4:2 One gmol of a monatomic gas performs a Carnot cycle between the temperatures 400 K and 300 K. On the upper isothermal transformation, the initial
volume is 1 L and the final volume 5 L. Find the work performed during a
cycle, and the amounts of heat exchanged with the two heat reservoirs.
1338 J; 5352 J; 4014 J
4:3 Assuming a heat source at (400 + e) K and a heat sink at (300 − e) K, where e
is an infinitesimally small number, being available for the operation of the
above Carnot engine in Problem 2, what are the “entropy flows,” Q*, during a
cycle into and out of the Carnot engine? Explain why they are equal in value.
13:38 J=K
4:4 What is the maximum efficiency of a heat engine operating between an upper
temperature of 400 °C and a lower temperature of 18 °C?
0:5675
4:5 Find the minimum amount of work needed to extract 4000 J of heat from a
body at the temperature of 0 °F, when the temperature of the environment is
100 °F.
870:19 J
4:6 Steam occupies one part of a partitioned insulated chamber of volume V 1 . The
initial pressure and temperature of the steam are 0.3 MPa and 350 °C. The
other part of the chamber contains a vacuum of volume V 2 (=2 V 1 ). The
partition is removed, and the steam disperses and fills the entire volume at the
end of the process. Determine the final temperature and pressure of the steam.
348:26
C; 100:08 kPa
References
1. Carnot S (1824) Reflections on the Motive Power of Fire. [Reprinted from Reflections on the
Motive Power of Fire and Other Papers, edited by E. Mendoza. Dover Publications, New
York (1960)]
2. Kuhn TS (1955) Carnot’s version of Carnot’s cycle. Am J Phys 23:91–95 (p. 94)
3. Jaynes ET (1984) The evolution of Carnot’s principle. EMBO Workshop on
Maximum-Entropy Methods (Orsay, France, April 24–28, 1984. Reprinted in Ercksen &
Smith [1988], 1:267–282)
4. Thomson W (Lord Kelvin) (1911) Mathematical and Physical Papers of William Thomson
1:1–571. Cambridge Univ Press
5. Fermi E (1956) Thermodynamics. Dover (p. 48)
4.8 Does the Heat-as-Energy Ontology …
89
volume is 1 L and the final volume 5 L. Find the work performed during a
cycle, and the amounts of heat exchanged with the two heat reservoirs.
1338 J; 5352 J; 4014 J
4:3 Assuming a heat source at (400 + e) K and a heat sink at (300 − e) K, where e
is an infinitesimally small number, being available for the operation of the
above Carnot engine in Problem 2, what are the “entropy flows,” Q*, during a
cycle into and out of the Carnot engine? Explain why they are equal in value.
13:38 J=K
4:4 What is the maximum efficiency of a heat engine operating between an upper
temperature of 400 °C and a lower temperature of 18 °C?
0:5675
4:5 Find the minimum amount of work needed to extract 4000 J of heat from a
body at the temperature of 0 °F, when the temperature of the environment is
100 °F.
870:19 J
4:6 Steam occupies one part of a partitioned insulated chamber of volume V 1 . The
initial pressure and temperature of the steam are 0.3 MPa and 350 °C. The
other part of the chamber contains a vacuum of volume V 2 (=2 V 1 ). The
partition is removed, and the steam disperses and fills the entire volume at the
end of the process. Determine the final temperature and pressure of the steam.
348:26
C; 100:08 kPa
References
1. Carnot S (1824) Reflections on the Motive Power of Fire. [Reprinted from Reflections on the
Motive Power of Fire and Other Papers, edited by E. Mendoza. Dover Publications, New
York (1960)]
2. Kuhn TS (1955) Carnot’s version of Carnot’s cycle. Am J Phys 23:91–95 (p. 94)
3. Jaynes ET (1984) The evolution of Carnot’s principle. EMBO Workshop on
Maximum-Entropy Methods (Orsay, France, April 24–28, 1984. Reprinted in Ercksen &
Smith [1988], 1:267–282)
4. Thomson W (Lord Kelvin) (1911) Mathematical and Physical Papers of William Thomson
1:1–571. Cambridge Univ Press
5. Fermi E (1956) Thermodynamics. Dover (p. 48)
4.8 Does the Heat-as-Energy Ontology …
89