Lecture 4

Systems of many microscopic particles following reversible laws of motion have irreversible collective dynamics. The new concepts microstates, macrostates, multiplicity and most likely state will help explaining this apparent contradiction.

Lecture notes.

Video on microstates, macrostates and multiplicity. Example: two state model.

 

As you see you will need some of your knowledge in statistics. Some questions to recap:

1 How many ways are there to arrange the cards in 52-cards?

A) 52!       B) 5252      C) 252        D) Some other number

2 You flip a coin 10 times.  How many sequences (like HHTTHTHTTH)  or microstates are possible?

A) 10!     B) 102        C) 210        D) Some other number

3 You flip a coin 10 times.  How many combinations are there with 2 heads and 8 tails?  (Like TTTHTTTTHT )

A) 1024     B) 100       C) 90         D) 45        E) Some other number

4 You flip a coin 10 times.  What is the probability that you will get 2 heads and 8 tails (in any order)?

A) 45/(210)         B) 45/100          C) 45/10!           D) 45/90  E) Some other number

 

Video on multiplicity of 3 models: 2-state paramagnet, random walk and Einstein crystal

 

5 Einstein solid with N = 3, q = 4.  What is W(N = 3, q = 4)?

A) 43         B) 34          C) 3×4 = 12        D) 15        E) Some other number

 

Video on coupled Einstein crystals: Thermal equilibrium.

 

6 Two Einstein solids, A and B, are in thermal contact.  The two solids are thermally isolated from the rest of the universe. NA?  = NB = 10.   qtot = qA + qB = 20. How many macrostates are there?

A) 10         B) 21         C) 2020      D)        E) 20

 

7  Two Einstein solids, A and B, are in thermal contact. The two solids are thermally isolated from the rest of the universe. NA?  = NB = 10.   qtot = qA + qB = 20.  Are all the microstates of solid A equally likely?

A) Yes      B) No

Video on Matlab calculation of multiplicity of coupled Einstein crystals and corresponding Matlab script

Video on Matlab simulation of "heat conduction" between coupled Einstein crystals and corresponding Matlab script

 

Is the development in this movie impossible or just very unlikely?

 

 

Publisert 26. aug. 2020 11:47 - Sist endret 28. aug. 2020 00:22