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

Options

A. `A(T_2-T_1)+B(T_2^2-T_1^2)`
B. `(A(T_2-T_1))/(v_2-v_1)-(B(T_2^2-T_1^2))/(v_2-v_1)`
C. `A(T_2-T_1)-B(T_2^2-T_1^2)`
D. `(A(T_2-t_2^2))/(v_2-v_1)`

Answer

C

Explanation

As `P = (AT - BT)^2/V rArr V =(AT-BT)^2/P`
Work done (W) = P DeltaV = P (V_2 - V_1)`
`rArr W = P [ (AT_2 - BT_2^2)/P - ((AT_1 - BT_1^2)/P)]`
` = A(T_2 - T_1) - B(T_2^2 - T_1^2)`.