1 mole of rigid diatomic gas performs a work of Q/5 when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{\mathrm{XR}}{8}$. The value of x is …………. (R is universal gas constant)

Given number of mole n = 1 [Heat supplied ] = $\left(\mathrm{\phi }\right)$
Work done=Q/5 By using first law of thermodynamics
$\begin{array}{l}\mathrm{\Delta Q}=\mathrm{\Delta U}+\mathrm{\Delta W}\\ \Rightarrow \mathrm{Q}=\mathrm{\Delta U}+\mathrm{Q}/5\\ \Rightarrow \mathrm{\Delta U}=4\mathrm{Q}/5={\mathrm{nC}}_{\mathrm{V}}\mathrm{\Delta T}\end{array}$

Where C_V is heat coefficient at constant volume and $\left(\mathrm{\Delta t}\right)$

is change in temperature. Degree of freedom of diatomic gas f = 5

$\begin{array}{l}\therefore \mathrm{Q}=\frac{5\mathrm{f}}{42}\mathrm{R\Delta T}\\ \Rightarrow \frac{\mathrm{Q}}{\mathrm{\Delta T}}=\mathrm{C}=\frac{5}{4}\times \frac{5}{2}\mathrm{R}=\frac{25}{8}\mathrm{R}\end{array}$

Hence, X = 25