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If <math>\phi(r)</math> was zero for all r - i.e., if the molecules did not exert any influence on each other g(r) = 1 for all r. Then from (1) the mean local density would be equal to the mean density <math>\rho</math>: the presence of a molecule at O would not influence the presence or absence of any other molecule and the gas would be ideal. As long as there is a <math>\phi(r)</math> the mean local density will always be different from the mean density <math>\rho</math> due to the interactions between molecules.
When the density of the gas gets higher the so called low-density limit (2) is not applicable anymore because the molecules attracted to and repelled by the molecule at O also repel and attract each other. The correction terms needed to correctly describe g(r) resembles the [[virial equation]], it is an expansion in the density:
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g(r) is of fundamental importance in thermodynamics for macroscopic thermodynamic quantities can be calculated using g(r). A few examples:
''The virial equation for the pressure:''
:<math>p=\rho kT-\frac{2\pi}{3kT}\rho^{2}\int d r r^{3} u^{\prime}(r) g(r, \rho, T) </math> (4)
''The energy equation:''
:<math>\frac{E}{NkT}=\frac{3}{2}+\frac{\rho}{2kT}\int d r \,4\pi r^{2} u(r)g(r, \rho, T) </math> (5)
''[[Compressibility equation|The compressibility equation]]:''
:<math>kT\left(\frac{\partial \rho}{\partial p}\right)=1+\rho \int d r [g(r)-1] </math> (6)
==Experimental==
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