Chemical potential: Difference between revisions

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identical particles
identical particles
:<math>Z_N= \left( \frac{2\pi m k_BT}{h^2} \right)^{3N/2} Q_N</math>
:<math>Z_N= \left( \frac{2\pi m k_BT}{h^2} \right)^{3N/2} Q_N</math>
and <math>Q_N</math> is the [[configurational integral]]
and <math>Q_N</math> is the  
[http://clesm.mae.ufl.edu/wiki.pub/index.php/Configuration_integral_%28statistical_mechanics%29 configurational integral]
:<math>Q_N = \frac{1}{N!} \int ... \int \exp (-U_N/k_B T) dr_1...dr_N</math>
:<math>Q_N = \frac{1}{N!} \int ... \int \exp (-U_N/k_B T) dr_1...dr_N</math>
==Kirkwood charging formula==
==Kirkwood charging formula==
See Ref. 2
See Ref. 2

Revision as of 18:27, 16 January 2008

Classical thermodynamics

Definition:

where is the Gibbs energy function, leading to

where is the Helmholtz energy function, is the Boltzmann constant, is the pressure, is the temperature and is the volume.

Statistical mechanics

The chemical potential is the derivative of the Helmholtz energy function with respect to the number of particles

where is the partition function for a fluid of identical particles

and is the configurational integral

Kirkwood charging formula

See Ref. 2

where is the intermolecular pair potential and is the pair correlation function.

See also

References

  1. T. A. Kaplan "The Chemical Potential", Journal of Statistical Physics 122 pp. 1237-1260 (2006)
  2. John G. Kirkwood "Statistical Mechanics of Fluid Mixtures", Journal of Chemical Physics 3 pp. 300-313 (1935)
  3. G. Cook and R. H. Dickerson "Understanding the chemical potential", American Journal of Physics 63 pp. 737-742 (1995)