# Difference between revisions of "Third law of thermodynamics"

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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== | ||

− | + | <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)] | ||

+ | *[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]] |

## Latest revision as of 17:28, 14 March 2017

The **third law of thermodynamics** (or **Nernst's theorem** after the experimental work of Walther Nernst in 1906 ^{[1]}) 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

where 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[edit]

The heat capacity (for either pressure or volume) tends to zero as one approaches absolute zero. From

one has

thus as , otherwise the integrand would become infinite.

Similarly for the thermal expansion coefficient

## References[edit]

- Related reading