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 dos matraces idénticos llenos de un gas ideal a diferentes temperaturas que pueden sufrir diferentes procesos termodinámicos.
Supongamos que, en un proceso de volumen constante, la temperatura del gas del primer matraz se incrementa para igualarla a la temperatura del segundo matraz.
Entonces, su energía interna será la misma que el cambio de calor y se puede escribir en términos de capacidad calorífica molar.
En un proceso de presión constante, si la temperatura se incrementa en la misma cantidad, entonces la energía interna del sistema cambia con el trabajo que se está realizando.
Como la energía interna es una función de estado, el cambio de energía interna del sistema es el mismo en ambos procesos.
Usando la ecuación del gas ideal en forma diferencial, el trabajo realizado se puede escribir en términos de cambio de temperatura.
Al anular los factores comunes en ambos lados, se obtiene la relación entre las capacidades caloríficas molares para ambos procesos.
Aquí, R es la constante universal del gas y, por lo tanto, la capacidad calorífica molar de un gas ideal bajo un proceso de presión constante es siempre mayor que la de un proceso de volumen constante.

<ol>
	<li>Young, H.D y Freedman, R.A. (2012). Física Universitaria con Física Moderna. San Francisco, CA: Pearson.637-638.</li>
	<li>OpenStax. (2019). Física Universitaria Vol. 2. [Versión web]. 126-127 Recuperado 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 un gas ideal ii

Para un sistema que experimenta un proceso termodinámico en condiciones de volumen constante, el calor absorbido se utiliza únicamente para aumentar la energía interna del sistema y no para realizar ningún tipo de trabajo. Mientras que para un sistema que experimenta un proceso termodinámico bajo condiciones de presión constante, la magnitud de calor absorbida se utiliza no solo para aumentar la energía interna (como función de la temperatura) sino también para realizar trabajo. La capacidad térmica molar es la magnitud de calor necesaria para aumentar la temperatura de 1 mol de gas en 1 unidad. Dado que parte del calor absorbido se utiliza para realizar trabajo, se requiere agregar más calor a un sistema bajo presión constante para aumentar su temperatura en 1 unidad, por lo que la capacidad térmica molar para un proceso a presión constante siempre es mayor que la capacidad térmica molar para un proceso a volumen constante. En consecuencia, a partir de la derivación, que se basó en la primera ley de la termodinámica, obtenemos la siguiente relación, es decir: <img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;"> Así, la diferencia entre las dos capacidades térmicas molares es una constante y es igual a la constante universal de los gases, R. También se conoce como la constante de los gases ideales o constante molar de los gases. Su valor es aproximadamente 8.314 y se expresa en la misma unidad SI que la capacidad térmica específica molar, J/mol·K. Por ejemplo, para He, los valores medidos para Cp y CV son 20.78 J/mol·K y 12.47 J/mol·K, respectivamente. Su diferencia es 8.31 J/mol·K, que está cerca de R.

Capacidades térmicas de un gas ideal II

Para un sistema que se somete a un proceso termodinámico en una condición de volumen constante, el calor absorbido se utiliza sólo para aumentar la capacidad interna del sistema.

Education

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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

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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