A gas follows the law $P{V}^2=\text{constant}$. What is the molar heat capacity of this gas if it is diatomic?

Solution

1. For a polytropic process $P{V}^x=\text{constant}$, the molar heat capacity is given by $C=C_v+\frac{R}{1-x}$.
2. For a diatomic gas, the molar heat capacity at constant volume is $C_v=\frac{5R}{2}$.
3. Given the process $P{V}^2=\text{constant}$, we have $x=2$.
4. Substituting these values, we get $$\begin{array}{rl}C& =\frac{5R}{2}+\frac{R}{1-2}\\ & =\frac{5R}{2}-R\\ & =\frac{3R}{2}\end{array}$$.
5. Hence the answer is (B).