Gas Cycles2nd Law of Thermodynamics

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.

• DU = 0 for a complete cycle.• The environment, however, has been

changed.

Work done by cycle

P

V

P2

V1

A

V2

B

P1C D

Work done by the gas is equal to the area circumscribed by the cycle.

WABCD

Work done by gas is positive for

clockwise cycles, negative for

counterclockwise cycles.

Work done by environment is

negative of work done by gas.

Sample Problem• Consider the cycle ABCDA, where– State A: 200 kPa, 1.0 m3

– State B: 200 kPa, 1.5 m3

– State C: 100 kPa, 1.5 m3

– State D: 100 kPa, 1.0 m3

• 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.

A: 200 kPa, 1.0 m3 B: 200 kPa, 1.5 m3

C: 100 kPa, 1.5 m3 D: 100 kPa, 1.0 m3

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).

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.)