Chemical potential: Difference between revisions

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and <math>Q_N</math> is the [[configurational integral]]
and <math>Q_N</math> is the [[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==
See Ref. 2
:<math>\beta \mu_{\rm ex} = \rho \int_0^1 d\lambda \int \frac{\partial \beta \Phi_{12} (r,\lambda)}{\partial \lambda} {\rm g}(r,\lambda) dr</math>
where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]] and <math>{\rm g}(r)</math> is the [[Pair distribution function | pair correlation function]].
==See also==
==See also==
*[[Ideal gas: Chemical potential]]
*[[Ideal gas: Chemical potential]]
==References==
==References==
#[http://dx.doi.org/10.1007/s10955-005-8067-x T. A. Kaplan "The Chemical Potential", Journal of Statistical Physics '''122''' pp. 1237-1260 (2006)]
#[http://dx.doi.org/10.1007/s10955-005-8067-x T. A. Kaplan "The Chemical Potential", Journal of Statistical Physics '''122''' pp. 1237-1260 (2006)]
#[http://dx.doi.org/10.1063/1.1749657  John G. Kirkwood "Statistical Mechanics of Fluid Mixtures", Journal of Chemical Physics '''3''' pp. 300-313 (1935)]
[[category:classical thermodynamics]]
[[category:classical thermodynamics]]
[[category:statistical mechanics]]
[[category:statistical mechanics]]

Revision as of 10:41, 8 June 2007

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)