Carnot Engine and Entropy Worksheet 2
1.
The pV-diagram above represents the states of an ideal gas during one cycle of
operation of a reversible heat engine. The cycle consists of the following four
processes.
Process
Nature of Process
AB
BC
CD
DA
Constant temperature (Th = 500 K)
Adiabatic
Constant temperature (Tc = 20O K)
Adiabatic
During process A B, the volume of the gas increases from Vo to 2V0 and the gas
absorbs 1,000joules of heat.
(a) The pressure at A is p0. Determine the pressure at B
(b) Using the first law of thermodynamics, determine the work performed by or on the
gas during the process AB.
(c) During the process AB, does the entropy of the gas increase, decrease, or remain
unchanged? Justify your answer.
(d) Calculate the heal Qc given off by the gas in the process CD.
(e) During the full cycle ABCDA, is the total work the gas performs on its surroundings
positive, negative, or zero? Justify your answer.
2.
Four samples of ideal gas are each initially at a pressure P0, a volume V0, and a
temperature T0 as shown on the diagram above. The samples are taken in separate
experiments from this initial state to the final scares I, II, III, and IV along the processes
shown on the diagram.
a) One of the processes is isothermal. Identify this one and explain.
b) One of the processes is adiabatic. Identify this one and explain.
c) In which process or processes does the gas do work? Explain.
d) In which process or processes is heat removed from the gas? Explain.
e) In which process or processes does the root-mean-square speed of the gas
molecules increase? Explain.
3.
A cylinder with a movable frictionless piston contains an ideal gas that is initially in state
1 at 1 x 105 Pa, 373 K, and 0.25 m3. The gas is taken through a reversible
thermodynamic cycle as shown in the PV diagram above.
a) Calculate the temperature of the gas when it is in state 2.
b) Calculate the temperature of the gas when it is in state 3.
c) Calculate the net work done on the gas during the cycle.
d) Was heat added to or removed from the gas during the cycle? Justify your answer.