Pressure P, volume V and temperature T of a certain material are related by `P = alpha T^(2)//V` where `alpha` is contant. Work done by the material when temperature changes from `T_(0)` to `2T_(0)` and pressure remains constant is

Options

A. `3alpha T_(0)^(2)`
B. `5alpha T_(0)^(2)`
C. `(2)/(3) alpha T_(0)^(2)`
D. `7 alpha T_(0)^(2)`

Answer

A

Explanation

The given relation is `P = (alpha T^(2))/(V) :. V = (alpha T^(2))/(P)`
As pressure is kept constant, so `dV = ((2 alpha T)/(P)) dT`
`:. W = int PdV = underset(T_(0))overset(2T_(0))int P ((2 alpha T)/(P)) dT = 2 alpha[(T^(2))/(2)]_(T_(0))^(2T_(0)) = 3 alpha T_(0)^(2)`