Editing Compressibility

:<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,

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

The ''compressibility'' <math>K</math> or <math>\kappa</math>, is given by

:<math>\kappa =\frac{1}{B}</math>

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>

(Note: in Hansen and McDonald the isothermal compressibility is written as <math>\chi_T</math>).
where <math>\rho</math> is the ''particle number density'' given by

:<math>\rho  = \frac{N}{V}</math>

where <math>N</math> is the total number of particles in the system, i.e.

:<math>N = \int_V \rho(r,t)~{\rm d}r</math>

==Compressibility of an Ideal Gas==
From the [[Equation of State: Ideal Gas | ideal gas law]]  we see that

:<math>Z= \frac{pV}{Nk_BT}=1</math>
@@ Line 1: / Line 1: @@
-The '''bulk modulus''' ''B'' gives the change in volume of a solid substance as the [[pressure]] on it is changed,
+:<math>Z= \frac{pV}{Nk_BT}</math>
-:<math>B = -V \frac{\partial p}{\partial V}</math>
+The bulk modulus <math>B</math> gives the change in volume of a solid substance as the pressure on it is changed,
-The '''compressibility''' ''K'' or <math>\kappa</math>, is given by
+:<math>B = -V \frac{\partial P}{\partial V}</math>
+The ''compressibility'' <math>K</math> or <math>\kappa</math>, is given by
 :<math>\kappa =\frac{1}{B}</math>
-==Isothermal compressibility==
-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>
+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>
 (Note: in Hansen and McDonald the isothermal compressibility is written as <math>\chi_T</math>).
-where <math>T</math> is the [[temperature]], <math>\rho</math> is the ''particle number density'' given by
+where <math>\rho</math> is the ''particle number density'' given by
 :<math>\rho  = \frac{N}{V}</math>
@@ Line 18: / Line 20: @@
 where <math>N</math> is the total number of particles in the system, i.e.
-:<math>N = \int_V \rho({\mathbf r},t)~{\rm d}{\mathbf r}</math>
+:<math>N = \int_V \rho(r,t)~{\rm d}r</math>
-==Adiabatic compressibility==
-The  '''adiabatic compressibility''',  <math>\kappa_S</math> is given by
-:<math>\kappa_S =-\frac{1}{V} \left.\frac{\partial V}{\partial p}\right\vert_{S}</math>
-where <math>S</math> is the [[entropy]].
+==Compressibility of an Ideal Gas==
-==See also==
+From the [[Equation of State: Ideal Gas | ideal gas law]]  we see that
-The [[compressibility equation]] in [[statistical mechanics]].
-[[category:classical thermodynamics]]
+:<math>Z= \frac{pV}{Nk_BT}=1</math>