Born-Green equation: Difference between revisions

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:<math>kT \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}=
:<math>k_B T \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}=
\frac{-\partial U(r_{12})}{\partial {\mathbf r}_1}-  \rho \int \left[ \frac{\partial U(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23})  ~ {\rm d}{\mathbf r}_3</math>
\frac{-\partial \Phi(r_{12})}{\partial {\mathbf r}_1}-  \rho \int \left[ \frac{\partial \Phi(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23})  ~ {\rm d}{\mathbf r}_3</math>
 
where <math>\Phi(r_{nm})</math> is the [[intermolecular pair potential]], ''T'' is the [[temperature]], and <math>k_B</math> is the [[Boltzmann constant]].
==References==
==References==
#[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]
#[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]
[[category:statistical mechanics]]
[[category:statistical mechanics]]

Revision as of 15:19, 10 July 2007

where is the intermolecular pair potential, T is the temperature, and is the Boltzmann constant.

References

  1. M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 188 pp. 10-18 (1946)