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One mole of an ideal gas at initial temp...

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-

A

`(3R T)/(2)`

B

`(5R T)/(2)`

C

`(5R T)/(3)`

D

`(7R T)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`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)`
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