Editing Nernst heat theorem (section)

== The theorem ==
The Nernst heat theorem says that as absolute zero is approached, the entropy change Δ''S'' for a chemical or physical transformation approaches 0.  This can be expressed mathematically as follows:

:<math> \lim_{T \to 0} \Delta S = 0 </math>

<br>The above equation is a modern statement of the theorem.  Nernst often used a form that avoided the concept of entropy.<ref>{{cite book | last = Nernst | first = Walther | title = The New Heat Theorem | url = https://archive.org/details/in.ernet.dli.2015.206086 | publisher = Methuen and Company, Ltd | year = 1926 }} – Reprinted in 1969 by Dover – See especially pages 78 &ndash; 85</ref>

[[Image:Nernst Walter graph.jpg|right|thumb|Graph of energies at low temperatures]]

Another way of looking at the theorem is to start with the definition of the [[Gibbs free energy]] (''G''), <math>G = H-TS</math>, where ''H'' stands for [[enthalpy]].  For a change from reactants to products at constant temperature and pressure the equation becomes <math>\Delta G = \Delta H - T\Delta S</math>.

In the limit of ''T'' = 0 the equation reduces to just Δ''G'' = Δ''H'', as illustrated in the figure shown here, which is supported by experimental data.<ref>{{cite book | last = Nernst | first = Walther | title = Experimental and Theoretical Applications of Thermodynamics to Chemistry | publisher = Charles Scribner's Sons | year = 1907 |location = New York | pages = [https://archive.org/details/experimentaland00nerngoog/page/n60 46]| url = https://archive.org/details/experimentaland00nerngoog| quote = Walther Nernst. }} – The labels on the figure have been modified.  The original labels were A and Q, instead of ΔG and ΔH, respectively.</ref> However, it is known from [[Gibbs–Helmholtz equation|thermodynamics]] that the slope of the Δ''G'' curve is −Δ''S''.  Since the slope shown here reaches the horizontal limit of 0 as ''T'' → 0 then the implication is that Δ''S'' → 0, which is the Nernst heat theorem.

The significance of the Nernst heat theorem is that it was later used by [[Max Planck]] to give the [[third law of thermodynamics]], which is that the entropy of all pure, perfectly crystalline homogeneous materials in complete internal equilibrium is 0 at [[absolute zero]].