Editing Third law of thermodynamics

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]]