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 PV)/(gamma -1)`

Answer

C

Explanation

Change in internal energy is equal to work done in adiabatic system
`DeltaW =-DeltaU` (Expansion in the system)
`=-1/(gamma -1) (P_(1)V_(1)-P_(2)V_(2))`
`DeltaU* =1/(1- gamma) (P_(2)V_(2)-P_(1)V_(1))`
Here, `V_(1)=V, V_(2) = 2V`
`therefore DeltaU =1/(1-gamma) [P xx 2V - PV] = (PV)/(1- gamma) rArr DeltaU =-(PV)/(gamma-1)`