JEE Main · PhysicsHard

$The molar heat capacity of a gas in a process $P V^2 = \text{constant}$ is given by what expression, where $R$ is the gas constant and $\gamma$ is the adiabatic index?$

Show correct answer & step-by-step solution

Correct answer: B — $\frac{R}{\gamma - 1} - R$

Solution

For a polytropic process

P V^{x} = constant

, the molar heat capacity is

C = C_{v} + \frac{R}{1 - x}

. With

C_{v} = \frac{R}{γ - 1}

and

x = 2

, we get

C = \frac{R}{γ - 1} + \frac{R}{1 - 2} = \frac{R}{γ - 1} - R