In the following P-V diagram the equation of state along the curved path is (V-2)²=4aP, where a is a constant. The total work done in the closed path is

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(1) -1/(3a). Along the curve P=((V-2)²)/(4a). The curve runs from V=1 to V=3, where P=1/(4a) at both ends, and the loop is closed by the horizontal line back at that pressure. Area under the curve: ∫₁³((V-2)²)/(4a) dV=[((V-2)³)/(12a)]₁³=1/(6a). Area under the straight leg: 1/(4a)×2=1/(2a). Enclosed area =1/(2a)-1/(6a)=1/(3a), and the loop is traversed so that the work is negative: W=-1/(3a).

In the following P-V diagram the equation of state along the curved path is (V-2)²=4aP, where a is a constant. The total work done in the closed path is

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