Pair distribution function

For a fluid of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} particles, enclosed in a volume Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} at a given temperature Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} (canonical ensemble) interacting via the `central' potential Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi(r)} , the two particle distribution function is defined as

${\rm {g}}_{N}^{(2)}(r_{1},r_{2})=V^{2}{\frac {\int ...\int e^{-\beta \Phi (r_{1},...,r_{N})}{\rm {d}}r_{3}...{\rm {d}}r_{N}}{\int e^{-\beta \Phi (r_{1},...,r_{N}){\rm {d}}r_{1}...{\rm {d}}r_{N}}}}$

See also

• Compressibility equation
• Pressure equation
• Energy equation