Question

An ideal monoatomic gas is taken along a process in which pressure varies with temperature as $p=\frac{a}{T}$, where $a$ is constant. Find molar specific heat of the gas for this process in terms of $R$.

Answer 1

$P=\frac{a}{T}$

For Monoatomic Gas,$PV=RT$

$\therefore \frac{RT}{V}=\frac{a}{T}{T}^2{V}^{-1}=ConstantT{V}^{-\frac{1}{2}}=Constant$

Compairing with$T{V}^{\gamma -1}\gamma -1=-\frac{1}{2}\gamma =\frac{1}{2}\therefore \frac{C_p}{C_v}=\frac{1}{2}\therefore C_v=2C_p$

And,

$C_p-C_v=R{C}_p-2C_p=RR=-C_p\therefore C_p=-R$