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-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_1^3)`
D. `A(T_2-T_1)^2=B/3(T_2-T_1)^3`

Answer

B

Explanation

Here `P=(AT-BT)^2/V`
`or PV=AT-BT^2`
Since Pis a constant
`:. PdV=(A-2BT)dT`…(i)
Work done = Pdv
`:. W = int_(T_1)^(T_2)(A-2BT)dT`
`=[AT-BT^2]_(T_1)^(T_2)" "("Using(i)")`
`=A(T_2-T_2)-B(T_1^2-T_1^2)`.