An ideal gas with adiabatic exponent $(γ = 1 .5)$ undergoes a process in which work done by the gas is same as increase in internal energy of the gas. The molar heat capacity of gas for the process is:

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C = 2R

C = R

C = 0

C = 4R

answer is A.

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Detailed Solution

$\int PdV = \int {nC}_{v} dt \Rightarrow dQ = 2 dU \Rightarrow nCdT = 2 dU$
$\Rightarrow nCdT = 2 {nC}_{v} dT \Rightarrow C = 2 C_{v} \Rightarrow C = \frac{2 R}{1 .5 - 1} = 4 R$

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