That the first error is not crucial in treating the problem of adiabatic heating is
shown in Sect. 6.6 by the demonstration that the treatment of dQ in Eqs. (12), (13),
and (15) is valid does not require that heat content Q itself is a state function. The
argument that the materiality of caloric as treated by Carnot is not a crucial requirement of Carnot’s theory is the main discovery of this disquisition: In the first place, it
will be noted that the caloric theory is a one-place relation theory dealing with heat
and its exchange. And, it will be argued that whereas caloric theory is a one-place
relation theory, Carnot’s theory is fundamentally different kind of relational theory
and, instead of being committed to a rigid ontology of heat doctrine, it has in fact
flexibility for adopting either the caloric theory’s or a rival theory’s ontology of heat.
Problems
2:1 A calorimeter contains 2000 g of water at 20 °C. A 500 g block of copper
heated to 90 °C is added to be submerged in the water. What is the final
temperature of the mixture?
2:2 We have one 3 kg block of ice at −40 °C. Determine how much heat has to
be added to bring the block of ice all the way to superheated steam vapor at
160 °C under the constant pressure of 1 atm. Note: Specific heat of ice is
0.499 cal/gK; latent heat of fusion for water is 79.56 cal/gm K; latent heat of
vaporization is 539.96 cal/gK; and specific heat of water vapor is
0.48 cal/gK. Make a temperature versus heat-input plot for the process.
2:3 The speed of sound in non-humid air at 20 °C is 343 m/s. Given Eq. (12), can the
speed of sound be changed by adjusting the speaker’s frequency or the speaker’s
amplitude? What will be the speed of sound in a non-humid air at 30 °C?
References
1. Lienhard JH (1983). Notes on the origins and evolution of the subject of heat transfer.
Mechanical Engineering June 1983:20–27
2. Lavoisier AL, Laplace PS (1783) Memoir on Heat (Reprint of translated version in Obesity
Research 2(No. 2), March 1994:189–202)
3. Psillos S (1994) A philosophical study of the transition from the caloric theory of heat to
thermodynamics: Resisting the pessimistic meta-induction. Stud Hist Phil Sci 25(No. 2):159–190
4. Truesdell C (1980) The Tragicomical History of Thermodynamics: 1822–1854. Springer, New
York
5. Maxwell JC (1888) Theory of Heat. Dover, 2001 (p. 73)
6. Kuhn TS (1958) The caloric theory of adiabatic compression. Isis 49(No.2):132–140
7. Mendoza E (1961) A sketch for a history of early thermodynamics. Physics Today 14
(No. 2):32–42
8. Fox R (1971) The Caloric Theory of Gases. Oxford Univ. Press
36
2 Calorimetry and the Caloric Theory of Heat …
shown in Sect. 6.6 by the demonstration that the treatment of dQ in Eqs. (12), (13),
and (15) is valid does not require that heat content Q itself is a state function. The
argument that the materiality of caloric as treated by Carnot is not a crucial requirement of Carnot’s theory is the main discovery of this disquisition: In the first place, it
will be noted that the caloric theory is a one-place relation theory dealing with heat
and its exchange. And, it will be argued that whereas caloric theory is a one-place
relation theory, Carnot’s theory is fundamentally different kind of relational theory
and, instead of being committed to a rigid ontology of heat doctrine, it has in fact
flexibility for adopting either the caloric theory’s or a rival theory’s ontology of heat.
Problems
2:1 A calorimeter contains 2000 g of water at 20 °C. A 500 g block of copper
heated to 90 °C is added to be submerged in the water. What is the final
temperature of the mixture?
2:2 We have one 3 kg block of ice at −40 °C. Determine how much heat has to
be added to bring the block of ice all the way to superheated steam vapor at
160 °C under the constant pressure of 1 atm. Note: Specific heat of ice is
0.499 cal/gK; latent heat of fusion for water is 79.56 cal/gm K; latent heat of
vaporization is 539.96 cal/gK; and specific heat of water vapor is
0.48 cal/gK. Make a temperature versus heat-input plot for the process.
2:3 The speed of sound in non-humid air at 20 °C is 343 m/s. Given Eq. (12), can the
speed of sound be changed by adjusting the speaker’s frequency or the speaker’s
amplitude? What will be the speed of sound in a non-humid air at 30 °C?
References
1. Lienhard JH (1983). Notes on the origins and evolution of the subject of heat transfer.
Mechanical Engineering June 1983:20–27
2. Lavoisier AL, Laplace PS (1783) Memoir on Heat (Reprint of translated version in Obesity
Research 2(No. 2), March 1994:189–202)
3. Psillos S (1994) A philosophical study of the transition from the caloric theory of heat to
thermodynamics: Resisting the pessimistic meta-induction. Stud Hist Phil Sci 25(No. 2):159–190
4. Truesdell C (1980) The Tragicomical History of Thermodynamics: 1822–1854. Springer, New
York
5. Maxwell JC (1888) Theory of Heat. Dover, 2001 (p. 73)
6. Kuhn TS (1958) The caloric theory of adiabatic compression. Isis 49(No.2):132–140
7. Mendoza E (1961) A sketch for a history of early thermodynamics. Physics Today 14
(No. 2):32–42
8. Fox R (1971) The Caloric Theory of Gases. Oxford Univ. Press
36
2 Calorimetry and the Caloric Theory of Heat …