Hard-spheres Gas
The first three virial coefficients for hard spheres can be determined analytically
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Higher-order ones can be determined numerically using Monte Carlo integration. We list
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A table of virial coefficients for up to eight dimensions can be found on the page Hard sphere: virial coefficients.
The hard sphere system exhibits a fluid-solid phase transition between the volume fractions of freezing and melting . The pressure diverges at random close packing for the metastable liquid branch and at close packing for the stable solid branch.
Read more about this topic: Hard Spheres
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