Heat capacity: Difference between revisions

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====Einstein====
====Einstein====
====Debye====
====Debye====
A low temperatures on has
:<math>c_v = \frac{12 \pi^4}{5} n k_B \left( \frac{T}{\Theta_D} \right)^3</math>
where <math>k_B</math> is the [[Boltzmann constant]], <math>T</math> is the [[temperature]] and <math>\Theta_D</math> is an empirical parameter known as the Debye temperature.
==See also==
==See also==
*[[Ideal gas: Heat capacity | Heat capacity of an ideal gas]]
*[[Ideal gas: Heat capacity | Heat capacity of an ideal gas]]
==References==
==References==
[[category: classical thermodynamics]]
[[category: classical thermodynamics]]

Revision as of 15:31, 21 January 2009

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

where is heat and is the entropy.

At constant volume

From the first law of thermodynamics one has

thus at constant volume, denoted by the subscript , then ,

At constant pressure

At constant pressure (denoted by the subscript ),

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

Liquids

Solids

Dulong and Petit

Einstein

Debye

A low temperatures on has

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

See also

References