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. $\frac{2}{5}R$
• B. $\frac{5}{2}R$
• C. $\frac{10}{3}R$
• D. $\frac{6}{7}R$

Answer 1

Answer: (C)

$dU=C_{V}dT=\left(\frac{5}{2}R\right)dT$ or $dT=\frac{2(dU)}{5R}$ ...(i)
From first law of thermodynamics
$dU=dQ-dW=Q-\frac{Q}{4}=\frac{3Q}{4}.$
Now molar heat capacity $C=\frac{dQ}{dT}=\frac{Q}{\frac{2(dU)}{5R}}$
$=\frac{5RQ}{2\left(\frac{3Q}{4}\right)}=\frac{10}{3}R.$