JEE Main · PhysicsHard

$A gas follows the law P V^{2} = constant . What is the molar heat capacity of this gas if it is diatomic?$

A. $C = \frac{5 R}{2}$
B. $C = R$
C. $C = \frac{3 R}{2}$
D. $C = 2 R$

Show correct answer & step-by-step solution

Correct answer: B — $C = R$

Solution

For a polytropic process P V^{x} = K, C = C_{v} + \frac{R}{1 - x} . For diatomic gas C_{v} = \frac{5 R}{2} . With x = 2, C = \frac{5 R}{2} + \frac{R}{1 - 2} = \frac{5 R}{2} - R = \frac{3 R}{2} .

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