Question

The molar heat capacity in a process of a diatomic gas if it does a work of $\frac{Q}{4}$ when a heat of Q is supplied to it is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$dU=C_{v}dT=\left(\frac{5}{2}R\right)dT$ or $dT=\frac{2\left(dU\right)}{5R}$

From first law of thermodynamics

$dU=dQ-dW=Q-\frac{Q}{4}=\frac{3Q}{4}$.Now molar heat

capacity $C=\frac{dQ}{dT}=\frac{Q}{\frac{2\left(dU\right)}{5R}}=\frac{5RQ}{2\left(\frac{3Q}{4}\right)}=\frac{10}{3}R$.