Question

If the ratio of sp.heat of a gas at constant pressure to that at constant volume is $\gamma$ , the change in internal energy 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

Answer: (C)

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

The change in internal energy in the process should have been,
U = $n{C}_v\Delta T$
Now, for this process, if $\frac{C_p}{C_v}=\gamma$ and $C_p-C_v=R$
Then, $C_v=\frac{R}{\gamma -1}$
U = $\frac{nR\Delta T}{\gamma -1}$
Now, $nR\Delta T=P(2V-V)$
Thus, U = $\frac{PV}{\gamma -1}$