Question

An ideal monoatomic gas undergoes a process where its pressure is inversely proportional to its temperature. The molar specific heat for the process is given by $\frac{xR}{2}$,then find $x$.

Answer 1

The given process is $T\propto \frac{1}{P}$

$⟹$ $PT=K=constant$

Comparing with $P{T}^{\frac{m}{1-m}}=constant$ we get $\frac{m}{1-m}=1$

$⟹$ $m=\frac{1}{2}$

For monoatomic gas $\gamma =1.67$

Molar specific heat of the gas $C=\frac{R}{\gamma -1}+\frac{R}{1-m}$

$\therefore$ $C=\frac{R}{1.67-1}+\frac{R}{1-\left(0.5\right)}=\frac{7}{2}R$