Q95 / 100 · BITSAT 2022 · Physics
One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the process is
- Correct answerA$3 R / 2$
- B$R / 2$
- C$5 R / 2$
- D$7 R / 2$
Solution
In the curve, $V \propto \frac{1}{T}$
$$
\begin{aligned}
& \Rightarrow V=m \frac{1}{T} \text { where, } m=\text { slope of curve. } \\
& \Rightarrow V T=\text { constant } \\
& \therefore \quad T d V+V d T=0 \\
& \Rightarrow \quad d V=-\frac{V}{T} d T \\
& \text { As, } Q=\Delta U+W \\
& C d T=C_V d T+p d V \\
& C d T=C_V d T-\frac{p}{T} V d T \\
& \Rightarrow \quad C=C_V-\frac{p V}{T} \\
& =C_V-R \quad\left(\because \frac{p V}{T}=R\right) \\
&
\end{aligned}
$$
For diatomic gas, $C_V=\frac{5}{2} R$
$$
\therefore \quad C=C_V-R=\frac{5}{2} R-R=\frac{3 R}{2}
$$
Hence, the correct answer is option: 'A'.