c="2062" href="#MJX-130-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true" transform="translate(754,0)"><use data-c="1D449" href="#MJX-130-NCM-I-1D449"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="PV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:PV" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:P" data-semantic-level-number="1" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true">V</mi></math></mjx-assistive-mml></mjx-container> work done indicates that the system loses energy when the volume increases. That is, an expanding gas does work on its surroundings, while a gas that is compressed has work done on it by the surroundings.</p> <div class="box-example"> <span id="Example_.5C(.5CPageIndex.7B1.7D.5C)"></span><span id="Example_.5C(.5CPageIndex.7B1.7D.5C)"></span><h5 class="box-legend"><span class="lt-icon-default">Example <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="130" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-131-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-131-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-131-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-131-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use data-c="35" href="#MJX-131-NCM-N-35"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(500,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-131-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="32" href="#MJX-131-NCM-N-32"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-131-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-131-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container></span></h5> <p class="lt-chem-21721" style="background-color: unset;">A sample of an ideal gas in the cylinder of an engine is compressed from 400 mL to 50.0 mL during the compression stroke against a constant pressure of 8.00 atm. At the same time, 140 J of energy is transferred from the gas to the surroundings as heat. What is the total change in the internal energy (ΔU) of the gas in joules?</p> <p class="lt-chem-21721" style="background-color: unset;"><strong>Given</strong>: initial volume, final volume, external pressure, and quantity of energy transferred as heat</p> <p class="lt-chem-21721" style="background-color: unset;">Asked for: total change in internal energy</p> <span id="Strategy:"></span><span id="Strategy:"></span><h6>Strategy:</h6> <ol start="1" style="list-style-type: upper-alpha;"> <li class="lt-chem-21721" style="background-color: unset;">Determine the sign of <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="131" style="font-size: 85%; position: relative;"><svg width="1.023ex" height="1.439ex" role="img" focusable="false" viewbox="0 -442 452 636" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-132-NCM-I-1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 280 412C307 412 327 399 340 373Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="q" data-semantic-structure="0"><g data-mml-node="mi" data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:q" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D45E" href="#MJX-132-NCM-I-1D45E"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="q" data-semantic-structure="0"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:q" data-semantic-level-number="0" data-speech-node="true">q</mi></math></mjx-assistive-mml></mjx-container> to use in Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="132" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-133-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-133-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-133-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-133-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.2.5}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.02:_The_First_Law_of_Thermodynamics#mjx-eqn:5.2.5"><g data-mml-node="mrow" data-latex="\ref{5.2.5}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.2.5};href:#mjx-eqn%3A5.2.5" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-133-NCM-N-35"></use><use data-c="2E" href="#MJX-133-NCM-N-2E" transform="translate(500,0)"></use><use data-c="32" href="#MJX-133-NCM-N-32" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-133-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="36" href="#MJX-133-NCM-N-36" transform="translate(1556,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.2.5}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.2.5" data-latex="\ref{5.2.5}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.2.5};href:#mjx-eqn%3A5.2.5" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.2.6</mtext></mrow></math></mjx-assistive-mml></mjx-container>.</li> <li class="lt-chem-21721" style="background-color: unset;">From Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="133" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.579ex" role="img" focusable="false" viewbox="0 -676 2056 698" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-134-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-134-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-134-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-134-NCM-N-37" d="M475 604C482 613 485 626 485 644L243 644C174 644 135 648 128 657C125 660 122 667 120 676L89 676L55 464L88 464C98 520 106 550 112 555C115 558 146 560 205 560L401 560L295 410C214 295 174 171 174 36C174-3 190-22 223-22C256-22 272-3 272 36L272 87C272 239 296 349 343 416Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.2.6}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.02:_The_First_Law_of_Thermodynamics#mjx-eqn:5.2.6"><g data-mml-node="mrow" data-latex="\ref{5.2.6}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="698" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.2.6};href:#mjx-eqn%3A5.2.6" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-134-NCM-N-35"></use><use data-c="2E" href="#MJX-134-NCM-N-2E" transform="translate(500,0)"></use><use data-c="32" href="#MJX-134-NCM-N-32" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-134-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="37" href="#MJX-134-NCM-N-37" transform="translate(1556,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.2.6}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.2.6" data-latex="\ref{5.2.6}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.2.6};href:#mjx-eqn%3A5.2.6" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.2.7</mtext></mrow></math></mjx-assistive-mml></mjx-container> calculate <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="134" style="font-size: 85%; position: relative;"><svg width="1.62ex" height="1.025ex" role="img" focusable="false" viewbox="0 -442 716 453" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-135-NCM-I-1D464" d="M590 391C590 382 595 372 606 362C629 340 641 313 641 281C641 264 635 237 623 198C586 78 539 18 482 18C435 18 412 45 412 100C412 119 416 142 423 171C441 243 460 314 477 387C479 394 480 398 480 401C480 421 469 431 447 431C427 431 414 421 407 401L367 245C352 187 341 167 341 115C341 107 341 101 342 98C319 45 290 18 255 18C205 18 180 47 180 104C180 141 197 204 231 293C242 323 248 344 248 357C248 406 212 442 163 442C118 442 84 417 59 367C39 328 29 301 29 287C29 278 34 273 45 273C58 273 60 279 64 293C88 373 120 413 160 413C174 413 181 403 181 384C181 369 175 347 164 317C127 220 108 154 108 117C108 32 165-11 252-11C294-11 328 10 355 53C375 10 416-11 479-11C541-11 590 30 625 112C648 164 691 302 691 369C691 384 690 394 689 399C685 418 666 442 644 442C618 442 590 417 590 391Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="w" data-semantic-structure="0"><g data-mml-node="mi" data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:w" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D464" href="#MJX-135-NCM-I-1D464"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="w" data-semantic-structure="0"><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:w" data-semantic-level-number="0" data-speech-node="true">w</mi></math></mjx-assistive-mml></mjx-container> from the values given. Substitute this value into Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="135" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-136-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-136-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-136-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-136-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.2.5}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.02:_The_First_Law_of_Thermodynamics#mjx-eqn:5.2.5"><g data-mml-node="mrow" data-latex="\ref{5.2.5}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.2.5};href:#mjx-eqn%3A5.2.5" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-136-NCM-N-35"></use><use data-c="2E" href="#MJX-136-NCM-N-2E" transform="translate(500,0)"></use><use data-c="32" href="#MJX-136-NCM-N-32" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-136-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="36" href="#MJX-136-NCM-N-36" transform="translate(1556,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.2.5}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.2.5" data-latex="\ref{5.2.5}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.2.5};href:#mjx-eqn%3A5.2.5" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.2.6</mtext></mrow></math></mjx-assistive-mml></mjx-container> to calculate <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="136" style="font-size: 85%; position: relative;"><svg width="3.604ex" height="1.67ex" role="img" focusable="false" viewbox="0 -716 1593 738" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-137-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-137-NCM-N-2062" d=""></path><path id="MJX-137-NCM-I-1D448" d="M642 680C623 680 559 683 540 683C525 683 518 675 518 659C518 650 525 645 539 644C582 644 603 631 603 605C603 599 602 592 600 585L511 232C496 175 467 126 424 84C377 39 325 17 269 17C195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641C292 643 309 644 338 644C364 644 375 644 375 668C375 678 369 683 358 683L231 680L104 683C88 683 81 674 81 659C81 652 84 647 89 646C99 645 107 644 112 644C143 643 161 641 166 640C171 639 173 636 173 631C173 629 172 622 169 611L74 230C69 211 67 192 67 172C67 57 150-22 265-22C330-22 390 3 445 54C498 102 532 158 548 223L636 574C649 625 677 643 739 644C753 645 760 653 760 668L760 672C757 679 752 683 743 683C724 683 661 680 642 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔU" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔU" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-137-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-137-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:U" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D448" href="#MJX-137-NCM-I-1D448"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔU" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔU" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:U" data-semantic-level-number="1" data-speech-node="true">U</mi></math></mjx-assistive-mml></mjx-container>.</li> </ol> <span id="Solution"></span><span id="Solution"></span><h6>Solution</h6> <p class="lt-chem-21721" style="background-color: unset;">A From Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="137" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-138-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-138-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-138-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-138-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.2.5}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.02:_The_First_Law_of_Thermodynamics#mjx-eqn:5.2.5"><g data-mml-node="mrow" data-latex="\ref{5.2.5}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.2.5};href:#mjx-eqn%3A5.2.5" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-138-NCM-N-35"></use><use data-c="2E" href="#MJX-138-NCM-N-2E" transform="translate(500,0)"></use><use data-c="32" href="#MJX-138-NCM-N-32" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-138-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="36" href="#MJX-138-NCM-N-36" transform="translate(1556,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.2.5}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.2.5" data-latex="\ref{5.2.5}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.2.5};href:#mjx-eqn%3A5.2.5" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.2.6</mtext></mrow></math></mjx-assistive-mml></mjx-container>, we know that ΔU = q + w. We are given the magnitude of q (140 J) and need only determine its sign. Because energy is transferred from the system (the gas) to the surroundings, q is negative by convention.</p> <p class="lt-chem-21721" style="background-color: unset;">B Because the gas is being compressed, we know that work is being done on the system, so <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="138" style="font-size: 85%; position: relative;"><svg width="1.62ex" height="1.025ex" role="img" focusable="false" viewbox="0 -442 716 453" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-139-NCM-I-1D464" d="M590 391C590 382 595 372 606 362C629 340 641 313 641 281C641 264 635 237 623 198C586 78 539 18 482 18C435 18 412 45 412 100C412 119 416 142 423 171C441 243 460 314 477 387C479 394 480 398 480 401C480 421 469 431 447 431C427 431 414 421 407 401L367 245C352 187 341 167 341 115C341 107 341 101 342 98C319 45 290 18 255 18C205 18 180 47 180 104C180 141 197 204 231 293C242 323 248 344 248 357C248 406 212 442 163 442C118 442 84 417 59 367C39 328 29 301 29 287C29 278 34 273 45 273C58 273 60 279 64 293C88 373 120 413 160 413C174 413 181 403 181 384C181 369 175 347 164 317C127 220 108 154 108 117C108 32 165-11 252-11C294-11 328 10 355 53C375 10 416-11 479-11C541-11 590 30 625 112C648 164 691 302 691 369C691 384 690 394 689 399C685 418 666 442 644 442C618 442 590 417 590 391Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="w" data-semantic-structure="0"><g data-mml-node="mi" data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:w" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D464" href="#MJX-139-NCM-I-1D464"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="w" data-semantic-structure="0"><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:w" data-semantic-level-number="0" data-speech-node="true">w</mi></math></mjx-assistive-mml></mjx-container> must be positive. From Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="139" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-140-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 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data-speech-node="true">5.2.6</mtext></mrow></math></mjx-assistive-mml></mjx-container>,</p> <p class="mt-align-center lt-chem-21721" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="140" style="font-size: 85%; min-width: 70.969ex; position: relative;"><svg width="100%" height="4.876ex" role="img" focusable="false" data-mjx-viewbox="0 -1327.5 31368.2 2155" aria-hidden="true" style="vertical-align: -1.872ex; min-width: 70.969ex;"><defs><path id="MJX-141-NCM-I-1D464" d="M590 391C590 382 595 372 606 362C629 340 641 313 641 281C641 264 635 237 623 198C586 78 539 18 482 18C435 18 412 45 412 100C412 119 416 142 423 171C441 243 460 314 477 387C479 394 480 398 480 401C480 421 469 431 447 431C427 431 414 421 407 401L367 245C352 187 341 167 341 115C341 107 341 101 342 98C319 45 290 18 255 18C205 18 180 47 180 104C180 141 197 204 231 293C242 323 248 344 248 357C248 406 212 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data-latex="w=-P_{\textrm{ext}}\Delta V=-8.00\textrm{ atm}(\textrm{0.0500 L} - \textrm{0.400 L})\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right)=284\textrm{ J} \nonumber " data-semantic-structure="(47 (46 (44 (37 1 2 (35 3 (34 (6 4 5) 32 7 33 8)) 9 (36 10 11)) 12 (40 (39 (31 13 (30 14 15 16) 17) 38 (26 18 (24 19 (23 20 21 22)) 25)) 27 28) 29) 0))"><g data-mml-node="mtable" data-latex="w=-P_{\textrm{ext}}\Delta V=-8.00\textrm{ atm}(\textrm{0.0500 L} - \textrm{0.400 L})\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right)=284\textrm{ J} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-id="47" data-semantic-children="46" data-semantic-attributes="latex:w=-P_{\textrm{ext}}\Delta V=-8.00\textrm{ atm}(\textrm{0.0500 L} - \textrm{0.400 L})\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right)=284\textrm{ J} \nonumber " data-semantic-owns="46" data-semantic-level-number="0" data-speech-node="true" 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href="#MJX-141-NCM-I-1D443"></use></g><g data-mml-node="TeXAtom" transform="translate(675,-150) scale(0.707)" data-mjx-texclass="ORD" data-latex="{\textrm{ext}}"><g data-mml-node="mtext" data-latex="\textrm{ext}" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-id="5" data-semantic-parent="6" data-semantic-attributes="latex:{\textrm{ext}};texclass:ORD" data-semantic-level-number="7" data-speech-node="true"><use data-c="65" href="#MJX-141-NCM-N-65"></use><use data-c="78" href="#MJX-141-NCM-N-78" transform="translate(444,0)"></use><use data-c="74" href="#MJX-141-NCM-N-74" transform="translate(972,0)"></use></g></g></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-id="32" data-semantic-parent="34" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true" transform="translate(1687.4,0)"><use data-c="2062" href="#MJX-141-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="\Delta" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="7" data-semantic-parent="34" data-semantic-attributes="latex:\Delta" data-semantic-level-number="6" data-speech-node="true" transform="translate(1687.4,0)"><use data-c="394" href="#MJX-141-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-id="33" data-semantic-parent="34" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true" transform="translate(2520.4,0)"><use data-c="2062" href="#MJX-141-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="8" data-semantic-parent="34" data-semantic-attributes="latex:V" data-semantic-level-number="6" data-speech-node="true" transform="translate(2520.4,0)"><use data-c="1D449" href="#MJX-141-NCM-I-1D449"></use></g></g></g><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-id="9" data-semantic-parent="37" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true" transform="translate(6395.7,0)"><use data-c="3D" href="#MJX-141-NCM-N-3D"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-id="36" data-semantic-children="11" data-semantic-content="10" data-semantic-parent="37" data-semantic-owns="10 11" data-semantic-level-number="4" data-speech-node="true" transform="translate(7451.5,0)"><g data-mml-node="mo" data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:6" data-semantic-id="10" data-semantic-parent="36" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="5" data-speech-node="true"><use data-c="2212" href="#MJX-141-NCM-N-2212"></use></g><g data-mml-node="mn" data-latex="8.00" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-id="11" data-semantic-parent="36" data-semantic-attributes="latex:8.00" data-semantic-level-number="5" data-speech-node="true" transform="translate(778,0)"><use data-c="38" href="#MJX-141-NCM-N-38"></use><use data-c="2E" href="#MJX-141-NCM-N-2E" transform="translate(500,0)"></use><use data-c="30" href="#MJX-141-NCM-N-30" transform="translate(778,0)"></use><use data-c="30" href="#MJX-141-NCM-N-30" transform="translate(1278,0)"></use></g></g></g><g data-mml-node="mtext" data-latex="\textrm{ atm}" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-id="12" data-semantic-parent="44" data-semantic-attributes="latex:\textrm{ atm}" data-semantic-level-number="3" data-speech-node="true" transform="translate(10007.5,0)"><use data-c="A0" href="#MJX-141-NCM-N-A0"></use><use data-c="61" href="#MJX-141-NCM-N-61" transform="translate(332,0)"></use><use data-c="74" href="#MJX-141-NCM-N-74" transform="translate(832,0)"></use><use data-c="6D" href="#MJX-141-NCM-N-6D" transform="translate(1221,0)"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-id="40" data-semantic-children="39,28" data-semantic-content="27" data-semantic-parent="44" data-semantic-owns="39 27 28" data-semantic-level-number="3" data-speech-node="true" transform="translate(12061.5,0)"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="39" data-semantic-children="31,26" data-semantic-content="38" data-semantic-parent="40" data-semantic-owns="31 38 26" data-semantic-level-number="4" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-id="31" data-semantic-children="30" data-semantic-content="13,17" data-semantic-parent="39" data-semantic-owns="13 30 17" data-semantic-level-number="5" data-speech-node="true"><g data-mml-node="mo" data-latex="(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-id="13" data-semantic-parent="31" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true"><use data-c="28" href="#MJX-141-NCM-N-28"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-annotation="depth:7" data-semantic-id="30" data-semantic-children="14,16" data-semantic-content="15" data-semantic-parent="31" data-semantic-owns="14 15 16" data-semantic-level-number="6" data-speech-node="true" transform="translate(389,0)"><g data-mml-node="mtext" data-latex="\textrm{0.0500 L}" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="factor:operator;clearspeak:unit;depth:8" data-semantic-id="14" data-semantic-parent="30" data-semantic-attributes="latex:\textrm{0.0500 L}" data-semantic-level-number="7" data-speech-node="true"><use data-c="30" href="#MJX-141-NCM-N-30"></use><use data-c="2E" href="#MJX-141-NCM-N-2E" transform="translate(500,0)"></use><use data-c="30" href="#MJX-141-NCM-N-30" transform="translate(778,0)"></use><use data-c="35" href="#MJX-141-NCM-N-35" transform="translate(1278,0)"></use><use data-c="30" href="#MJX-141-NCM-N-30" transform="translate(1778,0)"></use><use data-c="30" href="#MJX-141-NCM-N-30" transform="translate(2278,0)"></use><use data-c="20" href="#MJX-141-NCM-N-20" transform="translate(2778,0)"></use><use data-c="4C" href="#MJX-141-NCM-N-4C" transform="translate(3110,0)"></use></g><g data-mml-node="mo" data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:8" data-semantic-id="15" data-semantic-parent="30" data-semantic-attributes="latex:-" data-semantic-operator="infixop,−" data-semantic-level-number="7" data-speech-node="true" transform="translate(3957.2,0)"><use data-c="2212" href="#MJX-141-NCM-N-2212"></use></g><g data-mml-node="mtext" data-latex="\textrm{0.400 L}" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="factor:operator;clearspeak:unit;depth:8" data-semantic-id="16" data-semantic-parent="30" data-semantic-attributes="latex:\textrm{0.400 L}" data-semantic-level-number="7" data-speech-node="true" transform="translate(4957.4,0)"><use data-c="30" href="#MJX-141-NCM-N-30"></use><use data-c="2E" href="#MJX-141-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-141-NCM-N-34" transform="translate(778,0)"></use><use data-c="30" href="#MJX-141-NCM-N-30" transform="translate(1278,0)"></use><use data-c="30" href="#MJX-141-NCM-N-30" transform="translate(1778,0)"></use><use data-c="20" href="#MJX-141-NCM-N-20" transform="translate(2278,0)"></use><use data-c="4C" href="#MJX-141-NCM-N-4C" transform="translate(2610,0)"></use></g></g><g data-mml-node="mo" data-latex=")" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-id="17" data-semantic-parent="31" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true" transform="translate(8581.4,0)"><use data-c="29" href="#MJX-141-NCM-N-29"></use></g></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-id="38" data-semantic-parent="39" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true" transform="translate(8970.4,0)"><use data-c="2062" href="#MJX-141-NCM-N-2062"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="INNER" data-latex="\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-id="26" data-semantic-children="24" data-semantic-content="18,25" data-semantic-parent="39" data-semantic-attributes="latex:\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right);texclass:INNER" data-semantic-owns="18 24 25" data-semantic-level-number="5" data-speech-node="true" transform="translate(9137.1,0)"><g data-mml-node="mo" data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-id="18" data-semantic-parent="26" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true"><use data-c="28" href="#MJX-141-NCM-S5-28"></use></g><g data-mml-node="mfrac" data-latex="\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:7" data-semantic-id="24" data-semantic-children="19,23" data-semantic-parent="26" data-semantic-attributes="latex:\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}}" data-semantic-owns="19 23" data-semantic-level-number="6" data-speech-node="true" transform="translate(663,0)"><g data-mml-node="mtext" data-latex="\textrm{101.3 J}" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-id="19" data-semantic-parent="24" data-semantic-attributes="latex:\textrm{101.3 J}" data-semantic-level-number="7" data-speech-node="true" transform="translate(220,676)"><use data-c="31" href="#MJX-141-NCM-N-31"></use><use data-c="30" href="#MJX-141-NCM-N-30" transform="translate(500,0)"></use><use data-c="31" href="#MJX-141-NCM-N-31" transform="translate(1000,0)"></use><use data-c="2E" href="#MJX-141-NCM-N-2E" transform="translate(1500,0)"></use><use data-c="33" href="#MJX-141-NCM-N-33" transform="translate(1778,0)"></use><use data-c="20" href="#MJX-141-NCM-N-20" transform="translate(2278,0)"></use><use data-c="4A" href="#MJX-141-NCM-N-4A" transform="translate(2610,0)"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\mathrm{L\cdot atm}" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-id="23" data-semantic-children="20,22" data-semantic-content="21" data-semantic-parent="24" data-semantic-attributes="latex:\mathrm{L\cdot atm};texclass:ORD" data-semantic-owns="20 21 22" data-semantic-level-number="7" data-speech-node="true" transform="translate(247.3,-686)"><g data-mml-node="mi" data-latex="L" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-id="20" data-semantic-parent="23" data-semantic-attributes="latex:L" data-semantic-level-number="8" data-speech-node="true"><use data-c="4C" href="#MJX-141-NCM-N-4C"></use></g><g data-mml-node="mo" data-latex="\cdot" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-id="21" data-semantic-parent="23" data-semantic-attributes="latex:\cdot" data-semantic-operator="infixop,⋅" data-semantic-level-number="8" data-speech-node="true" transform="translate(847.2,0)"><use data-c="22C5" href="#MJX-141-NCM-N-22C5"></use></g><g data-mml-node="mi" data-latex="atm" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="depth:9" data-semantic-id="22" data-semantic-parent="23" data-semantic-attributes="latex:atm" data-semantic-level-number="8" data-speech-node="true" transform="translate(1347.4,0)"><use data-c="61" href="#MJX-141-NCM-N-61"></use><use data-c="74" href="#MJX-141-NCM-N-74" transform="translate(500,0)"></use><use data-c="6D" href="#MJX-141-NCM-N-6D" transform="translate(889,0)"></use></g></g><rect width="3324" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-id="25" data-semantic-parent="26" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true" transform="translate(4227,0)"><use data-c="29" href="#MJX-141-NCM-S5-29"></use></g></g></g><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-id="27" data-semantic-parent="40" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true" transform="translate(14304.9,0)"><use data-c="3D" href="#MJX-141-NCM-N-3D"></use></g><g data-mml-node="mn" data-latex="284" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-id="28" data-semantic-parent="40" data-semantic-attributes="latex:284" data-semantic-level-number="4" data-speech-node="true" transform="translate(15360.7,0)"><use data-c="32" href="#MJX-141-NCM-N-32"></use><use data-c="38" href="#MJX-141-NCM-N-38" transform="translate(500,0)"></use><use data-c="34" href="#MJX-141-NCM-N-34" transform="translate(1000,0)"></use></g></g><g data-mml-node="mtext" data-latex="\nonumber" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-id="29" data-semantic-parent="44" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="3" data-speech-node="true" transform="translate(28922.2,0)"><use data-c="A0" href="#MJX-141-NCM-N-A0"></use><use data-c="4A" href="#MJX-141-NCM-N-4A" transform="translate(332,0)"></use></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -1327.5 1 2155"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="46" data-semantic-level-number="2" data-speech-node="true" transform="translate(0,-31.5)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,0)"></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="w=-P_{\textrm{ext}}\Delta V=-8.00\textrm{ atm}(\textrm{0.0500 L} - \textrm{0.400 L})\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right)=284\textrm{ J} \nonumber " display="block" data-semantic-structure="(47 (46 (44 (37 1 2 (35 3 (34 (6 4 5) 32 7 33 8)) 9 (36 10 11)) 12 (40 (39 (31 13 (30 14 15 16) 17) 38 (26 18 (24 19 (23 20 21 22)) 25)) 27 28) 29) 0))"><mtable displaystyle="true" data-latex="w=-P_{\textrm{ext}}\Delta V=-8.00\textrm{ atm}(\textrm{0.0500 L} - \textrm{0.400 L})\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right)=284\textrm{ J} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="46" data-semantic-attributes="latex:w=-P_{\textrm{ext}}\Delta V=-8.00\textrm{ atm}(\textrm{0.0500 L} - \textrm{0.400 L})\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right)=284\textrm{ J} \nonumber " data-semantic-owns="46" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="44" data-semantic-content="0" data-semantic-parent="47" data-semantic-owns="44 0" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="46" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="text" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="37,12,40,29" data-semantic-parent="46" data-semantic-collapsed="(44 (c 41 42 43) 37 12 40 29)" data-semantic-owns="37 12 40 29" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="1,35,36" data-semantic-content="2,9" data-semantic-parent="44" data-semantic-owns="1 2 35 9 36" data-semantic-level-number="3" data-speech-node="true"><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:w" data-semantic-level-number="4" data-speech-node="true">w</mi><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="34" data-semantic-content="3" data-semantic-parent="37" data-semantic-owns="3 34" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="35" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="5" data-speech-node="true">−</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="6,7,8" data-semantic-content="32,33" data-semantic-parent="35" data-semantic-owns="6 32 7 33 8" data-semantic-level-number="5" data-speech-node="true"><msub data-latex="P_{\textrm{ext}}" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="4,5" data-semantic-parent="34" data-semantic-attributes="latex:P_{\textrm{ext}}" data-semantic-owns="4 5" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:P" data-semantic-level-number="7" data-speech-node="true">P</mi><mrow data-mjx-texclass="ORD" data-latex="{\textrm{ext}}"><mtext data-latex="\textrm{ext}" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:{\textrm{ext}};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">ext</mtext></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="34" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi mathvariant="normal" data-latex="\Delta" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="34" data-semantic-attributes="latex:\Delta" data-semantic-level-number="6" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="34" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="34" data-semantic-attributes="latex:V" data-semantic-level-number="6" data-speech-node="true">V</mi></mrow></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-children="11" data-semantic-content="10" data-semantic-parent="37" data-semantic-owns="10 11" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="5" data-speech-node="true">−</mo><mn data-latex="8.00" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:8.00" data-semantic-level-number="5" data-speech-node="true">8.00</mn></mrow></mrow><mtext data-latex="\textrm{ atm}" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:\textrm{ atm}" data-semantic-level-number="3" data-speech-node="true"> atm</mtext><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="39,28" data-semantic-content="27" data-semantic-parent="44" data-semantic-owns="39 27 28" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="31,26" data-semantic-content="38" data-semantic-parent="40" data-semantic-owns="31 38 26" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="30" data-semantic-content="13,17" data-semantic-parent="39" data-semantic-owns="13 30 17" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="14,16" data-semantic-content="15" data-semantic-parent="31" data-semantic-owns="14 15 16" data-semantic-level-number="6" data-speech-node="true"><mtext data-latex="\textrm{0.0500 L}" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="factor:operator;clearspeak:unit;depth:8" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:\textrm{0.0500 L}" data-semantic-level-number="7" data-speech-node="true">0.0500 L</mtext><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:-" data-semantic-operator="infixop,−" data-semantic-level-number="7" data-speech-node="true">−</mo><mtext data-latex="\textrm{0.400 L}" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="factor:operator;clearspeak:unit;depth:8" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:\textrm{0.400 L}" data-semantic-level-number="7" data-speech-node="true">0.400 L</mtext></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="39" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="24" data-semantic-content="18,25" data-semantic-parent="39" data-semantic-attributes="latex:\left(\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}} \right);texclass:INNER" data-semantic-owns="18 24 25" data-semantic-level-number="5" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="19,23" data-semantic-parent="26" data-semantic-attributes="latex:\dfrac{\textrm{101.3 J}}{\mathrm{L\cdot atm}}" data-semantic-owns="19 23" data-semantic-level-number="6" data-speech-node="true"><mtext data-latex="\textrm{101.3 J}" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:\textrm{101.3 J}" data-semantic-level-number="7" data-speech-node="true">101.3 J</mtext><mrow data-mjx-texclass="ORD" data-latex="\mathrm{L\cdot atm}" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="20,22" data-semantic-content="21" data-semantic-parent="24" data-semantic-attributes="latex:\mathrm{L\cdot atm};texclass:ORD" data-semantic-owns="20 21 22" data-semantic-level-number="7" data-speech-node="true"><mi mathvariant="normal" data-latex="L" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:L" data-semantic-level-number="8" data-speech-node="true">L</mi><mo data-latex="\cdot" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:\cdot" data-semantic-operator="infixop,⋅" data-semantic-level-number="8" data-speech-node="true">⋅</mo><mi data-mjx-auto-op="false" data-latex="atm" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:atm" data-semantic-level-number="8" data-speech-node="true">atm</mi></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mn data-latex="284" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:284" data-semantic-level-number="4" data-speech-node="true">284</mn></mrow><mtext data-latex="\nonumber" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="3" data-speech-node="true"> J</mtext></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21721" style="background-color: unset;">Thus</p> <p class="mt-align-center lt-chem-21721" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" tabindex="0" ctxtmenu_counter="141" style="font-size: 85%; position: 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w \\[4pt] &= −140 \,J + 284\, J \\[4pt] &= 144\, J\end{align*} \nonumber " data-semantic-structure="(48 (14 (4 (3 0 2 1)) (13 (12 10 6 (11 7 8 9)))) (35 15 (34 (33 26 17 (32 (29 18 (28 19 27 21)) 22 (31 23 30 25))))) (47 36 (46 (45 42 38 (44 39 43 41)))))"><g data-mml-node="mtable" data-latex="\begin{align*} ΔU &= q + w \\[4pt] &= −140 \,J + 284\, J \\[4pt] &= 144\, J\end{align*} \nonumber" data-semantic-type="table" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-id="48" data-semantic-children="14,35,47" data-semantic-attributes="latex:\begin{align*} ΔU &= q + w \\[4pt] &= −140 \,J + 284\, J \\[4pt] &= 144\, J\end{align*} \nonumber " data-semantic-owns="14 35 47" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mtr" data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-id="14" data-semantic-children="4,13" data-semantic-parent="48" data-semantic-owns="4 13" 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data-speech-node="true" transform="translate(1333.6,0)"><g data-mml-node="mn" data-latex="144" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-id="39" data-semantic-parent="44" data-semantic-attributes="latex:144" data-semantic-level-number="5" data-speech-node="true"><use data-c="31" href="#MJX-142-NCM-N-31"></use><use data-c="34" href="#MJX-142-NCM-N-34" transform="translate(500,0)"></use><use data-c="34" href="#MJX-142-NCM-N-34" transform="translate(1000,0)"></use></g><g data-mml-node="mspace" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:6" data-semantic-id="43" data-semantic-parent="44" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true" transform="translate(1500,0)"></g><g data-mml-node="mi" data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-id="41" data-semantic-parent="44" data-semantic-attributes="latex:J" data-semantic-level-number="5" data-speech-node="true" transform="translate(1667,0)"><use data-c="1D43D" href="#MJX-142-NCM-I-1D43D"></use></g></g></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="\begin{align*} ΔU &= q + w \\[4pt] &= −140 \,J + 284\, J \\[4pt] &= 144\, J\end{align*} \nonumber " display="block" data-semantic-structure="(48 (14 (4 (3 0 2 1)) (13 (12 10 6 (11 7 8 9)))) (35 15 (34 (33 26 17 (32 (29 18 (28 19 27 21)) 22 (31 23 30 25))))) (47 36 (46 (45 42 38 (44 39 43 41)))))"><mtable displaystyle="true" columnalign="right left" columnspacing="0em" rowspacing="0.7em 0.7em 0.30000000000000004em" data-break-align="bottom top" data-latex="\begin{align*} ΔU &= q + w \\[4pt] &= −140 \,J + 284\, J \\[4pt] &= 144\, J\end{align*} \nonumber" data-semantic-type="table" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="14,35,47" data-semantic-attributes="latex:\begin{align*} ΔU &= q + w \\[4pt] &= −140 \,J + 284\, J \\[4pt] &= 144\, J\end{align*} \nonumber " data-semantic-owns="14 35 47" data-semantic-level-number="0" data-speech-node="true"><mtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="4,13" data-semantic-parent="48" data-semantic-owns="4 13" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="3" data-semantic-parent="14" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-parent="4" data-semantic-owns="0 2 1" data-semantic-level-number="3" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="4" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:U" data-semantic-level-number="4" data-speech-node="true">U</mi></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="12" data-semantic-parent="14" data-semantic-owns="12" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="10,11" data-semantic-content="6" data-semantic-parent="13" data-semantic-owns="10 6 11" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="12" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="7,9" data-semantic-content="8" data-semantic-parent="12" data-semantic-owns="7 8 9" data-semantic-level-number="4" data-speech-node="true"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="11" data-semantic-attributes="latex:q" data-semantic-level-number="5" data-speech-node="true">q</mi><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="11" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="5" data-speech-node="true">+</mo><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="11" data-semantic-attributes="latex:w" data-semantic-level-number="5" data-speech-node="true">w</mi></mrow></mrow></mstyle></mtd></mtr><mtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="15,34" data-semantic-parent="48" data-semantic-owns="15 34" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="35" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="33" data-semantic-parent="35" data-semantic-owns="33" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="26,32" data-semantic-content="17" data-semantic-parent="34" data-semantic-owns="26 17 32" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="33" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="33" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="29,31" data-semantic-content="22" data-semantic-parent="33" data-semantic-owns="29 22 31" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-children="28" data-semantic-content="18" data-semantic-parent="32" data-semantic-owns="18 28" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="−" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="29" data-semantic-attributes="latex:−" data-semantic-operator="prefixop,−" data-semantic-level-number="6" data-speech-node="true">−</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="19,21" data-semantic-content="27" data-semantic-parent="29" data-semantic-owns="19 27 21" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="140" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:140" data-semantic-level-number="7" data-speech-node="true">140</mn><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="28" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:J" data-semantic-level-number="7" data-speech-node="true">J</mi></mrow></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="5" data-speech-node="true">+</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="23,25" data-semantic-content="30" data-semantic-parent="32" data-semantic-owns="23 30 25" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="284" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:284" data-semantic-level-number="6" data-speech-node="true">284</mn><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="31" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:J" data-semantic-level-number="6" data-speech-node="true">J</mi></mrow></mrow></mrow></mstyle></mtd></mtr><mtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="36,46" data-semantic-parent="48" data-semantic-owns="36 46" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="47" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="45" data-semantic-parent="47" data-semantic-owns="45" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="42,44" data-semantic-content="38" data-semantic-parent="46" data-semantic-owns="42 38 44" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="45" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="45" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="39,41" data-semantic-content="43" data-semantic-parent="45" data-semantic-owns="39 43 41" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="144" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:144" data-semantic-level-number="5" data-speech-node="true">144</mn><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="44" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true"></mspace><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:J" data-semantic-level-number="5" data-speech-node="true">J</mi></mrow></mrow></mstyle></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21721" style="background-color: unset;">In this case, although work is done on the gas, increasing its internal energy, heat flows from the system to the surroundings, decreasing its internal energy by 144 J. The work done and the heat transferred can have opposite signs.</p> </div> <div class="box-exercise"> <span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C)"></span><span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C)"></span><h5 class="box-legend"><span class="lt-icon-default">Exercise <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="142" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-143-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-143-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-143-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-143-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use data-c="35" href="#MJX-143-NCM-N-35"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(500,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-143-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="32" href="#MJX-143-NCM-N-32"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-143-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-143-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container></span></h5> <p class="lt-chem-21721" style="background-color: unset;">A sample of an ideal gas is allowed to expand from an initial volume of 0.200 L to a final volume of 3.50 L against a constant external pressure of 0.995 atm. At the same time, 117 J of heat is transferred from the surroundings to the gas. What is the total change in the internal energy (ΔU) of the gas in joules?</p> <dl> <dt><strong class="emphasis bold">Answer</strong></dt> <dd> <p class="lt-chem-21721" style="background-color: unset;">−216 J</p> </dd> </dl> </div> <div class="box-note"> <p class="lt-chem-21721" style="background-color: unset;">By convention (to chemists), both heat flow and work have a negative sign when energy is transferred from a system to its surroundings and vice versa.</p> </div> <span id="Summary"></span><span id="Summary"></span><h2 style="background-color: unset;" class="lt-chem-21721">Summary</h2> <p class="lt-chem-21721" style="background-color: unset;">In chemistry, the small part of the universe that we are studying is the <strong class="emphasis bold">system</strong>, and the rest of the universe is the <strong class="emphasis bold">surroundings</strong>. <strong class="emphasis bold">Open systems</strong> can exchange both matter and energy with their surroundings, <strong class="emphasis bold">closed systems</strong> can exchange energy but not matter with their surroundings, and <strong class="emphasis bold">isolated systems</strong> can exchange neither matter nor energy with their surroundings. A <strong class="emphasis bold">state function</strong> is a property of a system that depends on only its present <strong class="emphasis bold">state</strong>, not its history. A reaction or process in which heat is transferred from a system to its surroundings is <strong class="emphasis bold">exothermic</strong>. A reaction or process in which heat is transferred to a system from its surroundings is <strong class="emphasis bold">endothermic</strong>. The first law of thermodynamics states that the energy of the universe is constant. The change in the internal energy of a system is the sum of the heat transferred and the work done. The heat flow is equal to the change in the internal energy of the system plus the <span class="acronym-ignore">PV</span> work done. 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