= Pair-correlation expression for internal energy
{title2=$U/N=3k_BT/2+2\pi n\int_0^\infty r^2v(r)g(r)\,dr$}
For a classical monatomic homogeneous fluid with pairwise central <pair potential> $v(r)$, the mean interaction energy is one half the sum over neighbours of a tagged particle. Using the <radial distribution function> gives the displayed formula; the factor one half prevents counting each pair twice. The kinetic term follows from the <equipartition theorem>. Its use requires the relevant integral to exist and a thermodynamic state specified by number density and temperature. Quantum kinetic contributions, many-body forces and internal molecular modes require modifications.
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