Question

One mole of an ideal monoatomic gas undergoes the process $P=\alpha T^{1/2}$, where $\alpha$ is a constant. If the molar specific heat of the gas is given by $x\times R$,then find $x$.

Answer 1

The given process is $P=\alpha T^{1/2}$

$⟹$ $P{T}^{-1/2}=\alpha =constant$

Comparing with $P{T}^{\frac{m}{1-m}}=constant$ we get $\frac{m}{1-m}=\frac{-1}{2}$

$⟹$ $m=-1$

For monoatomic gas $\gamma =1.67$

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

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