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An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation between 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)/(C - C_V)
2. n = (C - C_V)/(C - C_P)
3. n = C_P/C_V
4. n = (C - C_P)/(C - C_V)

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

Solution

For PV^n=const the molar heat capacity is C = Cv + R/(1-n). Solving, 1-n = R/(C-Cv) and with R = Cp-Cv, n = 1 - (Cp-Cv)/(C-Cv) = (C-Cp)/(C-Cv).

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