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

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HS-PS3-3.

Heat Capacities of an Ideal Gas II

Consideriamo due fiasche identiche riempite con un gas ideale a temperature diverse che possono subire diversi processi termodinamici.
Supponiamo, in un processo a volume costante, che la temperatura del gas del primo pallone venga aumentata fino a eguagliare la temperatura del secondo pallone.
Quindi, la sua energia interna sarà la stessa della variazione di calore e può essere scritta in termini di capacità termica molare.
In un processo a pressione costante, se la temperatura viene aumentata della stessa quantità, l'energia interna del sistema cambia con un po' di lavoro in corso.
Poiché l'energia interna è una funzione di stato, la variazione di energia interna del sistema è la stessa in entrambi i processi.
Utilizzando l'equazione del gas ideale in forma differenziale, il lavoro svolto può essere scritto in termini di variazione di temperatura.
Annullando i fattori comuni su entrambi i lati, si ottiene la relazione tra le capacità termiche molari per entrambi i processi.
Qui, R è la costante universale del gas e, quindi, la capacità termica molare di un gas ideale in un processo a pressione costante è sempre maggiore di quella in un processo a volume costante.

<ol>
	<li>Young, H.D e Freedman, R.A. (2012). Fisica universitaria con fisica moderna. San Francisco, CA: Pearson.637-638.</li>
	<li>OpenStax. (2019). Fisica universitaria Vol. 2. [Versione web]. 126-127 Estratto da <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>

capacità termiche di un gas ideale ii

Per un sistema che subisce un processo termodinamico in condizioni di volume costante, il calore assorbito viene usato solo per aumentare l'energia interna del sistema e non per compiere alcun tipo di lavoro. Mentre per un sistema che subisce un processo termodinamico in condizioni di pressione costante, la quantità di calore assorbito viene usata non solo per aumentare l'energia interna (come funzione della temperatura) ma anche per compiere del lavoro. La capacità termica molare è la quantità di calore richiesta per aumentare la temperatura di 1 mole di gas di 1 unità. Poiché parte del calore assorbito viene usato per compiere lavoro, più calore deve essere aggiunto a un sistema sotto pressione costante per aumentare la sua temperatura di 1 unità, la capacità termica molare per un processo a pressione costante è sempre maggiore rispetto alla capacità termica molare per un processo a volume costante. Pertanto, dalla derivazione, che si basava sulla prima legge della termodinamica, otteniamo la seguente relazione, cioè:

<img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;" />

Così, la differenza tra le due capacità termiche molari è costante e è uguale alla costante dei gas universale, \R. È anche chiamata costante dei gas ideali o costante molare dei gas. Il suo valore è approssimativamente 8.314 e viene espresso nella stessa unità SI della capacità termica molare specifica J/mol∙K. Per esempio, per l'elio, i valori misurati per Cp e Cv sono rispettivamente 20.78 J/mol∙K e 12.47 J/mol∙K. La loro differenza è 8.31 J/mol∙K, che è vicina a R.

Capacità termiche di un gas ideale II

Per un sistema che subisce un processo termodinamico a una condizione di volume costante, il calore assorbito viene utilizzato solo per aumentare la temperatura interna dell'impianto ...

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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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