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

Considere um cilindro com um gás ideal de volume Vo a uma pressão de po equipado com um pistão sem atrito ligado a uma massa. O pistão permanece estacionário enquanto a pressão está em equilíbrio.
Se a massa diminuir pela metade, a pressão externa no pistão diminui proporcionalmente. A pressão interna mais alta do gás empurra o pistão para frente até que um novo equilíbrio seja alcançado.
O volume de gás aumenta. O sistema atinge um novo estado termodinâmico realizando trabalho.
Suponha que o mesmo estado final seja alcançado reduzindo a massa em dois estágios. Inicialmente, a pressão diminui para 0,75po, e o trabalho realizado é representado pela área sob a segunda curva.
Reduzindo ainda mais a massa no segundo estágio, o trabalho realizado pelo gás é igual à área sob a terceira curva. Portanto, o trabalho total realizado pelo gás no segundo processo é a soma das áreas sob as duas curvas.
Assim, o trabalho realizado pelo gás é diferente para diferentes processos e, portanto, é uma função dependente do caminho.

<ol>
 <li>Young, H.D., Freedman, R.A. Física da Universidade com Física Moderna. São Francisco, CA: Pearson. 628 (2012).</li>
 <li>OpenStax. Física Universitária Vol.2. Pg 110 [versão Web]. Obtido 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>

o caminho percorrido por processos termodinâmicos

Considere os dois processos termodinâmicos envolvendo um gás ideal, que são representados pelos caminhos AC e ABC na Figura 1:

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Figure_PT_1.png" style="text-align: center; height: 250px;" />

No primeiro processo para o caminho A até C, o gás é mantido em temperatura constante T. Ele passa por uma expansão de volume V1 para V2.

O trabalho realizado por um gás ideal é expresso como

<img alt="Equation1" src="/files/ftp_upload/13676/13676_Equation_PT_1.svg" style="text-align: center; height: 45px;" />

Substituindo a pressão como nRT/V a partir da equação do gás ideal e integrando os termos, o trabalho realizado por um gás ideal a temperatura constante é obtido como

<img alt="Equation2" src="/files/ftp_upload/13676/13676_Equation_PT_2.svg" style="text-align: center; height: 30px;" />

No segundo processo, para o caminho A até B, o gás ideal é primeiro expandido do volume V1 para V2 a uma pressão constante p1, aplicando calor. O gás é então resfriado a um volume constante V2 ao longo do caminho B até C, de forma que sua pressão caia para p2.

Para o caminho A até B, trabalho é realizado sob pressão constante, portanto

<img alt="Equation3" src="/files/ftp_upload/13676/13676_Equation_PT_3.svg" style="text-align: center; height: 13px;" />

Para o caminho B até C, uma vez que o volume permanece constante, nenhum trabalho é realizado pelo gás ou no gás pelas redondezas. Portanto, o trabalho total realizado pelo gás neste processo é o mesmo que o trabalho realizado para o caminho A até B.

Em ambos os processos, o gás expande de volume V1 para volume V2, de forma que sua pressão muda de p1 para p2. No entanto, o trabalho realizado em ambos os processos é diferente. Isso prova que o trabalho realizado por um sistema depende do caminho.

O Caminho Percorrido por Processos Termodinâmicos

Considere os dois processos termodinâmicos envolvendo um gás ideal que são representados pelos caminhos AC e ABC na Figura 1:

No primeiro processo do caminho A para ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

The First Law of Thermodynamics

A Primeira Lei da Termodinâmica

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

thermodynamic systems

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path between thermodynamics states

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...

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heat capacities of an ideal gas ii

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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...

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Compare two ideal-gas paths between the same states and see why an isothermal route and a constant-pressure-plus-volume route give different work values.

Path Dependence in Gas Work | JoVE K12

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

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HS-PS3-5

Path Dependence in Gas Work

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