Energy equation: Difference between revisions

Revision as of 13:05, 21 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

{\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 central potential, $U^{\rm {ex}}$ is the excess internal energy per particle, and ${\rm {g}}(r)$ is the pair distribution function.

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-The '''energy equation''' is given by
+The '''energy equation''' is given, in [[classical thermodynamics]], by
+:<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
 :<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
 [[excess internal energy]] per particle,  and <math>{\rm g}(r)</math> is the [[pair distribution function]].
 [[category:statistical mechanics]]
+[[category: classical thermodynamics]]