Name: path dependence in gas work
Uploaded: 2023-04-30T12:31:19.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

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

New Jersey Student Learning Standards for Science

High School

Physical Science

Energy

HS-PS3-4

Path Between Thermodynamics States

Considérons un cylindre avec un gaz parfait de volume Vo à une pression de po équipé d’un piston sans frottement attaché à une masse. Le piston reste stationnaire lorsque la pression est en équilibre.
Si la masse diminue de moitié, la pression externe sur le piston diminue proportionnellement. La pression interne plus élevée du gaz pousse le piston vers l’avant jusqu’à ce qu’un nouvel équilibre soit atteint.
Le volume de gaz augmente. Le système atteint un nouvel état thermodynamique en effectuant un travail.
Supposons que le même état final soit obtenu en réduisant la masse en deux étapes. Initialement, la pression diminue à 0,75po, et le travail effectué est représenté par l’aire sous la deuxième courbe.
En réduisant encore la masse dans la deuxième étape, le travail effectué par le gaz est égal à l’aire sous la troisième courbe. Par conséquent, le travail total effectué par le gaz dans le deuxième processus est la somme des aires sous les deux courbes.
Ainsi, le travail effectué par le gaz est différent pour différents processus et, par conséquent, il s’agit d’une fonction dépendante du chemin.

<ol>
 <li>Young, H.D., Freedman, R.A. Physique de l’Université avec la physique moderne. San Francisco, Californie : Pearson. 628 (2012).</li>
 <li>OpenStax. Physique universitaire Vol.2. Pg 110 [Version Web]. Récupéré 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>

chemin entre les états thermodynamiques

Considérons les deux processus thermodynamiques impliquant un gaz idéal qui sont représentés par les chemins AC et ABC sur la Figure 1 :

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Figure_PT_1.png" style="text-align: center; height: 250px;" />

Dans le premier processus pour le chemin A à C, le gaz est maintenu à une température constante T. Il subit une expansion du volume V1 au volume V1.

Le travail réalisé par un gaz idéal est exprimé comme suit :

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Equation_PT_1.svg" style="text-align: center; height: 45px;" />

En substituant la pression par nRT/V à partir de l'équation des gaz idéaux et en intégrant les termes, le travail réalisé par un gaz idéal à température constante est obtenu comme suit :

<img alt="Equation2" src="/files/ftp_upload/13676/13676_Equation_PT_2.svg" style="text-align: center; height: 30px;" />

Dans le deuxième processus, pour le chemin A à B, le gaz idéal est d'abord étendu du volume V1 au volume V2 à une pression constante p1 en fournissant de la chaleur. Le gaz est ensuite refroidi à un volume V2 constant le long du chemin B jusqu'à C, de telle sorte que sa pression diminue jusqu'à p2.

Pour le chemin A à B, un travail est effectué sous pression constante, donc :

<img alt="Equation3" src="/files/ftp_upload/13676/13676_Equation_PT_3.svg" style="text-align: center; height: 13px;" />

Pour le chemin B à C, puisque le volume reste constant, aucun travail n'est effectué par le gaz ou sur le gaz par l'environnement. Par conséquent, le travail total réalisé par le gaz dans ce processus est le même que le travail réalisé pour le chemin A à B.

Dans les deux processus, le gaz s'étend du volume V1 au volume V2, de telle sorte que sa pression varie de p1 à p2. Cependant, le travail réalisé dans les deux processus est différent. Cela prouve que le travail réalisé par un système dépend du chemin emprunté.

Chemin entre les états thermodynamiques

Considérons les deux processus thermodynamiques impliquant un gaz parfait qui sont représentés par les trajets AC et ABC de la figure 1 :

Dans le premier processus pour le chemin A vers ...

Education

Enseignement

JoVE Core

Physics

Physique

Unit 1

Unité 1

The First Law of Thermodynamics

Le premier principe de la thermodynamique

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

path dependence in gas work

Work done by an ideal gas can depend on the path it takes between two thermodynamic states. The transcript compares two routes from state A to state C for the same gas. In both cases, the gas expands from volume V1 to volume V2, but the work is not the same.

Along path AC, the gas stays at constant temperature T. It expands from V1 to V2. The work done by the gas is found from the pressure-volume relation for an ideal gas. After substituting pressure as nRT/V and integrating, the work for this isothermal process is obtained.

Along path ABC, the gas follows two steps. First, it expands from V1 to V2 at constant pressure p1 by applying heat. Then it is cooled at constant volume V2, and its pressure drops to p2. During the constant-pressure step AB, work is done by the gas. During the constant-volume step BC, no work is done because the volume does not change.

The total work for path ABC is therefore the same as the work done during AB. Even though both paths connect the same start and end states and the pressure changes from p1 to p2, the work values are different. This shows that work done by a system is path-dependent.

Path Dependence in Gas Work

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Path Dependence in Gas Work | JoVE K12

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HS-PS3-5

Path Dependence in Gas Work

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