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 a mass of gas when the volume changes from V to 2V at constant pressure p is

Options

A. `R // (gamma - 1)`
B. `pV`
C. `pV // (gamma - 1)`
D. `gamma pV // (gamma - 1)`

Answer

C

Explanation

c. `Delta U = n C_(v) Delta T`
Also, `(C_(P))/(C_(v)) = gamma`
Hence `(C_(P) - C_(V))/(C_(v)) = gamma`
`implies C_(V) = R//(gamma - 1)`
`Delta U = (nR)/(gamma - 1) Delta T = (p Delta V)/(gamma - 1) = (p(2 V - V))/(gamma - 1) = (pV)/(gamma - 1)`