Question

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

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

Answer 1

The correct option is C $2.5R$

Solution:- (C) $2.5R$

From the graph,

Volume is constant.

As we know that molar heat capacity of gas,

$C=\frac{dU}{dT}.....\left(1\right)$

As $U=fRT$

whereas $f$ is the degree of freedom

$\Rightarrow dU=C_{v}dT=\frac{5}{2}RdT(\because \text{the gas is diatomic})$

Now, from ${eq}^n\left(1\right)$, we have

$C=\frac{5RdT}{2dT}$

$\Rightarrow C=\frac{5}{2}R=2.5R$

Hence the molar heat capacity of the gas is $2.5R$.