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

Answer: (d). For PVⁿ = constant: C = Cv + (R)/(1 - n) with R = Cp - Cv. 1 - n = (Cp - Cv)/(C - Cv) n = (C - Cv - Cp + Cv)/(C - Cv) = (C - Cp)/(C - Cv) So the answer is (d).

An ideal gas undergoes a quasi static, reversible process in which… | JEE Main 2016

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Thermodynamic Processes

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^{n} =$ constant, then $n$ is given by (Here $C_p$ and $C_v$ are molar specific heat at constant pressure and constant volume, respectively:

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Answer: (d)

For $PV^{n} =$ constant: $C = C_v + \frac{R}{1 - n}$ with $R = C_p - C_v$ .
$1 - n = \frac{C_p - C_v}{C - C_v}$
$n = \frac{C - C_v - C_p + C_v}{C - C_v} = \frac{C - C_p}{C - C_v}$
So the answer is (d).

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