Third law of thermodynamics
The third law of thermodynamics (or Nernst's theorem after the experimental work of Walther Nernst in 1906
\[\lim_{T \rightarrow 0} \frac{S(T)}{N} = 0\]
where \(N\) 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.
[edit] Implications
The heat capacity (for either pressure or volume) tends to zero as one approaches absolute zero. From
\[C_{p,V}(T)= T \left. \frac{\partial S}{\partial T} \right\vert_{p,V} \]
one has
\[S(T) - S(0) = \int_0^x \frac{C_{p,V}(T)}{T} ~\mathrm{d}T\]
thus \(C \rightarrow 0\) as \(T \rightarrow 0\), otherwise the integrand would become infinite.
Similarly for the thermal expansion coefficient
\[\alpha := \frac{1}{V} \left. \frac{\partial V}{\partial T} \right\vert_p = -\frac{1}{V} \left. \frac{\partial S}{\partial p} \right\vert_T \rightarrow 0\]
[edit] References
- ↑ W. Nernst "Ueber die Berechnung chemischer Gleichgewichte aus thermischen Messungen" Königliche Gesellschaft der Wissenschaften zu Göttingen Mathematisch-physikalische Klasse. Nachrichten, pp. 1-40 (1906)
- Related reading
