Q. An ideal gas is taken around the cycle ABCA as shown in P-V diagram. What is the net work done by the gas during the cycle?
12 P1V1
6 P1V1
5P1V1
P1V1
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Net work done by the gas during the cycle is 5 P₁V₁
- We know that total work done in the process is equals to the work done in the process AB + work done in the process BC + work done in the process CA
Work done in the process AB is isochoric, so ΔV = 0, W = 0
Work done in the process BC is
W BC = - P ext (V₂-V₁)
From the graph it is very clear that P shows linear variation.
P avg BC = 1/2 × (6 P₁+P₁) = 7 P₁/2
W BC = - 7 P₁/2 (3 V₁- V₁) = - 7 P₁V₁
Work done in process CA is isobaric process.
So,
W = -Pext (V₂-V₁)
W CA = -P₁ (V₁-3V₁) = 2 P₁V₁
Now work done in process ABCA is
W ABCA = -7 P₁V₁ + 2 P₁V₁
W ABCA = -5 P₁V₁
Negative sign indicates work is done by the gas.
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