1. 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

2. 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

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
Since
finite at a given T
(*)
Requires quantum mechanics to
derive it in terms of statistical mechanics
From Nernst theorem
With Maxwell relation

4. 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

5. 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