Question

$P-V$ diagram of a diatomic gas is a straight line passing through origin. What is the molar heat capacity of the gas during the process?

• A. $R$
• B. $2R$
• C. $3.33R$
• D. $3R$

Answer 1

The correct option is D $3R$

Given that,
$P-V$ diagram is a straight passing through the origin.
Hence, $P\propto V$
$\Rightarrow P{V}^{-1}=$ constant
Comparing the above equation with $P{V}^x=$ constant
we get, $x=-1$

Molar specific heat capacity of a gas during a polytropic process is given by
$C=\frac{R}{\gamma -1}+\frac{R}{1-x}$
Given gas is diatomic in nature, thus the value of adiabatic exponent $\gamma =1.4$
$\therefore$ From the given data we get, $C=\frac{R}{1.4-1}+\frac{R}{1+1}$
$\Rightarrow C=\frac{10R}{4}+\frac{R}{2}=\frac{5R}{2}+\frac{R}{2}=3R$
Thus, option (d) is the correct answer.