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| In [[statistical mechanics]] and [[thermodynamics]] the '''compressibility equation''' refers to an equation which relates the isothermal [[compressibility]] (and indirectly the pressure) to the structure of the liquid. It reads:
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| <math>kT\left(\frac{\partial \rho}{\partial p}\right)=1+\rho \int d r [g(r)-1] </math> (1) | |
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| where <math>\rho</math> is the number density, g(r) is the [[radial distribution function]] and <math>kT\left(\frac{\partial \rho}{\partial p}\right)</math> is the isothermal [[compressibility]].
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| Using the Fourier representation of the [[Ornstein-Zernike equation]] the compressibility equation (1) can be rewritten in the form:
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| <math>\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} </math> (2)
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| 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]].
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| ==References==
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| #D.A. McQuarrie, Statistical Mechanics (Harper Collins Publishers) 1976
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| [[Category:Statistical mechanics]]
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| [[Category:Thermodynamic equations]]
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Latest revision as of 12:30, 12 May 2014
Royal Votaw is my title but I never truly favored that title. Interviewing is what she does in her day occupation but soon her spouse and her will start their own company. Her family life in Idaho. To keep birds is one of the issues he enjoys most.
Here is my web blog: www.newsfortrader.com