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

Options

A. `A - (B)/(2)(T_(2) - T_(1))`
B. `A (T_(2) - T_(1)) - B(T_(2)^(2) - T_(1)^(2))`
C. `(A)/(2)(T_(2)^(2) - T_(1)^(2))- (B)/(3)(T_(2)^(3) - T_(3)^(3))`
D. `A(T_(2) - T_(1))^(2) - (B)/(3)(T_(2) - T_(1))^(3)`

Answer

B

Explanation

`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))`