Question

The change in internal energy of a given mass of gas, when its volume changes from $V$ to $2V$ at constant pressure $p$ is( $ \frac{{{C}_{P}}}{{{C}_{V}}}=\gamma , $ universal gas constant =R)

• A. $ \frac{pV}{\gamma } $
• B. $ \frac{pV}{(2\gamma -1)} $
• C. $ \frac{pV}{2(\gamma -1)} $
• D. $ \frac{R}{(\gamma -1)} $
• E. $ \frac{pV}{(\gamma -1)} $

Answer 1

Answer: (E)

In case of gases whatever be the process
$ \Delta U=n{{C}_{V}}\Delta T $ or $ \Delta U=n\Delta T\left( \frac{R}{\gamma -1} \right) $ .. (i)
$ pV=nR{{T}_{1}} $
$ 2pV=nR{{T}_{2}} $
$ \Rightarrow $ $ pV=nR({{T}_{2}}-{{T}_{1}}) $
$ \frac{pV}{R}=n\Delta T $
$ [{{T}_{2}}-{{T}_{1}}=\Delta T] $
Substituting in Eq. (i) $ \Delta U=\frac{pV}{(\gamma -1)} $