Statistical Physics: Paramagnetic Solid with Spin S=1 and Magnetic Momentum µ_B

[ziad1985]

I have a paramagnatic solid, where the atoms have a spin S=1 , and a magnetic momentum
$\mu_{B}$
We have a magnetic field:
$\vec{B}$
Under the influence of B the atoms can take 3 value of energy e,-e,0
$e=g.\mu_{B}.B$
The solid is maintained at a Temperature T and N number of atoms.
The question are like the following:
1)write the partition function of each atom z, then deduce the one of the whole solid Z.
2)E(T)= ??
Limit of E(T--->0)= ??
Limit of E(T---> Large)= ??
3) same question for the entropy S(T)My work:
1)z=1+2.Cosh(e/KT)
Z=(1+2.Cosh(e/KT))^N

2)$E(T)=-N.\frac{2.e.Sinh(e/KT)}{1+2.Cosh(e/KT)}$
If T--->0 E(T)---> -N.e
if T--->Large E(T) ---> 0
3)S(T)=K.Ln(Z) +E/T
T---> 0 S(T)=N.K.Ln(2)
T---> Large S(T)=0I feel I messed it all up, anyone to help ?

 

[ziad1985]

I didn't write the steps in between, fairly easy, the limits I have checked them with a Matlab, and the derivatives I have checked them twice.
But I feel my work is not correct.
there is more questions, but need to check those before.