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The “Zeroth Law” of Thermodynamics
Definition: Thermal Equilibrium:
• 2 systems are in thermal equilibrium:
If & only if there is no NET flow of heat
between them when they are brought
into thermal contact.
• A system’s Temperature is an indicator of
Thermal Equilibrium
because, if 2 systems at the same temperature are in
thermal contact,
There is no net flow of
heat between them.
The “Zeroth Law” of Thermodynamics
A
TA
B
TB
• Consider 3 Objects, A, B C:
C
TC
The “Zeroth Law” of Thermodynamics
A
TA
B
TB
C
TC
• Consider 3 Objects, A, B C:
“If A is in thermal equilibrium with B &
if B is in thermal equilibrium with C,
then A is in thermal equilibrium with C”.
The “Zeroth Law” of Thermodynamics
A
TA
B
TB
C
TC
• Consider 3 Objects, A, B C:
“If A is in thermal equilibrium with B &
if B is in thermal equilibrium with C,
then A is in thermal equilibrium with C”.
• In terms of system Temperatures:
If TA = TB & TB = TC, then TA = TB.
The ZEROTH Law is
1. The main reason that
thermometers work!
& also
2. The main reason that
they are useful!!
A More General Discussion!
• As we know, if warm & cold objects are placed
in thermal contact, Heat Energy Q flows
from the Warm Object to the Cold Object
until Thermal Equilibrium is established.
A More General Discussion!
• As we know, if warm & cold objects are placed
in thermal contact, Heat Energy Q flows
from the Warm Object to the Cold Object
until Thermal Equilibrium is established.
“0th” Law of Thermodynamics
“If 2 systems are both in thermal
equilibrium with a 3rd system, they are
in thermal equilibrium with each
other”
th
“0 ”
Law of Thermodynamics
“If 2 systems are both in thermal
equilibrium with a 3rd system, they are
in thermal equilibrium with each other”
• The property which the 3 systems have in
common is known as a
Thermometric Parameter, X.
• So, generally,
The “0th” Law of Thermodynamics is
If X1 = X2 & X1 = X3, then X2 = X3.
The “Zeroth” Law of Thermodynamics
Example
The “Zeroth” Law of Thermodynamics
Example
Another Example of the “Zeroth” Law
a)
b)
B
C
A
VA, PA VC, PC
C
VB, PB VC, PC
“If 2 systems are in thermal equilibrium with a 3rd
system, they are in equilibrium with each other.”
c)
A
B
VA, PA VB, PB
The “0th Law” of Thermodynamics
“If 2 systems are in thermal equilibrium with
a 3rd system, they are in thermal equilibrium
with each other.”
• For gases, this leads to an Equation of State:
q = f(P,V )
where the parameter q (= temperature)
characterizes the equilibrium.
• Even more useful is the fact that this same value
of q also characterizes any other system which is
in thermal equilibrium with the first system,
regardless of its state.
The 3rd Law of Thermodynamics
•The 3rd Law of Thermodynamics is
a Quantum Mechanical Law that
fixes the absolute value of the entropy:
S → 0 as T → 0
The 3rd Law of Thermodynamics
•The 3rd Law of Thermodynamics is
a Quantum Mechanical Law that
fixes the absolute value of the entropy:
S → 0 as T → 0
•Reif’s statement of the 3rd Law is
S → S0 as T → 0+
with 0+ < ~ 0.01 K
Corollary to the 3rd Law:
The attainment of a temperature of T = 0 K
(“Absolute Zero”) is not possible.
• The 3rd Law says that the entropy-temperature curves for a
fixed external parameter, such as magnetic field, meet at T → 0.
So, it is impossible to reach T = 0 in a finite number of steps.
Adiabatic
Processes
Isothermal
Processes
Another Statement of
rd
The 3 Law of Thermodynamics
“As T  0, the entropy of a pure
substance S  0.”
• In general, we know that S = kBln(Ω)
• So, as the total system energy approaches its
ground quantum mechanical state of energy
E  E0, the temperature T  0
& Ω  1 so S  0
The
rd
3
Law of Thermodynamics
Entropy S = kBln(Ω)
As T  0 , E  E0, & Ω  1 so S  0
Ordered
System
Disordered
System
The 3rd Law of Thermodynamics
The entropy of a pure substance at
T = 0 is S = 0.