1. Thermal Physics Too many particles… can’t keep track!
Use pressure (p) and volume (V) instead.
Temperature (T) measures the tendency of an object to spontaneously give up/absorb energy to/from its surroundings. (p and T will turn out to be related to the too many particles mentioned above)
p, V, and T are related by the equation of state: f(p,V,T) = 0
e.g. pV = NkBT
Heat is energy in transit and it is somehow related to temperature

2. Zeroth law of thermodynamics
If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other. A C
Diathermal wall
C can be considered the thermometer. If C is at a certain temperature then A and B are also at the same temperature. B C

3. Temperature is related to heat and somehow related to the motion of particles
Need an absolute definition of temperature based on fundamental physics
A purely thermal physics definition is based on the Carnot engine
Can also be defined by statistical arguments

5. Combinatorial problemG B R B G R G B B B R G B G R R G R G B G B R G B R G G R B G B R R B R G B R B G G B R G R B B R G B G R G B R B G R R B G B B R G R G G R B

6. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

7. Microstates and Macrostates1

8. Microstates and Macrostates1

9. Microstates and Macrostates1
All these microstates belong to the macrostate of 1 head in 100 coins

10. Number of Microstates ()
Macrostate

11. n = 170;
x = 0:1:n;
y = factorial(n)./(factorial(x).*factorial(n-x));
figure;
plot(x,y);

12. How is all this @#$%^& related to thermal physics?
Each microstate is equally likely
The microstate of a system is continually changing
Given enough time, the system will explore all possible microstates and spend equal time in each of them (ergodic hypothesis).
How is all related to thermal physics?

15. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

16. Big question:
How do we relate the number of microstates for a particular macrostate to temperature?

17. E1 E2 + E - E T1 < T2 But no particular relation for E1 and E2
At thermal equilibrium the temperature (whatever it is) will be the same for both systems. Total energy E = E1 + E2 is conserved.

19. clear all;
n1 = 4;
n2 = 8;
e = 6;
i = 0;
for x = 0:1:n1
y1 =(factorial(n1)./(factorial(x).*factorial(n1-x)));
y2 = (factorial(n2)./(factorial(e-x).*factorial(n2-(e-x))));
i=i+1;
y(i)=y1*y2
x1(i)=x;
end
figure;
plot(x1,y);

20. Each microstate is equally likely
The microstate of a system is continually changing
Given enough time, the system will explore all possible microstates and spend equal time in each of them (ergodic hypothesis).

21. Most likely macrostate the system will find itself in is the one with the maximum number of microstates.

22. Zeroth law of thermodynamics
If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other. A C
Diathermal wall
C can be considered the thermometer. If C is at a certain temperature then A and B are also at the same temperature. B C

23. Most likely macrostate the system will find itself in is the one with the maximum number of microstates. E
(E) E1
1(E1) E2
2(E2)
System A
System C

24. Most likely macrostate the system will find itself in is the one with the maximum number of microstates. E
(E) E1
1(E1) E2
2(E2)

25. Ensemble: All the parts of a thing taken together, so that each part is considered only in relation to the whole.

26. E
(E)
Microcanonical ensemble: An ensemble of snapshots of a system with the same N, V, and E

27. Microcanonical ensemble: An ensemble of snapshots of a system with the same N, V, and E
Canonical ensemble: An ensemble of snapshots of a system with the same N, V, and T E2
2(E2) E1
1(E1)