Question

For a certain process, pressure of diatomic gas varies according to the relation $P=a{V}^2$, where a is constant. What is the molar heat capacity of the gas for this process?

• A. $\frac{6}{17}R$
• B. $\frac{17}{6}R$
• C. $\frac{13}{6}R$
• D. $\frac{7}{16}R$

Answer 1

Answer: (B)

$\frac{17}{6}R$

$P{V}^{-2}=\alpha$

Comparing with $P{V}^m$= constant, we get $m=-2$

Molar heat capacity $\left(C\right)=C_V+\frac{R}{1-m}$

For diatomic gas, $C_V=\frac{5R}{2}$

$\therefore C=\frac{5R}{2}+\frac{R}{1+2}=\frac{5R}{2}+\frac{R}{3}$

$\therefore C=\frac{17R}{6}$