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

Options

A. `6alphaT_(0)^(3)`
B. `(3)/(2)alphaT_(0)^(3)`
C. `2alphaT_(0)^(2)`
D. `3alphaT_(0)^(2)`

Answer

D

Explanation

`PV =propT^(2)`
`PdV=2propTdT`
`W=intPdV = int_(T_(0))^(2T_(0)) 2propTdT = 2prop((T^(2))/(2))_(T_(0))^(2T_(0))`
`= 3 prop T_(0)^(2)`