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

`p =(AT -BT^(2))/V` or `V=(AT - BT^(2))/p`
`therefore dV = (AdT - B xx 2TdT)/P`, since p is constant
or `pdv =(A-BT) dT`
`W = int_(T_(1))^(T_(2)) pdV = int_(T_(1))^(T_(2)) (A-2BT) dT rArr A(T_(2)-T_(1)) -B(T_(2)^(2)-T_(1)^(2))`