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Helium gas is subjected to a polytropic process in which the heat supplied to the gas is four times the work done by it. The molar heat capacity of the gas for the process is: (R is universal gas constant)

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$\frac{R}{2}$

answer is C.

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Detailed Solution

Given, $∆ Q = 4 ∆ W$

But, $∆W = ∆U = ∆Q$

$∴ ∆ U = 3 ∆ W = \frac{3}{4} ∆ Q$

$\Rightarrow {nC}_{v} ∆ T = \frac{3}{4} nC ∆ T or, C = \frac{4}{3} C_{v} = \frac{4}{3} [\frac{3 R}{2}] = 2 R$

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