The temperature of n moles of an ideal gas is increased from T to 4T through a process for which pressure `P = aT^(-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 ideal gas equation,
`PV = nRT` or `V = (nRT)/(P) :. P = (a)/(T)` (Given) …(i)
`:. V = (nRT^(2))/(a)`
or `dV = (2nRT)/(a) dT` …(ii)
Work done by the gas, dW = PdW or `W = underset(T)overset(4T)int (a)/(T) (2nRT)/(a) dT = [2nRT]_(T)^(4T) = 6nRT` (Using (i) and (ii))