Editing Compressibility
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 1: | Line 1: | ||
The ''' | 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 | :<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> | :<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 | :<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>). | (Note: in Hansen and McDonald the isothermal compressibility is written as <math>\chi_T</math>). | ||
where | where <math>\rho</math> is the ''particle number density'' given by | ||
:<math>\rho = \frac{N}{V}</math> | :<math>\rho = \frac{N}{V}</math> | ||
Line 18: | Line 21: | ||
where <math>N</math> is the total number of particles in the system, i.e. | where <math>N</math> is the total number of particles in the system, i.e. | ||
:<math>N = \int_V \rho( | :<math>N = \int_V \rho(r,t)~{\rm d}r</math> | ||
==See also== | ==See also== | ||
The [[compressibility equation]] in [[statistical mechanics]]. | The [[compressibility equation]] in [[statistical mechanics]]. | ||
==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> |