expansion to double the initial volume. The near balance of net force on the
piston results in slow expansion of gas along the same quasi-static path of
Problem 6.2. (Note that the process in the present case is reversible due to the
balanced net force and the slowness of expansion and heat extraction from the
bath.)
(3a) What is the ratio of the initial and final pressures? What is the ratio of the
initial and final temperatures? What is the difference between the initial and
final system entropies?
(3b) What is the useful work stored away in the work storage?
(3c) What is the heat extracted from the bath by the expanding gas? Is the heat
completely transformed into work?
(3d) What is the total entropy change of the composite system and the bath?
(3e) This process has exactly the same path as that of Problem 6.2. Explain
why the two processes are fundamentally different while they share the same
path.
References
1. Uffink J (2001) Bluff your way in the Second Law of Thermodynamics. Stud Hist Phil Sci
Part B: 2001 Studies in Hist and Philo of Modern Physics 32(No. 2): 305–395.
2. Born M (1949) Natural Philosophy of Cause and Chance. Oxford Univ Press (p. 38).
3. Carathéodory C (1909) Untersuchungen uber die Grundlagen der Thermodynamik. Math.
Ann. 67: 355–386. A translated text “Investigation into the foundations of thermodynamics”
is collected in J. Kestin, The Second Law of Thermodynamics (Dowden, Hutchinson and
Ross, 1976). Pages referred to this reference in-text are that of the translated text.
4. Wang LS (2006) The auxiliary components of thermodynamic theory and their non-empirical,
algorithmic nature. Physics Essays 19(2):174–199.
5. Callen HB (1st edition, 1960; 2nd edition, 1985) Thermodynamics and an Introduction to
Thermostatistics. Wiley, New York.
6. Plank M (1932) Theory of Heat, Volume V of Introduction to Theoretical Physics.
Macmillan, London. In which on p. 51, Planck wrote, “the content of the second law is not
exhausted if—as was done occasionally by Clausius and later with renewed emphasis by
Ostwald—every process in nature is resolved into a series of energy transformations [i.e., a
series of steps in a quasi-static process].”
7. Landsberg PT (1961) Thermodynamics. Interscience, New York (p. 94).
8. Samiullah M (2007) What is a reversible process? Am J Physics 75: 609.
9. Planck M (1969) Treatise on Thermodynamics, 3rd edition. Dover, New York.
10. Gibbs JW (1961) The Scientific Papers: Thermodynamics. Vol. 1. Dover
11. Prigogine I (1949) Le domaine de validité de la thermodynamique des phénomènes
irréversibles. Physica 15: 272.
12. Planck M (1887) Uber das Princip der Vermehrung der Entropie, in 3 parts. Ann. D. Phys.
30:562–582; 31:189–203; 32:462–503.
13. De Groot SR, Mazur P (1969) Non-Equilibrium Thermodynamics. North Holland,
Amsterdam.
14. Butler HW (2007) Tracing the second law. Mechanical Engineering, ASME, July 2007.
(pp. 38–40).
6.7 Conclusion: Nature as It Is and It Can Become
155
piston results in slow expansion of gas along the same quasi-static path of
Problem 6.2. (Note that the process in the present case is reversible due to the
balanced net force and the slowness of expansion and heat extraction from the
bath.)
(3a) What is the ratio of the initial and final pressures? What is the ratio of the
initial and final temperatures? What is the difference between the initial and
final system entropies?
(3b) What is the useful work stored away in the work storage?
(3c) What is the heat extracted from the bath by the expanding gas? Is the heat
completely transformed into work?
(3d) What is the total entropy change of the composite system and the bath?
(3e) This process has exactly the same path as that of Problem 6.2. Explain
why the two processes are fundamentally different while they share the same
path.
References
1. Uffink J (2001) Bluff your way in the Second Law of Thermodynamics. Stud Hist Phil Sci
Part B: 2001 Studies in Hist and Philo of Modern Physics 32(No. 2): 305–395.
2. Born M (1949) Natural Philosophy of Cause and Chance. Oxford Univ Press (p. 38).
3. Carathéodory C (1909) Untersuchungen uber die Grundlagen der Thermodynamik. Math.
Ann. 67: 355–386. A translated text “Investigation into the foundations of thermodynamics”
is collected in J. Kestin, The Second Law of Thermodynamics (Dowden, Hutchinson and
Ross, 1976). Pages referred to this reference in-text are that of the translated text.
4. Wang LS (2006) The auxiliary components of thermodynamic theory and their non-empirical,
algorithmic nature. Physics Essays 19(2):174–199.
5. Callen HB (1st edition, 1960; 2nd edition, 1985) Thermodynamics and an Introduction to
Thermostatistics. Wiley, New York.
6. Plank M (1932) Theory of Heat, Volume V of Introduction to Theoretical Physics.
Macmillan, London. In which on p. 51, Planck wrote, “the content of the second law is not
exhausted if—as was done occasionally by Clausius and later with renewed emphasis by
Ostwald—every process in nature is resolved into a series of energy transformations [i.e., a
series of steps in a quasi-static process].”
7. Landsberg PT (1961) Thermodynamics. Interscience, New York (p. 94).
8. Samiullah M (2007) What is a reversible process? Am J Physics 75: 609.
9. Planck M (1969) Treatise on Thermodynamics, 3rd edition. Dover, New York.
10. Gibbs JW (1961) The Scientific Papers: Thermodynamics. Vol. 1. Dover
11. Prigogine I (1949) Le domaine de validité de la thermodynamique des phénomènes
irréversibles. Physica 15: 272.
12. Planck M (1887) Uber das Princip der Vermehrung der Entropie, in 3 parts. Ann. D. Phys.
30:562–582; 31:189–203; 32:462–503.
13. De Groot SR, Mazur P (1969) Non-Equilibrium Thermodynamics. North Holland,
Amsterdam.
14. Butler HW (2007) Tracing the second law. Mechanical Engineering, ASME, July 2007.
(pp. 38–40).
6.7 Conclusion: Nature as It Is and It Can Become
155