Name: gas work in a piston cylinder
Uploaded: 2023-04-30T12:31:11.000Z
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K12 Standards

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

High School

Physical Science

Energy

HS-PS3-4

Work Done During Volume Change

Considérons un ballon de football gonflé ayant un volume de V. La pression agissant sur la balle est la pression atmosphérique.
Supposons que la balle tombe de la falaise et soit perforée ; l’air à l’intérieur de la balle se libère. En supposant une déflation uniforme, soit son rayon réduit d’une distance de dr.
L’amplitude de la force agissant sur la balle dépend de la pression atmosphérique et de la surface de la balle.
Par conséquent, le travail effectué par l'environnement sur la balle est égal au produit négatif de la pression atmosphérique, de la surface de la balle et de la variation de son rayon.
Cependant, le produit de la surface et de la dr est la variation du volume de la balle.
Par conséquent, lors d’une variation finie de volume de V1 à V2, le travail effectué peut être exprimé comme l’intégrale du produit de la pression et de la variation de volume.
Ici, le signe négatif indique que le travail est effectué sur le système par l’environnement. À l’inverse, le travail effectué par le système est considéré comme positif.

<ol>
	<li>OpenStax. (2019). Physique universitaire Vol. 1. [Version Web]. Pp 112 Tiré de <a href="https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy">https://openstax.org/books/university-physics-volume-2/pages/3-2-work-heat-and-internal-energy</a></li>
</ol>

travail effectué lors d'un changement de volume

En mécanique, du travail est effectué sur un objet lorsque la force agissant sur celui-ci déplace l'objet. En thermodynamique, le travail effectué sur un système peut être estimé lorsque le volume du système change au cours d'un processus thermodynamique.

Considérons un gaz confiné dans un cylindre équipé d'un piston mobile à une extrémité. Si le gaz s'étend du volume V1 au volume V2, il exerce une force sur le piston, de sorte que le piston se déplace d'une distance dr.

Le travail effectué par le gaz sur le piston peut être exprimé comme suit :

<img alt="Equation1" src="/files/ftp_upload/13675/13675_Equation_PT_1.svg" style="text-align: center; height: 10px;" />

Si p est la pression agissant sur la face du piston d'aire A, alors la force agissant sur le piston est:

<img alt="Equation2" src="/files/ftp_upload/13675/13675_Equation_PT_2.svg" style="text-align: center; height: 12px;" />

Par conséquent, le travail effectué peut être exprimé comme suit :

<img alt="Equation3" src="/files/ftp_upload/13675/13675_Equation_PT_3.svg" style="text-align: center; height: 12px;" />

La variation du volume du gaz dV correspond à A × dr. Par conséquent, le travail effectué par le gaz sur le piston lorsqu'il s'étend du volume V1 à V2 est exprimé comme suit :

<img alt="Equation4" src="/files/ftp_upload/13675/13675_Equation_PT_4.svg" style="text-align: center; height: 45px;" />

Ici, l'intégrale n'a de sens que pour un processus quasi-statique, ce qui signifie un processus qui se déroule par des étapes infinitésimales, en maintenant le système à l'équilibre thermique.

Si le piston comprime le gaz, le travail est effectué sur le gaz et donc, conventionnellement, il est considéré comme négatif.

Travail effectué lors d'un changement de volume

En mécanique, le travail est effectué sur un objet lorsque la force agissant sur celui-ci déplace l’objet. En thermodynamique, le travail effectué sur un système peut être estimé lorsque ...

Education

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Physics

Physique

Unit 1

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The First Law of Thermodynamics

Le premier principe de la thermodynamique

KEY TERMS AND CONCEPTS

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gas work in a piston cylinder

Gas work in a piston cylinder describes how pressure and volume change are related in thermodynamics. In mechanics, work happens when a force moves an object. In thermodynamics, work done on a system can be estimated when the system changes volume during a process.

A gas can be trapped in a cylinder with a movable piston at one end. When the gas expands from volume V1 to volume V2, it pushes on the piston and moves it by a small distance dr. If the pressure on the piston face is p and the piston area is A, the force on the piston is based on that pressure.

The work done by the gas can then be written in terms of pressure, area, and piston motion. Because the change in volume dV equals A dr, the work can also be expressed as an integral from V1 to V2. This form is meaningful only for a quasi-static process, which means the change happens in very small steps while the system stays in thermal equilibrium.

If the piston compresses the gas, the direction of work reverses. In that case, work is done on the gas, and it is conventionally treated as negative.

Gas Work in a Piston Cylinder

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work done during volume change

Gas work in a piston cylinder describes how pressure and volume change are related in thermodynamics. In mechanics, work happens when a force moves an object. In thermodynamics, work done on a system can be estimated when the system changes volume during a process. A gas can be trapped in a cylinder with a movable piston at one end. When the gas expands from volume V1 to volume V2, it pushes on the piston and moves it by a small distance dr. If the pressure on the piston face is p and the...

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key terms and concepts

Learn how gas pressure and piston motion create work during expansion or compression, and why quasi-static volume change matters in thermodynamics.

Gas Work in a Piston Cylinder | JoVE K12

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Florida Department of Education

SC.912.P.10

SC.912.P.10.2

SC.912.P.10.3

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HS-PS3-5

Gas Work in a Piston Cylinder

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