1. Gas Cycles 2 nd Law of Thermodynamics

2. 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.

3. 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.

4. 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.

5. 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

6. 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).

7. 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.)