Q146 / 180 · COMEDK 2024 (Memory Based) · Physics
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$\frac{5}{2} R$
- Correct answerC$\frac{10}{3} R$
- D$\frac{6}{7} R$
Solution
$d U=C_V d T=\left(\frac{5}{2} R\right) d T$ or $d T=\frac{2(d U)}{5 R}$
From first law of thermodynamics,
$d U=d Q-d W=Q-\frac{Q}{4}=\frac{3 Q}{4}$
Now, molar heat capacity,
$C=\frac{d Q}{d T}=\frac{Q}{\frac{2(d U)}{5 R}}=\frac{5 R Q}{2\left(\frac{3 Q}{4}\right)}=\frac{10}{3} R$
From first law of thermodynamics,
$d U=d Q-d W=Q-\frac{Q}{4}=\frac{3 Q}{4}$
Now, molar heat capacity,
$C=\frac{d Q}{d T}=\frac{Q}{\frac{2(d U)}{5 R}}=\frac{5 R Q}{2\left(\frac{3 Q}{4}\right)}=\frac{10}{3} R$
Hence, the correct answer is option: 'C'.