Compressibility: Difference between revisions

Revision as of 15:29, 22 May 2007

The compressibility, $Z$ , is given by

Z = \frac{p V}{N k_{B} T}

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

B = - V \frac{\partial P}{\partial V}

The compressibility $K$ or $κ$ , is given by

κ = \frac{1}{B}

The isothermal compressibility, $κ_{T}$ is given by

κ_{T} = - \frac{1}{V} {\frac{\partial V}{\partial P} |}_{T} = \frac{1}{ρ} {\frac{\partial ρ}{\partial P} |}_{T}

(Note: in Hansen and McDonald the isothermal compressibility is written as $χ_{T}$ ). where $ρ$ is the particle number density given by

ρ = \frac{N}{V}

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

N = \int_{V} ρ (r, t) d r

From the ideal gas law we see that

Z = \frac{p V}{N k_{B} T} = 1

@@ Line 1: / Line 1: @@
+The '''compressibility''', <math>Z</math>, is given by
 :<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>
@@ Line 9: / Line 10: @@
 :<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>