nicksauce

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**1. Homework Statement**

A certain magnetic system has N independent molecules per unit volume, each of which as 4 distinct energy levels: [tex]0, \Delta - \mu_BB, \Delta, \Delta + \mu_BB[/tex].

i) Write down the partition function, and hence find an expression for the Hemholtz function

ii) Use this expression to find the internal energy, U, and the magnetization M.

**2. Homework Equations**

[tex]F = -\frac{\ln{Z}}{\beta}[/tex]

[tex]U = F - T\frac{\partial F}{\partial T}[/tex]

**3. The Attempt at a Solution**

So I think I found the correct equations for the partition function, the hemholtz function and the energy, but I am not quite sure on how to calculate the magnetization. Any ideas?