# Two State paramagnet

1. Feb 4, 2009

### Vuldoraq

1. The problem statement, all variables and given/known data

Consider a two-state paramagnet with 10^23 elementary dipoles, with the total energy ﬁxed at zero so that exactly half the dipoles point up and half point down.

(a) How many microstates are “accessible” to this system?

(b) Suppose that the microstate of this system changes 10^9 times per second. How many
microstates will it explore in 10^10 years (the age of the universe)?

(c) Is it correct to say that, if you wait long enough, a system will eventually be found in
every“accessible”microstate? Explain youranswer, and discuss the meaning of the word
“accessible”.

2. Relevant equations

Multiplicity of a macrostate=$$\frac{N\factorial}{N(up)\factorial*N(down)\factorial}$$

3. The attempt at a solution

Hi, It's only really part (a) and (c) that I am stuck on.

Using the above formula with N(up)=N(down)=5*10^22 and N=10^23, gives

Number of microstates=$$\frac{10^{23}\factorial}{(5*10^{22})\factorial\*(5*10^{22})\factorial$$

This seems like a very large number, have I made an error?

Also, is it right to say that by accessible they mean the number of microstates possible given any restraints the system may have?

Thanks in advance for any help.

Edit:There should be factorials after all the N's in the above expressions and also the Latex generation has failed for some reason. Sorry, if you want me to write out without Latex just say. Thanks.

2. Feb 4, 2009

### Delphi51

I'm interested in this, though I know very little about it. Just an old retired school teacher.

The multiplicity formula doesn't make sense to me. Can you explain why it is?
It seems to me the part (a) is similar to the "how many difference license plate" questions we give in grade 12. How many different states for the first dipole x how many for the second, and so on so (2^10)^23. Yes, a HUGE number. I wonder if a calculator can show the answer? I hope you will post the awer so I can see it.

(b) and (c) boggle my mind! It could be changing to a microstate it had already been in previously, cutting down on the number "explored".