Question

$\gamma$ represents the ratio of the specific heats of a gas. For a given mass of the gas, the change in internal energy when the volume expands from V to 3V at constant pressure P is:

• A. $\frac{3PV}{\gamma -1}$
• B. $\frac{3PV}{\gamma +1}$
• C. $\frac{2PV}{\gamma +1}$
• D. $\frac{2PV}{\gamma -1}$

Answer 1

The correct option is D $\frac{2PV}{\gamma -1}$

$\Delta U=n{C}_V\Delta T\Delta U=n\frac{R}{\gamma -1}(T_2-T_1)\Delta U=\frac{nR{T}_2-nR{T}_1}{\gamma -1}\Delta U=\frac{P{V}_2-P{V}_1}{\gamma -1}\Delta U=\frac{P\times 3V-P\times V}{\gamma -1}=\frac{2PV}{\gamma -1}$