JEE MAIN - Physics (2021 - 25th February Morning Shift - No. 25)
In a certain thermodynamical process, the pressure of a gas depends on its volume as kV3. The work done when the temperature changes from 100$$^\circ$$C to 300$$^\circ$$C will be ___________ nR, where n denotes number of moles of a gas.
Answer
50
Explanation
$$P = k{v^3}$$
$$ \Rightarrow $$ $$p{v^{ - 3}} = k$$
$$ \Rightarrow $$ $$x = - 3$$
$$w = {{nR({T_1} - {T_2})} \over {x - 1}}$$
$$ = {{nR(100 - 300)} \over { - 3 - 1}}$$
$$ = {{nR( - 200)} \over { - 4}}$$
$$ = 50$$ nR
$$ \Rightarrow $$ $$p{v^{ - 3}} = k$$
$$ \Rightarrow $$ $$x = - 3$$
$$w = {{nR({T_1} - {T_2})} \over {x - 1}}$$
$$ = {{nR(100 - 300)} \over { - 3 - 1}}$$
$$ = {{nR( - 200)} \over { - 4}}$$
$$ = 50$$ nR
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