Which of the following graphs between pressure 'p' versus volume 'V' represents the maximum work done?
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Answer
(1) [figure]
Solution
Magnitude of work done by the gas = area under the p–V curve; for a cyclic process = area enclosed by the cycle.
(1) Reversible isothermal expansion from 22.4 L, 2.0 bar to 44.8 L, 1.0 bar (pV = 44.8 L bar, constant):
|w| = 2.303 pV V2V1
|w| = 2.303 44.8 2
|w| 31.0 L bar
(2) Volume constant (isochoric): V = 0 w = 0
(3) Cycle: expansion along the isotherm (31.0 L bar), compression at 1.0 bar from 44.8 L to 22.4 L (22.4 L bar), then isochoric step (0)
net |w| = 31.0 - 22.4 = 8.6 L bar
(4) Cycle between the same two states along two different paths net work = small area enclosed between the two curves.
Maximum work is done in (1).
Answer: (1)