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An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during the process the relation of pressure P and volume V is given by PVⁿ = constant, then n is given by (Here C_P and C_V are molar specific heat at constant pressure and constant volume, respectively):

1. n = C_P / C_V
2. n = (C - C_P) / (C - C_V)
3. n = (C_P - C) / (C - C_V)
4. n = (C - C_V) / (C - C_P)

Correct answer: n = (C - C_P) / (C - C_V)

Solution

The correct option relates the heat capacity C to the specific heat capacities at constant pressure and volume, showing how the heat capacity influences the relationship between pressure and volume during the process. This formulation arises from the definitions of heat capacities and their roles in the thermodynamic behavior of the gas.

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