Pressure P, voluume V and temperature T for a certain gas are related by P = (AT - BT^(2))/(V) where A and B are constant. The work done by the gas as its temperature change from T_(1) to T_(2) with pressure remaining constant is

Pressure P, voluume V and temperature T for a certain gas are related

1.	Pressure P, voluume V and temperature T for a certain gas are related by P = (AT - BT^(2))/(V) where A and B are constant. The work done by the gas as its temperature change from T_(1) to T_(2) with pressure remaining constant is
Answer» `A - (B)/(2)(T_(2) - T_(1))` `A (T_(2) - T_(1)) - B(T_(2)^(2) - T_(1)^(2))` `(A)/(2)(T_(2)^(2) - T_(1)^(2))- (B)/(3)(T_(2)^(3) - T_(3)^(3))` `A(T_(2) - T_(1))^(2) - (B)/(3)(T_(2) - T_(1))^(3)` Solution :`P = (AT - BT^(2))/(V)` or `PV = AT - BT^(2)` Since P is a constant `:. PdV = (A-2BT)DT` As `dW = PdV = (A-2BT)dT :. W = underset(T_(1))overset(T_(2))int (A-2Bt)dT` `= [At - BT^(2)]_(T_(1))^(T_(2)) = A(T_(2) - T_(1)) - B(T_(2)^(2) - T_(1)^(2))`