Born-Green equation: Difference between revisions

Revision as of 16:19, 10 July 2007

k_{B}T{\frac {\partial \ln {\rm {g}}(r_{12})}{\partial {\mathbf {r} }_{1}}}={\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}

where $\Phi (r_{nm})$ is the intermolecular pair potential, T is the temperature, and $k_{B}$ is the Boltzmann constant.

@@ Line 1: / Line 1: @@
-:<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==
 #[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]]