The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is universal gas constant =R)

Options

A. `(pV)/q`
B. `(pv)/((2gamma-1))`
C. `(pV)/(2(gamma-1))`
D. `(pV)/((gamma-1))`

Answer

D

Explanation

In case of gases whatever be the process
`Delta U=nC_vDelta T `
or `Delta U=n Delta T(R/(gamma-1))`
`pV=nR_1`
`2pV=nRT_2`
`implies pV=nR(T_2-T_1)`
`(pV)/R=n Delta T [T_2-T_=Delta T]`
Substituting in Eq. (i)
`Delta U= (pV)/((gamma-1))`