# Third law of Thermodynamics

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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

Experimental finding: for T=const.
We know: at P, T=const. equilibrium thermodynamics determined by Gmin. 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

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

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

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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