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Compressibility equation

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] (1)

where ρ is the number density, g(r) is the radial distribution function and kT\left(\frac{\partial \rho}{\partial p}\right) is the isothermal compressibility.

Using the Fourier representation of the Ornstein-Zernike equation the compressibility equation (1) can be rewritten in the form:

\frac{1}{kT}\left(\frac{\partial p}{\partial \rho}\right) = \frac{1}{1+\rho \int h(r) d \rm{r}}=\frac{1}{1+\rho \hat{H}(0)}=1-\rho\hat{C}(0)=1-\rho \int c(r) d \rm{r} (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.


  1. D.A. McQuarrie, Statistical Mechanics (Harper Collins Publishers) 1976
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Compressibility_equation". A list of authors is available in Wikipedia.
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