Name: isothermal expansion and heat transfer
Uploaded: 2025-08-19T15:10:28.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Louisiana Student Standards for Science

High School

Chemistry

Energy

HS-PS3-4

Isothermal Processes

Proces termodynamiczny, który zachodzi w stałej temperaturze, nazywany jest procesem izotermicznym.
Zamiana wrzącej wody w parę o stałej temperaturze 100 stopni Celsjusza jest przykładem procesu izotermicznego. Podobnie przemiana wody w lód w temperaturze 0 stopni Celsjusza jest również procesem izotermicznym.
Zmiana energii wewnętrznej wynosi zero dla tych procesów, ponieważ temperatura się nie zmienia. Tak więc, stosując pierwszą zasadę termodynamiki, wykonana praca równa się cieplowi.
Rozważmy teraz system gazu doskonałego zamknięty w szczelnie zamkniętej strzykawce gazowej o stałej temperaturze.
Gdy tłok jest powoli wciskany w kontrolowany sposób, gaz wewnątrz strzykawki jest sprężany. Zmniejszona objętość gazu powoduje wzrost ciśnienia, jednak temperatura pozostaje stała.
Zwolnienie tłoka w kontrolowany sposób prowadzi do rozprężania się gazu w stałej temperaturze.
Krzywa pV dla każdego procesu izotermicznego jest hiperboliczna, ponieważ ciśnienie jest odwrotnie proporcjonalne do objętości dla gazu doskonałego o stałej temperaturze.

<ol>
	<li>Young, H. D i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson. str. 635.</li>
	<li>Protokół OpenStax. (2019). Fizyka uniwersytecka Vol. 2. [Wersja internetowa]. str. 121 Źródło <a href="https://openstax.org/books/college-physics/pages/15-2-the-first-law-of-thermodynamics-and-some-simple-processes">https://openstax.org/books/college-physics/pages/15-2-the-first-law-of-thermodynamics-and-some-simple-processes</a></li>
</ol>

procesy izotermiczne

Proces termodynamiczny zachodzący w stałej temperaturze nazywany jest procesem izotermicznym. Ciepło powoli przepływa do układu lub z układu, aby utrzymać równowagę termiczną. Procesy obejmujące zmiany fazowe, takie jak odparowanie wody w parę lub zamrożenie wody w lód w stałej temperaturze, są przykładami procesów izotermicznych.

Gaz doskonały może również podlegać rozszerzaniu lub sprężaniu izotermicznemu.

Rozważmy na przykład 1 mol gazu doskonałego w izolowanej butli o początkowej objętości V i ciśnieniu p. Załóżmy, że ciepło dodane do układu powoduje kwazistatyczne rozprężanie gazu przy stałej temperaturze 300 K. Jaka jest ilość ciepła dodana do układu, jeśli objętość gazu zmieni się na 2V ?

Tutaj znane ilości to liczba moli gazu, początkowa i końcowa objętość gazu. Należy obliczyć nieznaną ilość, ciepło.

Zgodnie z pierwszą zasadą termodynamiki

<img alt="Równanie1" src="/files/ftp_upload/13682/13682_Equation_PT_1.svg" style="text-align: center; height: 13px;" />

Ponieważ temperatura jest stała, zmiana energii wewnętrznej w tym procesie wynosi zero. Zatem ciepło dodane do układu jest równe pracy wykonanej przez system.

<img alt="Równanie2" src="/files/ftp_upload/13682/13682_Equation_PT_2.svg" style="text-align: center; height: 13px;" />

Teraz praca wykonana przez gaz doskonały podczas rozprężania izotermicznego jest dana wzorem,

<img alt="Równanie3" src="/files/ftp_upload/13682/13682_Equation_PT_3.svg" style="text-align: center; height: 32px;" />

Podstawiając liczbę moli, stałą gazu, temperaturę, objętość początkową i końcową objętość gazu, wykonana praca wynosi 1728,85 J.

Ponieważ praca wykonana przez układ jest równa ciepłu dodanemu do układu, przyjmuje się, że do układu dostarczono 1728,85 J ciepła, aby rozprężyć go izotermicznie do 2V.

Procesy izotermiczne

Proces termodynamiczny, który zachodzi w stałej temperaturze, nazywany jest procesem izotermicznym. Ciepło powoli przepływa do systemu lub z systemu, aby...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

The First Law of Thermodynamics

Pierwsza zasada termodynamiki

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

isothermal expansion and heat transfer

An isothermal process is a thermodynamic process that happens at constant temperature. During the process, heat slowly flows into the system or out of the system so thermal equilibrium is maintained.

Phase changes are common examples of isothermal processes. Water can evaporate into steam at a constant temperature, and water can also freeze into ice at a constant temperature. An ideal gas can also undergo isothermal expansion or compression.

Here, an ideal gas in an isolated cylinder expands quasistatically at 300 K. The gas starts with 1 mole at volume V and pressure p. The volume then changes to 2V, and the heat added to the system must be found.

By the first law of thermodynamics, the change in internal energy is zero because the temperature stays constant. That means the heat added to the system equals the work done by the system. For an ideal gas in isothermal expansion, the work is calculated from the initial and final volume.

Substituting the number of moles, gas constant, temperature, and volumes gives a work value of 1728.85 J. Since the work done by the gas equals the heat added, 1728.85 J of heat is applied to expand the gas isothermally to 2V.

Isothermal Expansion and Heat Transfer

thermodynamic systems

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isothermal processes

An isothermal process is a thermodynamic process that happens at constant temperature. During the process, heat slowly flows into the system or out of the system so thermal equilibrium is maintained. Phase changes are common examples of isothermal processes. Water can evaporate into steam at a constant temperature, and water can also freeze into ice at a constant temperature. An ideal gas can also undergo isothermal expansion or compression. Here, an ideal gas in an isolated cylinder expands...

isochoric and isobaric processes

Constant Volume and Pressure in Thermodynamics

Thermodynamic processes can happen at constant volume or at constant pressure. An isochoric process is a constant-volume process. In this case, the volume does not change, so the work done by the system is zero. The first law of thermodynamics still applies, so any heat added or removed changes the internal energy of the system only. A simple example is heating 1000 g of water from 40 degrees celsius to 70 degrees celsius at constant volume. Because the process is isochoric, no work is done by...

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heat capacities of an ideal gas ii

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heat capacities of an ideal gas iii

Ideal Gas Heat Capacity and Degrees of Freedom

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adiabatic processes for an ideal gas

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pressure and volume in an adiabatic process

pressure-and-volume-in-an-adiabatic-process

Free Expansion: Pressure, Volume, and Temperature

Free expansion shows how pressure, volume, and temperature behave when a gas expands without doing work. It is an adiabatic process, but it is not the same as adiabatic expansion. In free expansion, no work is done and the internal energy does not change. In adiabatic expansion, work is done and the internal energy changes. For an adiabatic process, the pressure-volume relation comes from the adiabatic condition. That relation does not apply to free expansion, even though the expansion is...

work done in an adiabatic process

Adiabatic Compression in an Engine Cylinder

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Gas cooling and heating in throttling is explained by the Joule-Thomson effect, also called the Joule-Kelvin effect. It describes how a fluid changes temperature when it passes through a valve or porous plug in a thermally insulated system. This type of flow is called a throttling process. In the experiment, a high-pressure gas is forced through a throttle valve or porous plug into a lower-pressure region. The gas expands as it moves into the larger volume. Work is done on the gas as it is...

key terms and concepts

Learn how isothermal processes keep temperature constant while heat equals work during ideal gas expansion, with phase change and cylinder examples.

Isothermal Expansion and Heat Transfer | JoVE K12

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New Jersey Student Learning Standards for Science

Physical Science

HS-PS3-1

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New York State Science Learning Standards

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HS-PS3-6

Isothermal Expansion and Heat Transfer

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