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**Third law of Thermodynamics**

Nernst heat theorem: In the neighborhood of absolute zero, all reactions in a liquid or solid in internal equilibrium take place with no change in entropy. (consider e.g. a chemical reaction ) 1 2 Albert Einstein Max Planck Robert Milikan Walther Nernst Max von Laue Motivated by considering reactions in the limit of decreasing temperature

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**Experimental finding: for T=const.**

We know: at P, T=const. equilibrium thermodynamics determined by Gmin. controls reaction Experimental finding: for T=const. heat flow into bath (exotherm) but sometimes also out of the bath (endotherm) (see thermodynamic potentials) With and Nernst proposed as a general principle: for G, H , and From T

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**Planck made further hypothesis known as the third law**

Entropy of every solid or liquid substance in internal equilibrium at absolute zero is itself zero Some consequences of the third law Since finite at a given T (*) Requires quantum mechanics to derive it in terms of statistical mechanics From Nernst theorem With Maxwell relation

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**It is impossible to reach the absolute zero temperature**

with a finite sequence of isothermal and adiabatic changes of pressure or other variables like the magnetic field, e.g., in the case of adiabatic demagnetization. Gas compression refrigeration T+Tad T T-Tad +P -Q -P +Q S P=P-P’ P isothermal compression P’ adiabatic expansion T According to 3rd law: S(T,P)=S(T,P’) for T=0 T=0 not achievable in a finite # of compression and expansion steps

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**W: # of possible microstates**

3rd law and Boltzmann’s entropy expression S=kB ln W Although we don’t focus on stat. mechanics it is useful to get an idea how the third law is related to the Boltzmann formula -Consider system described by a Hamilton operator with a discrete spectrum of energy-eigenvalues having a lower bound (ground state): E2 E1 @ sufficient low T system will be in its ground state E0 If there are g0 eigenstates with the same energy E0 we say ground state is degenerate # of microstates representing the same macro state is W=g0 and, hence If ground state is non degenerate and

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