Question

The volume of one mole of an ideal gas with the adiabatic exponent $\gamma$ is changed according to the relation $V=\frac{a}{T}$ where a is a constant. Find the amount of heat absorbed by the gas in the process, if the temperature is increased by $\Delta T$.

Answer 1

The given process is $V=\frac{a}{T}$

$⟹$ $VT=a=constant$

Comparing with $T{V}^{m-1}=constant$ we get $m-1=1$

$⟹$ $m=2$

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

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

Number of moles of the gas $n=1$

Heat absorbed by the gas $Q=nC\Delta T$

$\therefore$ $Q=1\times \frac{(\gamma -2)R}{\gamma -1}\times \Delta T=\frac{(\gamma -2)}{(\gamma -1)}R\Delta T$