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

K12 Standards

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New Jersey Student Learning Standards for Science

High School

Physical Science

Energy

HS-PS3-4

Path Between Thermodynamics States

Considere un cilindro con un gas ideal de volumen Vo a una presión de po equipado con un pistón sin fricción unido a una masa. El pistón permanece estacionario mientras la presión está en equilibrio.
Si la masa se reduce a la mitad, la presión externa sobre el pistón se reduce proporcionalmente. La mayor presión interna del gas empuja el pistón hacia adelante hasta que se alcanza un nuevo equilibrio.
El volumen de gas aumenta. El sistema alcanza un nuevo estado termodinámico mediante la realización de trabajos.
Supongamos que se logra el mismo estado final reduciendo la masa en dos etapas. Inicialmente, la presión disminuye a 0,75po, y el trabajo realizado está representado por el área bajo la segunda curva.
Reduciendo aún más la masa en la segunda etapa, el trabajo realizado por el gas es igual al área bajo la tercera curva. Por lo tanto, el trabajo total realizado por el gas en el segundo proceso es la suma de las áreas bajo las dos curvas.
Por lo tanto, el trabajo realizado por el gas es diferente para diferentes procesos y, por lo tanto, es una función dependiente de la trayectoria.

<ol>
 <li>Young, H.D., Freedman, R.A. Física Universitaria con Física Moderna. San Francisco, CA: Pearson. 628 (2012).</li>
 <li>OpenStax. Física Universitaria Vol.2. Pág. 110 [Versión web]. Obtenido 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>

camino entre estados termodinámicos

Considere los dos procesos termodinámicos que involucran un gas ideal y que están representados por las rutas AC y ABC en la Figura 1: 
 <img alt="Equation1" src="/files/ftp_upload/13676/13676_Figure_PT_1.png" style="text-align: center; height: 250px;"> 

 En el primer proceso para la ruta de A a C, el gas se mantiene a una temperatura constante T. Experimenta una expansión desde el volumen V1 hasta el volumen V2. 

 El trabajo realizado por un gas ideal se expresa como: 
 <img alt="Equation1" src="/files/ftp_upload/13676/13676_Equation_PT_1.svg" style="text-align: center; height: 45px;"> 

 Sustituyendo la presión como nRT/V en la ecuación del gas ideal e integrando los términos, se obtiene el trabajo realizado por un gas ideal a temperatura constante como: 
 <img alt="Equation2" src="/files/ftp_upload/13676/13676_Equation_PT_2.svg" style="text-align: center; height: 30px;"> 

 En el segundo proceso, para la ruta de A a B, el gas ideal primero se expande desde el volumen V1 hasta el volumen V2 a una presión constante p1 mediante la aplicación de calor. Luego, el gas se enfría a volumen constante V2 a lo largo de la ruta B hacia C, de manera que su presión disminuye a p2. 

 Para la ruta de A a B, se realiza trabajo bajo presión constante, por lo tanto: 
 <img alt="Equation3" src="/files/ftp_upload/13676/13676_Equation_PT_3.svg" style="text-align: center; height: 13px;"> 

 Para la ruta de B a C, dado que el volumen permanece constante, el gas no realiza trabajo ni se realiza trabajo sobre el gas por el entorno. Por lo tanto, el trabajo total realizado por el gas en este proceso es el mismo que el trabajo realizado para la ruta de A a B. 

 En ambos procesos, el gas se expande desde el volumen V1 hasta el volumen V2, de manera que su presión cambia de p1 a p2. Sin embargo, el trabajo realizado en ambos procesos es diferente. Esto demuestra que el trabajo realizado por un sistema depende del camino.

Camino entre estados termodinámicos

Considere los dos procesos termodinámicos que involucran un gas ideal que están representados por las trayectorias AC y ABC en la Figura 1:

En el primer proceso para la ruta A a ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

The First Law of Thermodynamics

La primera ley de la termodinámica

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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SC.912.P.10.2

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HS-PS3-5

Path Dependence in Gas Work

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