This work was begun quite some time ago at the University of Oxford during the tenure of an Overseas Scholarship of the Royal Commission for the Exhibition of 1851 and was completed at Banga­ lore when the author was being supported by a maintenance allowance from the CSIR Pool for unemployed scientists. It is hoped that significant developments taking place as late as the beginning of 1965 have been incorporated. The initial impetus and inspiration for the work came from Dr. K. Mendelssohn. To him and to Drs. R. W. Hill and N. E. Phillips, who went through the whole of the text, the author is obliged in more ways than one. For permission to use figures and other materials, grateful thanks are tendered to the concerned workers and institutions. The author is not so sanguine as to imagine that all technical and literary flaws have been weeded out. If others come across them, they may be charitably brought to the author's notice as proof that physics has become too vast to be comprehended by a single onlooker. E. S. RAJA GoPAL Department of Physics Indian Institute of Science Bangalore 12, India November 1965 v Contents Introduction ................................................................. .

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1 Elementary Concepts of Specific Heats.- 1.1. Definitions.- 1.2. Thermodynamics of Simple Systems.- 1.3. Difference Between Cp and Cv.- 1.4. Variation of Specific Heats with Temperature and Pressure.- 1.5. Statistical Calculation of Specific Heats.- 1.6. Different Modes of Thermal Energy.- 1.7. Calorimetry.- 2 Lattice Heat Capacity.- 2.1. Dulong and Petit's Law.- 2.2. Equipartition Law.- 2.3. Quantum Theory of Specific Heats.- 2.4. Einstein's Model.- 2.5. Debye's Model.- 2.6. Comparison of Debye's Theory with Experiments.- 2.7. Shortcomings of the Debye Model.- 2.8. The Born-Von Kármán Model.- 2.9. Calculation of g(v).- 2.10. Comparison of Lattice Theory with Experiments.- 2.11. Debye ? in Other Properties of Solids.- 3 Electronic Specific Heat.- 3.1. Specific Heat of Metals.- 3.2. Quantum Statistics of an Electron Gas.- 3.3. Specific Heat of Electrons in Metals.- 3.4. Electronic Specific Heat at Low Temperatures.- 3.5. Specific Heat and Band Structure of Metals.- 3.6. Specific Heat of Alloys.- 3.7. Specific Heat of Semiconductors.- 3.8. Phenomenon of Superconductivity.- 3.9. Specific Heat of Superconductors.- 3.10. Recent Studies.- 4 Magnetic Contribution to Specific Heats.- 4.1. Thermodynamics of Magnetic Materials.- 4.2. Types of Magnetic Behavior.- 4.3. Spin Waves-Magnons.- 4.4. Spin Wave Specific Heats.- 4.5. The Weiss Model for Magnetic Ordering.- 4.6. The Heisenberg and Ising Models.- 4.7. Specific Heats Near the Transition Temperature.- 4.8. Paramagnetic Relaxation.- 4.9. Schottky Effect.- 4.10. Specific Heat of Paramagnetic Salts.- 4.11. Nuclear Schottky Effects.- 5 Heat Capacity of Liquids.- 5.1. Nature of the Liquid State.- 5.2. Specific Heat of Ordinary Liquids and Liquid Mixtures.- 5.3. Liquid 4He at Low Temperatures.- 5.4. Phonon and RotonSpecific Heats.- 5.5. Transition in Liquid 4He.- 5.6. Specific Heat of Liquid 3He.- 5.7. Liquid 3He as a Fermi Liquid.- 5.8. Mixtures of 4He and 3He.- 5.9. Supercooled Liquids-Glasses.- 6 Specific Heats of Gases.- 6.1. Cp and Cv of a Gas.- 6.2. Classical Theory of Cv of Gases.- 6.3. Quantum Theory of Cv of Gases.- 6.4. Rotational Partition Function.- 6.5. Homonuclear Molecules-Isotopes of Hydrogen.- 6.6. Vibrational and Electronic Specific Heats.- 6.7. Calorimetric and Statistical Entropies-Disorder in Solid State.- 6.8. Hindered Rotation.- 6.9. Entropy of Hydrogen.- 7 Specific-Heat Anomalies.- 7.1. Spurious and Genuine Anomalies.- 7.2. Cooperative and Noncooperative Anomalies.- 7.3. Order-Disorder Transitions.- 7.4. Onset of Molecular Rotation.- 7.5. Ferroelectricity.- 7.6. Transitions in Rare-Earth Metals.- 7.7. Liquid-Gas Critical Points.- 7.8. Models of Cooperative Transitions.- 8 Miscellaneous Problems in Specific Heats.- 8.1. Specific Heat Near Phase Transitions.- 8.2. Specific Heat at Saturated Vapor Pressure.- 8.3. Relaxation of Rotational and Vibrational Specific Heats.- 8.4. Defects in Solids.- 8.5. Surface Effects.- 8.6. Compilations of Specific-Heat Data.- 8.7. Tabulations of Specific-Heat Functions.- Appendix (Six-Figure Tables of Einstein and Debye Internal-Energy and Specific-Heat Functions).- Author Index.