Question

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma$, the change in internal energy of a mass of gas, when the volume changes from $V$ to $2V$ at constant pressure $P$, is :-

• A. $\frac{R}{(\gamma -1)}$
• B. $PV$
• C. $\frac{PV}{(\gamma -1)}$
• D. $\frac{\gamma PV}{(\gamma -1)}$

Answer 1

The correct option is C $\frac{PV}{(\gamma -1)}$

Let $\Delta U$ be the chane in internal energy and $n$ be the number of moles.
From formula,
$\Delta U=n{C}_v\Delta T=n\left(\frac{R}{\gamma -1}\right)\Delta T$
$\Rightarrow \Delta U=\frac{nR\Delta T}{\gamma -1}=\frac{P(2V-V)}{\gamma -1}$
$\Rightarrow \Delta U=\frac{PV}{\gamma -1}$
Hence, option $\left(c\right)$ is the correct answer.