Heat capacity

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The heat capacity is defined as the differential of heat with respect to the temperature T,

where Q is heat and S is the entropy.

Contents 1 At constant volume 2 At constant pressure 3 Liquids 4 Solids 4.1 Petit and Dulong 4.2 Einstein 4.3 Debye 5 See also 6 References

[edit] At constant volume

From the first law of thermodynamics one has

thus at constant volume, denoted by the subscript V, then dV = 0,

[edit] At constant pressure

At constant pressure (denoted by the subscript p),

where H is the enthalpy. The difference between the heat capacity at constant pressure and the heat capacity at constant volume is given by

[edit] Liquids

• Claudio A. Cerdeiriña, Diego González-Salgado, Luis Romani, María del Carmen Delgado, Luis A. Torres and Miguel Costas "Towards an understanding of the heat capacity of liquids. A simple two-state model for molecular association", Journal of Chemical Physics 120 pp. 6648-6659 (2004)

[edit] Solids

[edit] Petit and Dulong

^[1]

[edit] Einstein

[edit] Debye

A low temperatures on has

where k_B is the Boltzmann constant, T is the temperature and Θ_D is an empirical parameter known as the Debye temperature.

[edit] See also

• Heat capacity of an ideal gas
• Yang-Yang anomaly

[edit] References

1. ↑ Alexis-Thérèse Petit and Pierre-Louis Dulong "Recherches sur quelques points importants de la Théorie de la Chaleur", Annales de Chimie et de Physique 10 pp. 395-413 (1819)