`gamma` represents the ratio of two 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 to constant pressure P is

Options

A. `(3PV)/((gamma - 1))`
B. `(3PV)/((gamma + 1))`
C. `(2PV)/((gamma + 1))`
D. `(2PV)/((gamma - 1))`

Answer

D

Explanation

The change in internal energy is `DeltaU = nC_(V)Delta T`
But `C_(V) = (R )/((gamma - 1)) :. Delta U = (nR Delta T)/((gamma - 1))`
According to the ideal gas equation, PV = nRT
At constant pressure, `Pdelta V = nR Delta T`
`:. Delta U = (PDelta V)/((gamma - 1)) = (P(3V - V))/((gamma- 1)) = (2PV)/((gamma - 1))`