Compressibility - Revision history

Carl McBride: /* Isothermal compressibility */

2008-02-13T16:07:42Z

Isothermal compressibility

← Older revision		Revision as of 18:07, 13 February 2008
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	(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 <math>\rho</math> is the ''particle number density'' given by		where <math>T</math> is the [[temperature]], <math>\rho</math> is the ''particle number density'' given by

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

	==Adiabatic compressibility==		==Adiabatic compressibility==
	The '''adiabatic compressibility''', <math>\kappa_S</math> is given by		The '''adiabatic compressibility''', <math>\kappa_S</math> is given by

2008-02-13T16:05:13Z

← Older revision		Revision as of 18:05, 13 February 2008
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	:<math>\kappa =\frac{1}{B}</math>		:<math>\kappa =\frac{1}{B}</math>
			==Isothermal compressibility==
	The '''isothermal compressibility''', <math>\kappa_T</math> is given by		The '''isothermal compressibility''', <math>\kappa_T</math> is given by

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	:<math>N = \int_V \rho({\mathbf r},t)~{\rm d}{\mathbf r}</math>		:<math>N = \int_V \rho({\mathbf r},t)~{\rm d}{\mathbf 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]].
	==See also==		==See also==
	The [[compressibility equation]] in [[statistical mechanics]].		The [[compressibility equation]] in [[statistical mechanics]].

	[[category:classical thermodynamics]]		[[category:classical thermodynamics]]

2008-01-29T15:06:51Z

Added internal link

← Older revision		Revision as of 17:06, 29 January 2008
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	The '''bulk modulus''' ''B'' gives the change in volume of a solid substance as the pressure on it is changed,		The '''bulk modulus''' ''B'' 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>

2007-07-10T13:59:05Z

← Older revision		Revision as of 15:59, 10 July 2007
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	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(r,t)~{\rm d}r</math>		:<math>N = \int_V \rho({\mathbf r},t)~{\rm d}{\mathbf r}</math>
	==See also==		==See also==
	The [[compressibility equation]] in [[statistical mechanics]].		The [[compressibility equation]] in [[statistical mechanics]].

	[[category:classical thermodynamics]]		[[category:classical thermodynamics]]

2007-06-21T12:16:32Z

← Older revision		Revision as of 14:16, 21 June 2007
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	The '''~~compressibility~~'''~~, <math>Z</math>, is given by~~		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>~~

	~~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>

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

	:<math>\kappa =\frac{1}{B}</math>		:<math>\kappa =\frac{1}{B}</math>
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	==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>~~
	[[category:classical thermodynamics]]		[[category:classical thermodynamics]]

2007-06-21T12:11:28Z

← Older revision		Revision as of 14:11, 21 June 2007
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	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>

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

2007-06-21T12:11:03Z

← Older revision		Revision as of 14:11, 21 June 2007
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	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>

	(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>).

2007-05-25T16:02:37Z

← Older revision		Revision as of 18:02, 25 May 2007
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	:<math>Z= \frac{pV}{Nk_BT}=1</math>		:<math>Z= \frac{pV}{Nk_BT}=1</math>
			[[category:classical thermodynamics]]

2007-05-22T13:29:51Z

← Older revision		Revision as of 15:29, 22 May 2007
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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>

2007-05-22T13:24:06Z

← Older revision		Revision as of 15:24, 22 May 2007
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	:<math>N = \int_V \rho(r,t)~{\rm d}r</math>		:<math>N = \int_V \rho(r,t)~{\rm d}r</math>
			==See also==
			The [[compressibility equation]] in [[statistical mechanics]].
	==Compressibility of an Ideal Gas==		==Compressibility of an Ideal Gas==
	From the [[Equation of State: Ideal Gas \| ideal gas law]] we see that		From the [[Equation of State: Ideal Gas \| ideal gas law]] we see that

	:<math>Z= \frac{pV}{Nk_BT}=1</math>		:<math>Z= \frac{pV}{Nk_BT}=1</math>