1. The “Zeroth Law” of Thermodynamics

2. 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.

3. The “Zeroth Law” of ThermodynamicsB TB C TC A TA
Consider 3 Objects, A, B C:

4. The “Zeroth Law” of ThermodynamicsB TB C TC A TA
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”.

5. The “Zeroth Law” of ThermodynamicsB TB C TC A TA
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.

6. The ZEROTH Law is The main reason that thermometers work!
& also
The main reason that they are useful!!

7. 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. 7

8. A More General Discussion! “0th” Law of Thermodynamics
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” 8

9. “0th” Law of Thermodynamics The “0th” Law of Thermodynamics is
“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. 9

10. The “Zeroth” Law of Thermodynamics
Example

11. The “Zeroth” Law of Thermodynamics
Example

12. Another Example of the “Zeroth” Lawb) B C A C
VA, PA
VC, PC
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

13. 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.

14. 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 14

15. 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 15

16. 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. 16

17. 3rd Law: Attainment of a temperature of
T = 0 K (“Absolute Zero”) is not possible.
This 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.
Isothermal
Processes
Adiabatic
Processes 17

18. The 3rd Law of Thermodynamics
Another Statement of
The 3rd 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

19. The 3rd Law of Thermodynamics
Entropy S = kBln(Ω)
As T  0 , E  E0, & Ω  1 so S  0
Ordered System
Disordered System

20. The 3rd Law of Thermodynamics The entropy of a pure substance at
T = 0 is S = 0.