# Neon gas has undertaken a process in which the pressure and the volume are changed according to the equation $P=kV^k$. The molar hear capacity of the gas for the process is given by?

$(A) C = 3R/2 + R/(k+1)$ $(B) C = 3R/2+R/(k-1)$ $(C) C = 3R/2 - R/(k+1)$ $(D) C = 3R/2 - R/(k-1)$

We know that $PV = n RT$ and are given $P = kV^k$.
$\Rightarrow PV = nRT = kV^{k+1}$
Differentiating, we get $nR dT = (k+1)kV^n dV \rightarrow (k+1) PdV = nRdT$
Now, $dQ = dU + pDV$
$\Rightarrow nCdT = nC_vdT + \large\frac{nRdT}{k+1}$
$\Rightarrow C = C_v + R/(k+1)$
$\Rightarrow C = 3R/2 + R/(k+1)$
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