Energy equation

From SklogWiki
Jump to: navigation, search

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

and in statistical mechanics it is obtained via the thermodynamic relation

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.