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Published byGilbert Elliot Modified over 2 years ago

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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. Walther Nernst (consider e.g. a chemical reaction ) 1 2 Albert Einstein Max Planck Robert Milikan Max von Laue Motivated by considering reactions in the limit of decreasing temperature

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

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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 From Nernst theorem With Maxwell relationMaxwell relation (*)(*) Requires quantum mechanics to derive it in terms of statistical mechanics

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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. S T P P’ isothermal compression adiabatic expansion Gas compression refrigeration T+ T ad T T T- T ad T +P+P -Q -P-P +Q P=P-P’ According to 3 rd 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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3 rd law and Boltzmann’s entropy expressionBoltzmann’s entropy expression W: # of possible microstates S=k B 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): E0E0 E1E1 sufficient low T system will be in its ground state If there are g 0 eigenstates with the same energy E 0 we say ground state is degenerate # of microstates representing the same macro state is W=g 0 and, hence If ground state is non degenerate and

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