Isothermal-isobaric ensemble - Revision history

Nice and Tidy: Improved 'reference' link.

2009-09-03T15:41:52Z

Improved 'reference' link.

← Older revision		Revision as of 17:41, 3 September 2009
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	== ~~References~~ ==		== Related reading ==
			*[http://molsim.chem.uva.nl/frenkel_smit Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition (2002)] ISBN 0-12-267351-4

	~~# D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press~~
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

2009-03-10T10:44:36Z

Slight tidy.

← Older revision		Revision as of 12:44, 10 March 2009
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	~~Ensemble~~ variables:		The '''isothermal-isobaric ensemble''' has the following variables:

	* N is the number of particles		* <math>N</math> is the number of particles
	* p is the [[pressure]]		* <math>p</math> is the [[pressure]]
	* T is the [[temperature]]		* <math>T</math> is the [[temperature]]

	The classical [[partition function]], for a one-component atomic system in 3-dimensional space, is given by		The classical [[partition function]], for a one-component atomic system in 3-dimensional space, is given by

2009-02-27T14:28:07Z

correction

← Older revision		Revision as of 16:28, 27 February 2009
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	The classical [[partition function]], for a one-component atomic system in 3-dimensional space, is given by		The classical [[partition function]], for a one-component atomic system in 3-dimensional space, is given by

	:<math> Q_{NpT} = \frac{\beta p}{\Lambda^3 N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^)^{3N} \exp \left[ - \beta U \left(V,(R^)^{3N} \right) \right]		:<math> Q_{NpT} = \frac{\beta p}{\Lambda^{3N} N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^)^{3N} \exp \left[ - \beta U \left(V,(R^)^{3N} \right) \right]
	</math>		</math>

2008-02-13T10:15:29Z

← Older revision		Revision as of 12:15, 13 February 2008
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	* <math> \left. V \right. </math> is the Volume:		* <math> \left. V \right. </math> is the Volume:

	*<math> \beta := \frac{1}{k_B T} </math>;		*<math> \beta := \frac{1}{k_B T} </math>, where <math>k_B</math> is the [[Boltzmann constant]]

	*<math> \left. \Lambda \right. </math> is the [[de Broglie thermal wavelength]]		*<math> \left. \Lambda \right. </math> is the [[de Broglie thermal wavelength]]

2008-02-13T10:14:22Z

← Older revision		Revision as of 12:14, 13 February 2008
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	* T is the [[temperature]]		* T is the [[temperature]]

	The [[~~classical~~ partition function]], for a one-component atomic system in 3-dimensional space, is given by		The classical [[partition function]], for a one-component atomic system in 3-dimensional space, is given by

	:<math> Q_{NpT} = \frac{\beta p}{\Lambda^3 N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^)^{3N} \exp \left[ - \beta U \left(V,(R^)^{3N} \right) \right]		:<math> Q_{NpT} = \frac{\beta p}{\Lambda^3 N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^)^{3N} \exp \left[ - \beta U \left(V,(R^)^{3N} \right) \right]

2008-02-13T10:13:47Z

← Older revision		Revision as of 12:13, 13 February 2008
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	Ensemble variables:		Ensemble variables:

	* N ~~(Number~~ of particles)		* N is the number of particles
	* p ~~(Pressure)~~		* p is the [[pressure]]
	* T ~~(Temperature)~~		* T is the [[temperature]]

	The [[classical partition function]], for a one-component atomic system in 3-dimensional space, is given by		The [[classical partition function]], for a one-component atomic system in 3-dimensional space, is given by
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	* <math> \left. V \right. </math> is the Volume:		* <math> \left. V \right. </math> is the Volume:

	*<math> \beta = \frac{1}{k_B T} </math>;		*<math> \beta := \frac{1}{k_B T} </math>;

	*<math> \left. \Lambda \right. </math> is the [[de Broglie thermal wavelength]]		*<math> \left. \Lambda \right. </math> is the [[de Broglie thermal wavelength]]
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	# D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press		# D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press
			[[category: statistical mechanics]]

2007-03-09T14:45:28Z

← Older revision	Revision as of 16:45, 9 March 2007
(No difference)

2007-02-27T16:25:48Z

← Older revision		Revision as of 18:25, 27 February 2007
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	*<math> \beta = \frac{1}{k_B T} </math>;		*<math> \beta = \frac{1}{k_B T} </math>;

	*<math> \left. \Lambda \right. </math> is the [[de Broglie wavelength]]		*<math> \left. \Lambda \right. </math> is the [[de Broglie thermal wavelength]]

	<math> \left( R^ \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math>		<math> \left( R^ \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math>

2007-02-27T10:03:08Z

← Older revision		Revision as of 12:03, 27 February 2007
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	~~Variables~~:		Ensemble variables:

	* N (Number of particles)		* N (Number of particles)
	* p (Pressure)		* p (Pressure)
	* T (Temperature)		* T (Temperature)
	* V (Volume)

	The [[classical partition function]], for a one-component atomic system in 3-dimensional space, is given by		The [[classical partition function]], for a one-component atomic system in 3-dimensional space, is given by
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	where		where

			* <math> \left. V \right. </math> is the Volume:

	*<math> \beta = \frac{1}{k_B T} </math>;		*<math> \beta = \frac{1}{k_B T} </math>;

	*<math> \Lambda </math> is the [[de Broglie wavelength]]		*<math> \left. \Lambda \right. </math> is the [[de Broglie wavelength]]

	<math> \left( R^ \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math>		<math> \left( R^ \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math>

2007-02-26T10:16:25Z

← Older revision		Revision as of 12:16, 26 February 2007
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	* V (Volume)		* V (Volume)

	The classical partition function, for a one-component atomic system in 3-dimensional space, is given by		The [[classical partition function]], for a one-component atomic system in 3-dimensional space, is given by

	<math> Q_{NpT} = \frac{\beta p}{\Lambda^3 N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^)^{3N} \exp \left[ - \beta U \left(V,(R^)^{3N} \right) \right]		:<math> Q_{NpT} = \frac{\beta p}{\Lambda^3 N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^)^{3N} \exp \left[ - \beta U \left(V,(R^)^{3N} \right) \right]
	</math>		</math>

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	*<math> \beta = \frac{1}{k_B T} </math>;		*<math> \beta = \frac{1}{k_B T} </math>;

	*<math> \Lambda </math> is the ~~'''~~de Broglie~~'''~~ wavelength		*<math> \Lambda </math> is the [[de Broglie wavelength]]

	<math> \left( R^ \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math>		<math> \left( R^ \right)^{3N} </math> represent the reduced position coordinates of the particles; i.e. <math> \int d ( R^*)^{3N} = 1 </math>