Fermi liquid theory: Difference between revisions
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The | [[Image:Walther Nernst.jpg|thumb|right|130px|Walther Nernst]] | ||
The '''Nernst heat theorem''' was formulated by [[Walther Nernst]] early in the twentieth century and was used in the development of the [[third law of thermodynamics]]. | |||
== The theorem == | |||
The Nernst heat theorem says that as absolute zero is approached, the entropy change ΔS for a chemical or physical transformation approaches 0. This can be expressed mathematically as follow | |||
:<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 | publisher = Methuen and Company, Ltd | year = 1926 | pages = }}- Reprinted in 1969 by Dover - See especially pages 78 – 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), G = H - TS, 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 ΔG = ΔH, 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 = 46| url = http://books.google.com/books?id=sYsJAAAAIAAJ&printsec=frontcover&dq=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 ΔG curve is -ΔS. Since the slope shown here reaches the horizontal limit of 0 as T → 0 then the implication is that ΔS → 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 is 0 at [[absolute zero]]. | |||
== See also == | |||
* [[Theodore William Richards]] | |||
* [[Entropy]] | |||
== References and notes == | |||
<references /> | |||
== Further reading == | |||
* {{cite book | last = Denbigh | first = Kenneth | title = The Principles of Chemical Equilibrium | publisher = Cambridge University Press | edition = 3 | year = 1971 }}- See especially pages 421 – 424 | |||
== External links == | |||
* [http://www.nernst.de/#theorem Nernst heat theorem] | |||
[[Category:Thermochemistry]] | |||
[[de:Nernst-Theorem]] | |||
Revision as of 08:47, 3 February 2014
The Nernst heat theorem was formulated by Walther Nernst early in the twentieth century and was used in the development of the third law of thermodynamics.
The theorem
The Nernst heat theorem says that as absolute zero is approached, the entropy change ΔS for a chemical or physical transformation approaches 0. This can be expressed mathematically as follow
The above equation is a modern statement of the theorem. Nernst often used a form that avoided the concept of entropy.[1]
Another way of looking at the theorem is to start with the definition of the Gibbs free energy (G), G = H - TS, where H stands for enthalpy. For a change from reactants to products at constant temperature and pressure the equation becomes .
In the limit of T = 0 the equation reduces to just ΔG = ΔH, as illustrated in the figure shown here, which is supported by experimental data.[2] However, it is known from thermodynamics that the slope of the ΔG curve is -ΔS. Since the slope shown here reaches the horizontal limit of 0 as T → 0 then the implication is that ΔS → 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 is 0 at absolute zero.
See also
References and notes
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534- Reprinted in 1969 by Dover - See especially pages 78 – 85 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534- The labels on the figure have been modified. The original labels were A and Q, instead of ΔG and ΔH, respectively.
Further reading
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534- See especially pages 421 – 424