Third law of thermodynamics - Revision history

Carl McBride: /* References */ Added a recent publication

2017-03-14T16:28:44Z

References: Added a recent publication

← Older revision		Revision as of 18:28, 14 March 2017
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	;Related reading		;Related reading
	*[http://dx.doi.org/10.1088/0305-4470/22/1/021 P. T. Landsberg "A comment on Nernst's theorem", Journal of Physics A: Mathematical and General '''22''' pp. 139-141 (1989)]		*[http://dx.doi.org/10.1088/0305-4470/22/1/021 P. T. Landsberg "A comment on Nernst's theorem", Journal of Physics A: Mathematical and General '''22''' pp. 139-141 (1989)]
			*[http://dx.doi.org/10.1038/ncomms14538 Lluís Masanes and Jonathan Oppenheim "A general derivation and quantification of the third law of thermodynamics", Nature Communications '''8''' 14538 (2017)]

	[[category: classical thermodynamics]]		[[category: classical thermodynamics]]
	[[category: quantum mechanics]]		[[category: quantum mechanics]]

Carl McBride: Added original reference

2012-01-13T15:11:58Z

Added original reference

← Older revision		Revision as of 17:11, 13 January 2012
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	The '''third law of thermodynamics''' (or '''Nernst's theorem''' after the experimental work of Walther Nernst) states that the [[entropy]] of a system approaches a minimum (that of its ground state) as one approaches the [[temperature]] of absolute zero. One can write		The '''third law of thermodynamics''' (or '''Nernst's theorem''' after the experimental work of Walther Nernst in 1906 <ref>[http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN252457811_1906 W. Nernst "Ueber die Berechnung chemischer Gleichgewichte aus thermischen Messungen" Königliche Gesellschaft der Wissenschaften zu Göttingen Mathematisch-physikalische Klasse. Nachrichten, pp. 1-40 (1906)]</ref>) states that the [[entropy]] of a system approaches a minimum (that of its ground state) as one approaches the [[temperature]] of absolute zero. One can write

	:<math>\lim_{T \rightarrow 0} \frac{S(T)}{N} = 0</math>		:<math>\lim_{T \rightarrow 0} \frac{S(T)}{N} = 0</math>
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	:<math>\alpha := \frac{1}{V} \left. \frac{\partial V}{\partial T} \right\vert_p = -\frac{1}{V} \left. \frac{\partial S}{\partial p} \right\vert_T \rightarrow 0</math>		:<math>\alpha := \frac{1}{V} \left. \frac{\partial V}{\partial T} \right\vert_p = -\frac{1}{V} \left. \frac{\partial S}{\partial p} \right\vert_T \rightarrow 0</math>
	==References==		==References==
	#[http://dx.doi.org/10.1088/0305-4470/22/1/021 P. T. Landsberg "A comment on Nernst's theorem", Journal of Physics A: Mathematical and General '''22''' pp. 139-141 (1989)]		<references/>
			;Related reading
			*[http://dx.doi.org/10.1088/0305-4470/22/1/021 P. T. Landsberg "A comment on Nernst's theorem", Journal of Physics A: Mathematical and General '''22''' pp. 139-141 (1989)]
	[[category: classical thermodynamics]]		[[category: classical thermodynamics]]
	[[category: quantum mechanics]]		[[category: quantum mechanics]]

Carl McBride: Corrected typos.

2010-01-22T11:22:32Z

Corrected typos.

← Older revision		Revision as of 13:22, 22 January 2010
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	where <math>N</math> is the number of particles. Note that there are systems whose ground state entropy is not zero, for example metastable states or glasses, or systems with weakly or non-coupled spins that are not subject to an ordering field.		where <math>N</math> is the number of particles. Note that there are systems whose ground state entropy is not zero, for example metastable states or glasses, or systems with weakly or non-coupled spins that are not subject to an ordering field.
	==Implications==		==Implications==
	The [[heat capacity]] (for either [[pressure]] or volume) tends to zero as one approaches absolute zero. ~~Form~~		The [[heat capacity]] (for either [[pressure]] or volume) tends to zero as one approaches absolute zero. From

	:<math>C_{p,V}(T)= T \left. \frac{\partial S}{\partial T} \right\vert_{p,V} </math>		:<math>C_{p,V}(T)= T \left. \frac{\partial S}{\partial T} \right\vert_{p,V} </math>
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	thus <math>C \rightarrow 0</math> as <math>T \rightarrow 0</math>, otherwise the integrand would become infinite.		thus <math>C \rightarrow 0</math> as <math>T \rightarrow 0</math>, otherwise the integrand would become infinite.

	Similarly for [[thermal expansion coefficient]]		Similarly for the [[thermal expansion coefficient]]

	:<math>\alpha := \frac{1}{V} \left. \frac{\partial V}{\partial T} \right\vert_p = -\frac{1}{V} \left. \frac{\partial S}{\partial p} \right\vert_T \rightarrow 0</math>		:<math>\alpha := \frac{1}{V} \left. \frac{\partial V}{\partial T} \right\vert_p = -\frac{1}{V} \left. \frac{\partial S}{\partial p} \right\vert_T \rightarrow 0</math>

Carl McBride: New page: The '''third law of thermodynamics''' (or '''Nernst's theorem''' after the experimental work of Walther Nernst) states that the entropy of a system approaches a minimum (that of its gr...

2008-11-07T18:20:58Z

New page: The '''third law of thermodynamics''' (or '''Nernst's theorem''' after the experimental work of Walther Nernst) states that the entropy of a system approaches a minimum (that of its gr...

New page

The '''third law of thermodynamics''' (or '''Nernst's theorem''' after the experimental work of Walther Nernst) states that the [[entropy]] of a system approaches a minimum (that of its ground state) as one approaches the [[temperature]] of absolute zero. One can write

:<math>\lim_{T \rightarrow 0} \frac{S(T)}{N} = 0</math>

where <math>N</math> is the number of particles. Note that there are systems whose ground state entropy is not zero, for example metastable states or glasses, or systems with weakly or non-coupled spins that are not subject to an ordering field.
==Implications==
The [[heat capacity]] (for either [[pressure]] or volume) tends to zero as one approaches absolute zero. Form

:<math>C_{p,V}(T)= T \left. \frac{\partial S}{\partial T} \right\vert_{p,V} </math>

one has

:<math>S(T) - S(0) = \int_0^x \frac{C_{p,V}(T)}{T} ~\mathrm{d}T</math>

thus <math>C \rightarrow 0</math> as <math>T \rightarrow 0</math>, otherwise the integrand would become infinite.

Similarly for [[thermal expansion coefficient]]

:<math>\alpha := \frac{1}{V} \left. \frac{\partial V}{\partial T} \right\vert_p = -\frac{1}{V} \left. \frac{\partial S}{\partial p} \right\vert_T \rightarrow 0</math>
==References==
#[http://dx.doi.org/10.1088/0305-4470/22/1/021 P. T. Landsberg "A comment on Nernst's theorem", Journal of Physics A: Mathematical and General '''22''' pp. 139-141 (1989)]
[[category: classical thermodynamics]]
[[category: quantum mechanics]]