Question

One mole of an ideal monoatomic gas undergoes a process as shown in the figure. Find the molar specific heat of the gas in the process.

Answer 1

From the graph shown, $V\propto \frac{1}{T}$

$⟹$ $TV=K=constant$................(1)

For a polytropic process,

$P{V}^m=constant$

$\frac{nRT}{V}{V}^m=constant$

$T{V}^{m-1}=constant$.............(2)

On comparing (1) and (2)

$m-1=1$

$m=2$

For monoatomic gas, $\gamma =\frac{5}{3}$

$\therefore$ Molar specific heat capacity of the gas in polytropic process is given as

$C=\frac{R}{\gamma -1}+\frac{R}{1-m}$

$\therefore$ $C=\frac{R}{\frac{5}{3}-1}+\frac{R}{1-2}=\frac{R}{2}$