Scaled particle theory
The Scaled Particle Theory (SPT) is an equilibrium theory of hard-sphere fluids which gives an approximate expression for the equation of state of hard-sphere mixtures and for their thermodynamic properties such as the surface tension. One-component case 

Consider the one-component homogeneous hard-sphere fluid with molecule radius . To obtain its equation of state in the form  (where  is the pressure,  is the density of the fluid and  is the temperature) one can find the expression for the chemical potential  and then use the Gibbs–Duhem equation to express  as a function of . The chemical potential of the fluid can be written as a sum of an ideal-gas contribution and an excess part: . The excess chemical potential is equivalent to the reversible work of inserting an additional molecule into the fluid. Note that inserting a spherical particle of radius  is equivalent to creating a cavity of radius  in the hard-sphere fluid. The SPT theory gives an approximate expression for this work . In case of inserting a molecule  it is

,

where  is the packing fraction,  is the Boltzmann constant. This leads to the equation of state

which is equivalent to the compressibility equation of state of the Percus-Yevick theory. References 

Statistical mechanics