Thermal Physics: Understanding the Relationship Between Pressure, Volume, and Temperature

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

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5. Microstates and Macrostates 1

6. Microstates and Macrostates 1

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

8. Most likely macrostate the system will find itself in is the one with the maximum number of microstates. Number of Microstates () Macrostate

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

10. 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 this @#$%^& related to thermal physics?

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

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

16. 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);

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

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

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

20. 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)