Name: ideal gas heat capacity differences
Uploaded: 2023-04-30T12:32:12.000Z
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HS-PS3-3.

Heat Capacities of an Ideal Gas II

Considérons deux flacons identiques remplis d’un gaz parfait à des températures différentes qui peuvent subir différents processus thermodynamiques.
Supposons que, dans un processus à volume constant, la température du gaz du premier flacon soit augmentée pour correspondre à la température du deuxième ballon.
Ensuite, son énergie interne sera la même que le changement de chaleur et peut être écrite en termes de capacité calorifique molaire.
Dans un processus à pression constante, si la température est augmentée de la même quantité, l'énergie interne du système change avec certains travaux effectués.
Comme l’énergie interne est une fonction d’état, le changement d’énergie interne du système est le même dans les deux processus.
En utilisant l’équation des gaz parfaits sous forme différentielle, le travail effectué peut être écrit en termes de changement de température.
En annulant les facteurs communs des deux côtés, on obtient la relation entre les capacités thermiques molaires des deux procédés.
Ici, R est la constante universelle des gaz et, par conséquent, la capacité calorifique molaire d’un gaz parfait sous un procédé à pression constante est toujours supérieure à celle d’un procédé à volume constant.

<ol>
	<li>Young, H.D et Freedman, R.A. (2012). La physique universitaire avec la physique moderne. San Francisco, Californie : Pearson.637-638.</li>
	<li>OpenStax. (2019). Physique universitaire Vol. 2. [Version Web]. 126-127 Tiré 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>

capacités thermiques d'un gaz idéal ii

Pour un système qui subit un processus thermodynamique dans des conditions de volume constant, la chaleur absorbée est utilisée uniquement pour augmenter l'énergie interne du système et non pour accomplir un travail quelconque. Alors que pour un système qui subit un processus thermodynamique dans des conditions de pression constante, la quantité de chaleur absorbée est utilisée non seulement pour augmenter l'énergie interne (en fonction de la température) mais aussi pour accomplir un certain travail. La capacité thermique molaire est la quantité de chaleur requise pour augmenter la température de 1 mole de gaz de 1 unité. Étant donné que une partie de la chaleur absorbée est utilisée pour effectuer un travail, plus de chaleur doit être ajoutée à un système sous une pression constante pour augmenter sa température de 1 unité, la capacité thermique molaire pour un processus à pression constante est toujours plus grande que la capacité thermique molaire pour un processus à volume constant. Par conséquent, à partir de la dérivation, qui était basée sur le premier principe de la thermodynamique, nous obtenons la relation suivante, qui est

<img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;" />

Ainsi, la différence entre les deux capacités thermiques molaires est une constante et est égale à la constante des gaz parfaits, R. Elle est également appelée constante des gaz idéaux ou constante molaire des gaz. Sa valeur est d'environ 8,314 et est exprimée dans la même unité SI que la capacité thermique molaire spécifique J/mol·K. Par exemple, pour He, les valeurs mesurées pour Cp et Cv sont respectivement de 20,78 J/mol·K et de 12,47 J/mol·K. Leur différence est de 8,31 J/mol·K, qui est proche de R.

Capacités thermiques d'un gaz idéal II

Pour un système qui subit un processus thermodynamique à volume constant, la chaleur absorbée n'est utilisée que pour augmenter la ...

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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

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