Question

For a diatomic gas undergoing a reversible process with its pressure inversely proportional to absolute temperature, its molar heat capacity is $\frac{xR}{2}$. The value of $x$ is:

• A. $9$
• B. $7$
• C. $12$
• D. $8$

Answer 1

The correct option is A $9$

Given that for a diatomic gas undergoing a reversible process, its pressure is inversely proportional to absolute temperature.

$\therefore P\propto \frac{1}{T}$ or $PT=$ constant or $P\left(\frac{PV}{nR}\right)=$ constant

$\therefore P{V}^{1/2}=$ constant

Hence, the value of $\gamma$ is $\frac{1}{2}$.
Molar heat capacity $=C=C_V+\frac{R}{1-\gamma }=\frac{5R}{2}+\frac{R}{1-\frac{1}{2}}$ $=\frac{9R}{2}$
$\therefore x=9$

Hence, the value of $x$ is $9$.