First slide

Work done by gas

Question

P-T curve of a cyclic process is shown. If number of moles of the gas are n, the work done by the gas in the given process is

Moderate

A

$nR (T_{1} + T_{3} - T_{4} + T_{2})$
B

$nR (T_{1} - T_{3} - T_{4} + T_{2})$
C

$nR (T_{1} + T_{3} + T_{4} - T_{2})$
D

$nR (T_{1} + T_{3} - T_{4} - T_{2})$

Solution

Since paths AB and CD are isochoric, therefore work done during AB and CD is zero. Paths BC and DA are isobaric.
Hence $W_{BC} = nR ∆ T = nR (T_{3} - T_{2})$
$W_{DA} = nR (T_{1} - T_{4})$
Total work done = $W_{BC} + W_{DA} = nR (T_{1} + T_{3} - T_{4} - T_{2})$

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