Miscellaneous Problems in Specific Heats

• E. S. R. Gopal
Part of the The International Cryogenics Monograph Series book series (INCMS)

Abstract

In the previous chapters, various aspects of specific heats of solids, liquids, and gases have been discussed. It is a common experience to find that two phases can coexist over a range of pressure and temperature. Consider, for instance, water and its vapor contained in a vessel of volume V. If the temperature is raised slightly, a small quantity of water is converted into steam, absorbing latent heat in the process, and a new equilibrium pressure is established. In a P-T plane (Fig. 8.1), this will be represented as an equilibrium curve. Quantities such as the density, specific heat, and compressibility remain finite but different in the two phases. An interesting relation among the thermodynamic quantities at such an equilibrium curve is furnished by the Clausius-Clapeyron equation. To derive this, apply Maxwell’s relation (∂P/∂T) υ = (∂S/∂V) T [equation (1.11)] to the system. The latent heat L12 is equal to T dS at the phase boundary, and so
$$\frac{{DP}}{{DT}} = \frac{{{S_2} - {S_1}}}{{{V_2} - {V_1}}} = \frac{{{L_{12}}}}{{T({V_2} - {V_1})}}$$
(8.1)
where D/DT stands for the derivative along the equilibrium curve. This simple equation, in which all the quantities can be determined experimentally, forms a rigorous practical test of the first and second laws of thermodynamics.

Keywords

Latent Heat Natural Rubber Equilibrium Curve Vitreous Silica Debye Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

1. 1.
H. N. V. Temperley, Changes of States, Cleaver-Hume, London, 1956.Google Scholar
2. 1a.
A. B. Pippard, Elements of Classical Thermodynamics, Cambridge University Press, Cambridge, 1957, chapters 8 and 9.Google Scholar
3. 2.
A. J. Hughes and A. W. Lawson, J. Chem. Phys. 36, 2098 (1962).
4. 3.
C. W. Garland and J. S. Jones, J. Chem. Phys. 39, 2874 (1963).
5. 4.
R. Viswanathan and E. S. R. Gopal, Physica 27, 765, 981 (1961);
6. 4a.
R. Viswanathan and E. S. R. Gopal, Physica 29, 18 (1963).
7. 4b.
C. W. Garland, J. Chem. Phys. 41, 1005 (1964).
8. 4c.
M. P. Mokhnatkin, Soviet Phys.-Solid State 5, 1495 (1964).Google Scholar
9. 5.
D. Turnbull, Solid State Phys. 3, 225 (1956).
10. 6.
J. S. Rowlinson, Liquids and Liquid Mixtures, Butterworth, London, 1959, p.40.Google Scholar
11. 7.
J. J. Markham, R. T. Beyer, and R. B. Lindsay, Rev. Mod. Phys. 23, 353 (1951).
12. 7a.
R. O. Davies and J. Lamb, Quart. Rev. Chem. Soc. (London) 11, 134 (1957).
13. 7b.
G. S. Verma, Rev. Mod. Phys. 31, 1052 (1959).Google Scholar
14. 7c.
K. F. Herzfeld and T. A. Litovitz, Absorption and Dispersion of Ultrasonic Waves, Academic, New York, 1959.Google Scholar
15. 8.
P. Flubacher, A. J. Leadbetter, and J. A. Morrison, Proc. Phys. Soc. (London) 78, 1449 (1961).
16. 8a.
R. H. Beaumont, H. Chihara, and J. A. Morrison, Proc. Phys. Soc. (London) 78, 1462 (1961).
17. 9.
E. C. Heltemes and C. A. Swenson, Phys. Rev. Letters, 7, 363 (1961);
18. 9a.
E. C. Heltemes and C. A. Swenson, Phys. Rev. 128, 1512 (1962).
19. 9b.
D. O. Edwards, A. S. McWilliams, and J. G. Daunt, Phys. Letters 1, 218 (1962).
20. 9c.
F. W. de Wette, Phys. Rev. 129, 1160 (1963).
21. 10.
G. Borelius, Solid State Phys. 15, 1 (1963).
22. 11.
A. R. Ubbelohde, Quart. Rev. Chem. Soc. (London) 4, 356 (1950).
23. 12.
J. D. Hoffman and B. F. Decker, J. Phys. Chem. 57, 520 (1953).
24. 12a.
R. E. Meyer and N. H. Nachtrieb, J. Chem. Phys. 23, 405 (1955).
25. 13.
A. B. Lidiard, Handbuch der Physik, XX (II), 246 (1957).
26. 14.
A. J. E. Foreman and A. B. Lidiard, Phil. Mag. 8, 97 (1963).
27. 14a.
G. F. Nardelli and N. Terzi, J. Phys. Chem. Solids 25, 815 (1964).
28. 15.
A. Eucken and H. Werth, Z. anorg. allgem. Chem. 188, 152 (1930).
29. 15a.
C. G. Maier and C. T. Anderson, J. Chem. Phys. 2, 513 (1934).
30. 15b.
D. L. Martin, Can. J. Phys. 38, 17 (1960).
31. 15c.
F. A. Otter and D. E. Mapother, Phys. Rev. 125, 1171 (1962).
32. 16.
P. H. Keesom, K. Lark-Horovitz, and N. Pearlman, Science 116, 630 (1952).
33. 16a.
W. DeSorbo and W. W. Tyler, J. Chem. Phys. 26, 244 (1957).
34. 16b.
B. B. Goodman, L. Montpetit, and L. Weil, Compt. rend. acad, sci (Paris) 248, 956 (1959).Google Scholar
35. 17.
W. H. Lien and N. E. Phillips, J. Chem. Phys. 29, 1415 (1958).
36. 18.
M. Dupuis, R. Mazo, and L. Onsager, J. Chem. Phys. 33, 1452, (1960).
37. 18a.
R. Stratton, J. Chem. Phys. 37, 2972 (1962).
38. 19.
A. A. Maradudin, E. W. Montroll, and G. H. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation, Academic, New York, 1963, chapter 6.Google Scholar