One mole of an ideal gas at initial temperature T, undergoes a quasi-static process during which the volume V is doubled. During the process the internal energy U obeys the equation `U=aV(3)` where a is a constant. The work done during this process is-

Options

A. `(3R T)/(2)`
B. `(5R T)/(2)`
C. `(5R T)/(3)`
D. `(7R T)/(3)`

Answer

D

Explanation

`U=aV^3 implies (f nRT)/(2)=aV^3`
`P=CV^2 implies W=int_(V)^(2V) P d V = int_V^(2V) CV^2 dV=C/3(8V^3-V^3)=(7V^3C)/(3)`
`(f RT)/(2)=aV^3 implies PV=RT implies (fPV)/(2) = aV^3 implies P=(2a)/(f)V^2 implies C=(2a)/(f)`
`W=7/3 xx V^3 xx (2a)/(f) = (7)/(3f) f n R T = (7RT)/(3)`