Folie 1

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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
)
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Max Planck
Albert Einstein
Robert Milikan
Walther Nernst
Max von Laue
Motivated by considering reactions in the limit
of decreasing temperature
2
We know at P, Tconst. equilibrium
thermodynamics determined by G?min.
controls reaction
Experimental finding
for
heat flow into bath (exotherm) but sometimes also
out of the bath (endotherm)
Tconst.
(see thermodynamic potentials)
and
With
Nernst proposed as a general principle
for
?G, ?H
,
and
From
T
3
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
finite at a given T
Since
()
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.
S
?PP-P
P
isothermal compression
P
adiabatic expansion
T
According to 3rd law
S(T,P)S(T,P) for T0
T0 not achievable in a finite of compression
and expansion steps
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W of possible microstates
3rd law and Boltzmanns entropy expression
SkB ln W
Although we dont 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
_at_ 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 Wg0 and, hence
and
If ground state is non degenerate