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Pressure P, volume V and temperature T f...

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

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
For a certain gas,
pressure , `p = (AT - BT^(2))/V " or , " V = (AT - BT^(2))/p ` ...(i)
Work done by the gas at constant pressure ,
` W = p Delta V = p(V_(2) - V_(1))`
` = p [((AT_(2) - BT_(2)^(2))/p) - ((AT_(1) - BT_(1)^(2))/p) ] ` [Using eqn (i) ]
` A (T_(2) - T_(1)) - B (T_(2)^(2) - T_(1)^(2))`
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