Question

P-V diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process will be
(where $R$ is universal gas constant)

• A. $4R$
• B. $3R$
• C. $\frac{4}{3}R$
• D. $2.5R$

Answer 1

Answer: (B)

As $P-V$ diagram is a straight line passing through origin, therefore,
$P\propto V$ or $P{V}^{-1}=$ constant
In the process, $P{V}^x=$ constant, molar heat capacity is given by
$C=\frac{R}{\gamma -1}+\frac{R}{1-x}$
where $x=-1$ here and $\gamma =1.4$ for diatomic gas.
$\therefore C=\frac{R}{1.4-1}+\frac{R}{1-\left(-1\right)}=\frac{5}{2}R+\frac{R}{2}$
$C=3R$