If the ratio of specific heat of a gas of constant pressure to that at constant volume is `gamma`, the change in internal energy of the 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 p V)/(gamma-1)`

Answer

C

Explanation

`Delta U = nC_(V) Delta T`
Also, `(C_p)/(C_v) = gamma`, hence, `(C_p-C_v)/(C_v)= gamma-1`
This is `C_(v) = R//(gamma-1)`. This gives
`Delta U = (nR)/(gamma-1)Delta T = (pDelta V)/(gamma-1) = (p(2V-V))/(gamma-1) = (pV)/(gamma-1)`.