Statements of the third law
•The third law of thermodynamics is concerned with the
behavior of systems in equilibrium as temperature
approaches absolute zero.
S
T
đQ
 S0
T
•As long as we deal in differences in entropy, knowledge of
S0 is unnecessary.
•However, absolute entropy IS important, e.g.
F = U - TS
G = H - TS
Statements of the third law
•The Gibbs-Helmholtz equation:
 G 
G  H T 


T

P
•For an isothermal process:
   G  
G  H  T 


T

P
•These equations imply:
lim G  lim H
T 0
T 0
lim G  lim H
T 0
T 0
Statements of the third law
lim G  lim H
T 0
T 0
lim G  lim H
T 0
T 0
•Nernst postulated the following:
   G  
lim 
 0,

T 0
 T  P
   H  
lim 
0

T 0
 T  P
Statements of the third law
lim G  lim H
T 0
T 0
lim G  lim H
T 0
T 0
•Nernst postulate implies that:
   G2  G1  
 G2 G1 
lim 
 lim 

 lim  S1  S2   0


T 0
T
T  T 0

 P T 0  T
Statements of the third law
lim G  lim H
T 0
T 0
lim G  lim H
T 0
T 0
•The Nernst formulation of the Third Law:
‘All reactions in a liquid or solid in thermal equilibrium
take place with no change of entropy in the neighborhood
of absolute zero.’
Statements of the third law
lim G  lim H
T 0
T 0
lim G  lim H
T 0
T 0
•Planck later postulated that:
 G 
lim 
 0,

T 0  T 
P
 H 
lim 
0

T 0  T 
P

lim S  0
T 0
Statements of the third law
lim G  lim H
T 0
T 0
lim G  lim H
T 0
T 0
•Planck’s statement of the Third Law:
‘The entropy of a true equilibrium state of a system at
absolute zero is zero.’
Statements of the third law
lim G  lim H
T 0
T 0
lim G  lim H
T 0
T 0
•Another statement of the Third Law is:
‘It is impossible to reduce the temperature of a system to
absolute zero using a finite number of processes.’
Step 1: Isothermal increase of H
S
H
H1
M
H2 > H1
T3 T2
T1
T
dU  TdS  HdM
TdS (T , H )  CH dT  T  M / T  H dH
Step 2: Adiabatic demagnetization
S
B1
M
B2 > B1
T3 T2
T1
T
dU  TdS  HdM
TdS (T , H )  CH dT  T  M / T  H dH