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The difference between the heat capacity at constant pressure and the heat capacity at constant volume is given by | The difference between the heat capacity at constant pressure and the heat capacity at constant volume is given by | ||
:<math>C_p -C_V = \left( p + \left. \frac{\partial U}{\partial V} \right\vert_T \right) \left. \frac{\partial V}{\partial T} \right\vert_p</math> | :<math>C_p -C_V = \left( p + \left. \frac{\partial U}{\partial V} \right\vert_T \right) \left. \frac{\partial V}{\partial T} \right\vert_p</math> | ||
==Excess heat capacity== | ==Excess heat capacity== | ||
In a classical system the excess heat capacity for a monatomic fluid is given by subtracting the [[Ideal gas: Energy |ideal internal energy]] (which is kinetic in nature) | In a classical system the excess heat capacity for a monatomic fluid is given by subtracting the [[Ideal gas: Energy |ideal internal energy]] (which is kinetic in nature) | ||
:<math>C_v^{ex} = C_v - \frac{3}{2} | :<math>C_v^{ex} = C_v - \frac{3}{2}Nk_BT</math> | ||
in other words the excess heat capacity is associated with the component of the internal energy due to the intermolecular potential, and for that reason it is also known as the ''configurational'' heat capacity. Given that the excess internal energy for a pair potential is given by (Eq. 2.5.20 in <ref>J-P. Hansen and I. R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition) ISBN 0-12-370535-5 </ref>): | in other words the excess heat capacity is associated with the component of the internal energy due to the intermolecular potential, and for that reason it is also known as the ''configurational'' heat capacity. Given that the excess internal energy for a pair potential is given by (Eq. 2.5.20 in <ref>J-P. Hansen and I. R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition) ISBN 0-12-370535-5 </ref>): | ||
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For many-body distribution functions things become more complicated <ref>[http://dx.doi.org/10.1063/1.468220 Ben C. Freasier, Adam Czezowski, and Richard J. Bearman "Multibody distribution function contributions to the heat capacity for the truncated Lennard‐Jones fluid", Journal of Chemical Physics '''101''' pp. 7934-7938 (1994)]</ref>. | For many-body distribution functions things become more complicated <ref>[http://dx.doi.org/10.1063/1.468220 Ben C. Freasier, Adam Czezowski, and Richard J. Bearman "Multibody distribution function contributions to the heat capacity for the truncated Lennard‐Jones fluid", Journal of Chemical Physics '''101''' pp. 7934-7938 (1994)]</ref>. | ||
==Liquids== | ==Liquids== | ||
<ref>[http://dx.doi.org/10.1063/1.1667469 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)]</ref> | |||
==Solids== | ==Solids== | ||
====Petit and Dulong==== | ====Petit and Dulong==== | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
[[category: classical thermodynamics]] | [[category: classical thermodynamics]] |