Question

If the ratio of specific heat of an ideal gas at constant pressure to that at constant volume is $\gamma$, the change in internal energy of the given 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

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

The change in internal energy is given by
$\Delta U=n{C}_V\Delta T$

$[C_V=\frac{R}{\gamma -1}]$

$\Rightarrow \Delta U=n\frac{R}{(\gamma -1)}\Delta T$

Using ideal gas equation, $PV=nRT$
For constant pressure $P\Delta V=nR\Delta T$

$\Rightarrow \Delta U=\frac{P\Delta V}{\gamma -1}=\frac{P(2V-V)}{(\gamma -1)}$

$\Delta U=\frac{PV}{(\gamma -1)}$