Editing Third law of thermodynamics
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The '''third law of thermodynamics''' (or '''Nernst's theorem''' after the experimental work of Walther Nernst | 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> | :<math>\lim_{T \rightarrow 0} \frac{S(T)}{N} = 0</math> | ||
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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. | 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> | :<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 | 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> | :<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)] | |||
[[category: classical thermodynamics]] | [[category: classical thermodynamics]] | ||
[[category: quantum mechanics]] | [[category: quantum mechanics]] | ||