- #1

Dassinia

- 144

- 0

## Homework Statement

As a model of a paramagnet, consider a system of N fixed particles with spin 1/2 in a magnetic fiels H along z axis. Each particle has an energy e=μH (spin up) or e=-μH

Using S=kln(Ω), show that

S=k [ (N-E/e)/2 ln( 2N/(N-E/e) ) + (N+E/e)/2 ln( 2N/(N+E/e) ) ]

## Homework Equations

## The Attempt at a Solution

Ω= N!/(N+!N-!)

I used the Stirling approximation

ln(Ω)= NlnN - ( n

_{+}ln(n+) + n

_{-}ln(n-) )

Then replaced

n

_{+}=1/2 (N+E/e)

n

_{-}=1/2(N-E/e)

S= N*lnN + 1/2(N+E/e) ln (2/ (N+E/e)) + 1/2(N-E/e) ln (2/(N-E/e)

Then I don't know what to do with the N*lnN to get the (2N) in the numerator inside the ln .?

Thanks