Compressibility equation
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In statistical mechanics and thermodynamics the compressibility equation refers to an equation which relates the isothermal compressibility (and indirect the pressure) to the structure of the liquid. It reads:
![kT\left(\frac{\partial \rho}{\partial p}\right)=1+\rho \int d r [g(r)-1]](../../../math/7/3/9/7398478c87fd42d409c1fda60f0c2b07.png)
(1)
where ρ is the number density, g(r) is the radial distribution function and 
is the isothermal compressibility.
Using the Fourier representation of the Ornstein-Zernike equation the compressibility equation (1) can be rewritten in the form:
(2)
where h(r) and c(r) are the indirect and direct correlation functions respectively. The compressibility equation is one of the many integral equations in statistical mechanics.
[edit] References
- D.A. McQuarrie, Statistical Mechanics (Harper Collins Publishers) 1976
