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 the mass of gas, when the volume changes from $Vto2V$ 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

Answer: (C)

$\frac{PV}{\gamma -1}$

At constant pressure, change in internal energy$\Delta U=n{C}_v\Delta T$
Now,$\frac{C_p}{C_v}=\gamma$
$\Rightarrow 1$+$\frac{R}{C_v}$=$\gamma$
$\Rightarrow C_v=\frac{R}{\gamma -1}$
Using Charle's law, final temperature=2\times initial temperatue=2T
Thus, $\Delta U=n{C}_v(2T-T)=n{C}_{v}T=\frac{nRT}{\gamma -1}=\frac{PV}{\gamma -1}$