Energy equation: Difference between revisions

Latest revision as of 14:31, 29 June 2007

The energy equation is given, in classical thermodynamics, by

\left.{\frac {\partial U}{\partial V}}\right\vert _{T}=T\left.{\frac {\partial p}{\partial T}}\right\vert _{V}-p

U={\frac {\partial (A/T)}{\partial (1/T)}}

and making use of the Helmholtz energy function and the canonical partition function one arrives at

{\frac {U^{\rm {ex}}}{N}}={\frac {\rho }{2}}\int _{0}^{\infty }\Phi (r)~{\rm {g}}(r)~4\pi r^{2}~{\rm {d}}r

where $\Phi (r)$ is a two-body central potential, $U^{\rm {ex}}$ is the excess internal energy per particle, and ${\rm {g}}(r)$ is the radial distribution function.

@@ Line 3: / Line 3: @@
 :<math>\left. \frac{\partial U}{\partial V} \right\vert_T   = T \left. \frac{\partial p}{\partial T} \right\vert_V -p  </math>
-and in [[statistical mechanics]] by
+and in [[statistical mechanics]] it is obtained via the [[thermodynamic relations | thermodynamic relation]]
+:<math>U = \frac{\partial (A/T)}{\partial (1/T)}</math>
+and making use of the [[Helmholtz energy function]] and the canonical [[partition function]] one arrives at
 :<math>\frac{U^{\rm ex}}{N}= \frac{\rho}{2} \int_0^{\infty} \Phi(r)~{\rm g}(r)~4 \pi r^2~{\rm d}r</math>
-where <math>\Phi(r)</math> is a ''central'' potential, <math>U^{\rm ex}</math> is the
+where <math>\Phi(r)</math> is a ''two-body central'' potential, <math>U^{\rm ex}</math> is the
-[[excess internal energy]] per particle,  and <math>{\rm g}(r)</math> is the [[pair distribution function]].
+[[excess internal energy]] per particle,  and <math>{\rm g}(r)</math> is the [[radial distribution function]].
 [[category:statistical mechanics]]
 [[category: classical thermodynamics]]