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The pressure p, volume V and temperature...

The 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 when the temperature changes from `T_(1)` to `T_(2)` while the pressure remains constant, is given by

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))`

Text Solution

Verified by Experts

The correct Answer is:
C
Work done, `W int_(V_1)^(V_2) dV = p(V_(2) - V_(1))`
According to the given relation,
`V_(1) = (AT_(1) - BT_(1)^(2))/(p),V_(2) = (AT_(2) - BT_(2)^(2))/(p)`
`:. 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))`.
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