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

Pressure P, volume V and temperature T of a certain material are relat

1.	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
Answer» `3alpha T_(0)^(2)` `5alpha T_(0)^(2)` `(2)/(3) alpha T_(0)^(2)` `7 alpha T_(0)^(2)` SOLUTION :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)`