The temperature of n moles of an ideal gas is increased from T to 4T through a process for which pressure `PaT^(-1)` where a is a constant .Then the work done by the gas is

Options

A. nRT
B. 4nRT
C. 2nRT
D. 6nRT

Answer

D

Explanation

According to an ideal gas equation
PV=nRT or `V=(nRT)/(P)`
`P=(a)/(T)` (Given)
`V=(nRT^(2))/(a)`
`rArr` dV =`(2naRT)/(a)dT`
work done by the gas , dW=PdV
or `W=overset(4T)underset(T)int(a)/(t)(2nRT)/(a)dT`
`=[(2nRT)]_(T)^(4T)=6nRT`