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Gas Cycles 2 nd Law of Thermodynamics
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Work done by a cycle When a gas undergoes a complete cycle, it starts and ends in the same state. The gas is identical before and after the cycle, so there is no identifiable change in the gas. U = 0 for a complete cycle. The environment, however, has been changed.
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Work done by cycle P V P2P2 V1V1 A V2V2 B P1P1 C D Work done by the gas is equal to the area circumscribed by the cycle. W ABCD Work done by gas is positive for clockwise cycles, negative for counterclockwise cycles. Work done by environment is negative of work done by gas.
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Sample Problem Consider the cycle ABCDA, where – State A: 200 kPa, 1.0 m 3 – State B: 200 kPa, 1.5 m 3 – State C: 100 kPa, 1.5 m 3 – State D: 100 kPa, 1.0 m 3 A) Sketch the cycle. B) Graphically estimate the work done by the gas in one cycle. C) Estimate the work done by the environment in one cycle.
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A: 200 kPa, 1.0 m 3 B: 200 kPa, 1.5 m 3 C: 100 kPa, 1.5 m 3 D: 100 kPa, 1.0 m 3
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Problem Calculate the heat necessary to change the temperature of one mole of an ideal gas from 300K to 500K A) at constant volume. B) at constant pressure (assume 1 atmosphere).
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Second Law of Thermodynamics No process is possible whose sole result is the complete conversion of heat from a hot reservoir into mechanical work. (Kelvin-Planck statement.) No process is possible whose sole result is the transfer of heat from a cooler to a hotter body. (Clausius statement.)
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