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)(R_(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))-(B)/(3)(T_(2)-T_(1))^(3)`

Answer

B

Explanation

Here P`=(AT-BT^(2))/(V)`
or `PV=AT-BT^(2)`
since P is a constant
PdV =(a-2BT)dT
Work done =PdV
`W=overset(T_(2))underset(T_(1))int(A-2BT)dT=[(AT-BT^(2))]_(t_(1))T(T_(2))` ltrbgt `=A(T_(2)-T_(1))-B(T_(2)^(2)-T_(1)^(2))`