Name: ideal gas heat capacity differences
Uploaded: 2023-04-30T12:32:12.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

new-york-state-science-learning-standards

New York State Science Learning Standards

High School

Physical Science

HS. Energy

HS-PS3-3.

Heat Capacities of an Ideal Gas II

Considere dois frascos idênticos cheios de um gás ideal em diferentes temperaturas que podem passar por diferentes processos termodinâmicos.
Suponha que, em um processo de volume constante, a temperatura do gás do primeiro frasco seja aumentada para igualar a temperatura do segundo frasco.
Então, sua energia interna será a mesma da mudança de calor e pode ser escrita em termos de capacidade térmica molar.
Em um processo de pressão constante, se a temperatura for aumentada na mesma quantidade, a energia interna do sistema muda com algum trabalho sendo feito.
Como a energia interna é uma função de estado, a mudança de energia interna do sistema é a mesma em ambos os processos.
Usando a equação do gás ideal na forma diferencial, o trabalho realizado pode ser escrito em termos de mudança de temperatura.
Ao cancelar os fatores comuns em ambos os lados, obtém-se a relação entre as capacidades térmicas molares para ambos os processos.
Aqui, R é a constante universal do gás e, portanto, a capacidade térmica molar de um gás ideal sob um processo de pressão constante é sempre maior do que sob um processo de volume constante.

<ol>
	<li>Young, H.D. e Freedman, R.A. (2012). Física Universitária com Física Moderna. São Francisco, CA: Pearson.637-638.</li>
	<li>OpenStax. (2019). Física Universitária Vol. 2. [Versão Web]. 126-127 Obtido de <a href="https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas">https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas</a></li>
</ol>

capacidades térmicas de um gás ideal ii

Para um sistema que passa por um processo termodinâmico em condições de volume constante, o calor absorvido é usado apenas para aumentar a energia interna do sistema, e não para realizar qualquer tipo de trabalho. Por outro lado, para um sistema passando por um processo termodinâmico em condições de pressão constante, a quantidade de calor absorvido é utilizada não apenas para aumentar a energia interna (como uma função da temperatura) mas também para realizar algum trabalho. A capacidade térmica molar é a quantidade de calor necessária para aumentar a temperatura de 1 mol de gás em 1 unidade. Como parte do calor absorvido é utilizado para realizar trabalho, mais calor deve ser adicionado a um sistema sob pressão constante para aumentar sua temperatura em 1 unidade. Portanto, a capacidade térmica molar para um processo a pressão constante é sempre maior do que a capacidade térmica molar para um processo a volume constante. Consequentemente, a partir da derivação, que foi baseada na primeira lei da termodinâmica, obtemos a seguinte relação,

<img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;" />

Assim, a diferença entre as duas capacidades térmicas molares é uma constante, e é igual à constante universal dos gases, R. Ela também é chamada de constante dos gases ideais, ou constante molar dos gases. Seu valor é de aproximadamente 8,314, e é expressa na mesma unidade do SI que o calor específico molar J/mol·K. Por exemplo, para o gás hélio, os valores medidos para Cp e CV são 20,78 J/mol·K e 12,47 J/mol·K, respectivamente. Sua diferença é de 8,31 J/mol·K, que é próximo de R.

Capacidades térmicas de um gás ideal II

Para um sistema que passa por um processo termodinâmico em uma condição de volume constante, o calor absorvido é usado apenas para aumentar a capacidade interna do sistema.

Education

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Physics

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Unit 1

Unidade 1

The First Law of Thermodynamics

A Primeira Lei da Termodinâmica

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

ideal gas heat capacity differences

Ideal gas heat capacities depend on whether the gas is heated at constant volume or constant pressure. At constant volume, the heat absorbed only raises the internal energy of the system. No work is done in this case.

At constant pressure, the situation is different. The heat absorbed increases the internal energy and also does work. Molar heat capacity is the heat needed to raise the temperature of 1 mole of gas by 1 unit. Because some of the added heat goes into work, more heat is needed at constant pressure than at constant volume.

From the first law of thermodynamics, the two molar heat capacities are related by a simple equation. The difference between the constant-pressure heat capacity, Cp, and the constant-volume heat capacity, Cv, is a constant. That constant is the universal gas constant, R, also called the ideal gas constant or molar gas constant.

The value of R is about 8.314 and it uses the same SI unit as molar specific heat capacity, J/mol·K. A helium example shows this relationship clearly. For He, Cp is 20.78 J/mol·K and Cv is 12.47 J/mol·K. Their difference is 8.31 J/mol·K, which is close to R.

Ideal Gas Heat Capacity Differences

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Ideal Gas Heat Capacity Differences | JoVE K12

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Ideal Gas Heat Capacity Differences

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