Helmholtz energy function: Difference between revisions

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{{Stub-general}}
[[Hermann Ludwig Ferdinand von Helmholtz]]  
[[Hermann Ludwig Ferdinand von Helmholtz]]  
Definition of '''A''' (for ''arbeit''):
Definition of '''A''' (for ''arbeit''):
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*[[Canonical ensemble]]
*[[Canonical ensemble]]
*[[Grand canonical ensemble]]
*[[Grand canonical ensemble]]
 
==References==
#[http://dx.doi.org/10.1063/1.2794041      Enrique de Miguel, Ramona G. Marguta  and Elvira M. del Río "System-size dependence of the free energy of crystalline solids", Journal of Chemical Physics '''127''' 154512 (2007)]
[[Category: Classical thermodynamics]]
[[Category: Classical thermodynamics]]

Revision as of 11:55, 19 October 2007

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Hermann Ludwig Ferdinand von Helmholtz Definition of A (for arbeit):

where U is the internal energy, T is the temperature and S is the entropy. (TS) is a conjugate pair. The differential of this function is

From the second law of thermodynamics one obtains

thus one arrives at

.

For A(T,V) one has the following total differential

The following equation provides a link between classical thermodynamics and statistical mechanics:

where is the Boltzmann constant, T is the temperature, and is the canonical ensemble partition function.

See also

References

  1. Enrique de Miguel, Ramona G. Marguta and Elvira M. del Río "System-size dependence of the free energy of crystalline solids", Journal of Chemical Physics 127 154512 (2007)