Question

The pressure $P$ of an ideal diatomic gas varies with its absolute temperature $T$ as shown in the figure. The molar heat capacity of the gas during this process is:
[$R$ is the gas constant]

• A. $1.7R$
• B. $3.25R$
• C. $2.5R$
• D. $4.2R$

Answer 1

The correct option is C $2.5R$

From the given graph, we can deduce that $P\propto T$
Also for an ideal gas, we know that $PV=nRT$
or $P=\left(\frac{nR}{V}\right)T$

Since $P-T$ graph is a straight line passsing through the origin, we can say that the volume remains constant i.e the process is isochoric.
Molar heat capacity at constant volume is given by $C_V=\frac{fR}{2}$
For a diatomic molecule, number of degrees of freedom $\left(f\right)=5$
$\Rightarrow C_V=\frac{5R}{2}$
Thus, option (c) is the correct answer.