Compressibility: Difference between revisions

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The '''compressibility''', <math>Z</math>, is given by
:<math>Z= \frac{pV}{Nk_BT}</math>
:<math>Z= \frac{pV}{Nk_BT}</math>


The bulk modulus <math>B</math> gives the change in volume of a solid substance as the pressure on it is changed,
The '''bulk modulus''' <math>B</math> gives the change in volume of a solid substance as the pressure on it is changed,


:<math>B = -V \frac{\partial P}{\partial V}</math>
:<math>B = -V \frac{\partial P}{\partial V}</math>
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:<math>\kappa =\frac{1}{B}</math>
:<math>\kappa =\frac{1}{B}</math>


The  ''isothermal compressibility'',  <math>\kappa_T</math> is given by
The  '''isothermal compressibility''',  <math>\kappa_T</math> is given by


:<math>\kappa_T =-\frac{1}{V} \left.\frac{\partial V}{\partial P}\right\vert_{T} =  \frac{1}{\rho} \left.\frac{\partial \rho}{\partial P}\right\vert_{T}</math>
:<math>\kappa_T =-\frac{1}{V} \left.\frac{\partial V}{\partial P}\right\vert_{T} =  \frac{1}{\rho} \left.\frac{\partial \rho}{\partial P}\right\vert_{T}</math>

Revision as of 14:29, 22 May 2007

The compressibility, , is given by

The bulk modulus gives the change in volume of a solid substance as the pressure on it is changed,

The compressibility or , is given by

The isothermal compressibility, is given by

(Note: in Hansen and McDonald the isothermal compressibility is written as ). where is the particle number density given by

where is the total number of particles in the system, i.e.

See also

The compressibility equation in statistical mechanics.

Compressibility of an Ideal Gas

From the ideal gas law we see that