Helmholtz energy function - Revision history

Carl McBride: Defined as

2015-02-20T17:53:04Z

Defined as

← Older revision		Revision as of 19:53, 20 February 2015
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	Definition of <math>A</math> (for ''arbeit''):		Definition of <math>A</math> (for ''arbeit''):

	:<math>~~\left.~~A~~\right.~~=U-TS</math>		:<math>A:=U-TS</math>

	where ''U'' is the [[internal energy]], ''T'' is the [[temperature]] and ''S'' is the [[Entropy\|entropy]].		where ''U'' is the [[internal energy]], ''T'' is the [[temperature]] and ''S'' is the [[Entropy\|entropy]].

2012-03-21T14:46:42Z

Added mention of quantum correction

← Older revision		Revision as of 16:46, 21 March 2012
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	where <math>k_B</math> is the [[Boltzmann constant]], ''T'' is the [[temperature]], and <math>Q_{NVT}</math> is the [[Canonical ensemble \| canonical ensemble partition function]].		where <math>k_B</math> is the [[Boltzmann constant]], ''T'' is the [[temperature]], and <math>Q_{NVT}</math> is the [[Canonical ensemble \| canonical ensemble partition function]].
			==Ideal gas==
			:''Main article: [[Ideal gas Helmholtz energy function]]''
			==Quantum correction==
			A quantum correction can be calculated by making use of the [[Wigner-Kirkwood expansion]] of the partition function, resulting in (Eq. 3.5 in <ref>[http://dx.doi.org/10.1080/00268977900102921 J.G. Powles and G. Rickayzen "Quantum corrections and the computer simulation of molecular fluids", Molecular Physics '''38''' pp. 1875-1892 (1979)]</ref>):

			:<math>\frac{A-A_{ {\mathrm{classical}} }}{N} = \frac{\hbar^2}{24m(k_BT)^2} \langle F^2 \rangle </math>

			where <math>\langle F^2 \rangle</math> is the mean squared force on any one atom due to all the other atoms.
	==See also==		==See also==
	*[[Canonical ensemble]]		*[[Canonical ensemble]]
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	==References==		==References==
			<references/>
	[[Category: Classical thermodynamics]]		[[Category: Classical thermodynamics]]

2011-10-19T10:38:49Z

Slight tidy

← Older revision		Revision as of 12:38, 19 October 2011
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	~~{{Stub-general}}~~		'''Helmholtz energy function''' ([[Hermann Ludwig Ferdinand von Helmholtz]])
	[[Hermann Ludwig Ferdinand von Helmholtz]]		Definition of <math>A</math> (for ''arbeit''):
	Definition of ~~'''~~A~~'''~~ (for ''arbeit''):

	:<math>\left.A\right.=U-TS</math>		:<math>\left.A\right.=U-TS</math>

2007-10-19T11:35:10Z

2007-10-19T11:18:47Z

← Older revision		Revision as of 13:18, 19 October 2007
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	*[[Canonical ensemble]]		*[[Canonical ensemble]]
	*[[Grand canonical ensemble]]		*[[Grand canonical ensemble]]
			*[[Helmholtz energy function of solids]]
	==References==		==References==
	[[Category: Classical thermodynamics]]		[[Category: Classical thermodynamics]]

2007-10-19T11:15:57Z

References

← Older revision		Revision as of 13:15, 19 October 2007
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	*[[Grand canonical ensemble]]		*[[Grand canonical ensemble]]
	==References==		==References==
	#[http://dx.doi.org/10.1063/1.2794041 Enrique de Miguel, Ramona G. Marguta and Elvira M. del Río "System-size dependence of the free energy of crystalline solids", Journal of Chemical Physics '''127''' 154512 (2007)]
	[[Category: Classical thermodynamics]]		[[Category: Classical thermodynamics]]

2007-10-19T10:55:48Z

← Older revision		Revision as of 12:55, 19 October 2007
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			{{Stub-general}}
	[[Hermann Ludwig Ferdinand von Helmholtz]]		[[Hermann Ludwig Ferdinand von Helmholtz]]
	Definition of '''A''' (for ''arbeit''):		Definition of '''A''' (for ''arbeit''):
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	*[[Canonical ensemble]]		*[[Canonical ensemble]]
	*[[Grand canonical ensemble]]		*[[Grand canonical ensemble]]
			==References==
			#[http://dx.doi.org/10.1063/1.2794041 Enrique de Miguel, Ramona G. Marguta and Elvira M. del Río "System-size dependence of the free energy of crystalline solids", Journal of Chemical Physics '''127''' 154512 (2007)]
	[[Category: Classical thermodynamics]]		[[Category: Classical thermodynamics]]

2007-06-25T09:46:28Z

← Older revision		Revision as of 11:46, 25 June 2007
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	:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math>		:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math>

			where <math>k_B</math> is the [[Boltzmann constant]], ''T'' is the [[temperature]], and <math>Q_{NVT}</math> is the [[Canonical ensemble \| canonical ensemble partition function]].
	==See also==		==See also==
	*[[Canonical ensemble]]		*[[Canonical ensemble]]

2007-05-28T11:24:52Z

← Older revision		Revision as of 13:24, 28 May 2007
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	:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math>		:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math>
			==See also==

	See also
	*[[Canonical ensemble]]		*[[Canonical ensemble]]
	*[[Grand canonical ensemble]]		*[[Grand canonical ensemble]]

	[[Category: Classical thermodynamics]]		[[Category: Classical thermodynamics]]

2007-05-21T15:04:37Z

← Older revision		Revision as of 17:04, 21 May 2007
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	:<math>\left.dA\right.=dU-TdS-SdT</math>		:<math>\left.dA\right.=dU-TdS-SdT</math>

	From the [[Second law of thermodynamics]] one obtains		From the [[Second law of thermodynamics \| second law of thermodynamics]] one obtains

	:<math>\left.dA\right.=TdS -pdV -TdS-SdT</math>		:<math>\left.dA\right.=TdS -pdV -TdS-SdT</math>

← Older revision		Revision as of 13:35, 19 October 2007
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	*[[Canonical ensemble]]		*[[Canonical ensemble]]
	*[[Grand canonical ensemble]]		*[[Grand canonical ensemble]]
	*[[Helmholtz energy function of solids]]		*[[Computing the Helmholtz energy function of solids]]

	==References==		==References==
	[[Category: Classical thermodynamics]]		[[Category: Classical thermodynamics]]