Statistical Physics/thermodynamics

[vauxhall]

Homework Statement

The atomic nuclei of the atoms in a solid have spin one. Each nucleus may therefore exist in three different quantal states with spin projection m=-1,0,+1. Due to the symmetri of the electrical field inside the solid these states have eneries E=$$\epsilon$$ for m=$$\pm$$1 and E=0 for m=0.

Calculate the contribution to the energy from the nuclei at temperature T. Consider the contribution from the nuclei tp the specific heat. Plot this function and discuss how it can be observed.

Homework Equations

Helmholtz free energy: F= U-TS
The necessary energy to create a system minus the heat we can get from the surrounding at temperature T.
Stirlings formula: ln $$\Omega$$=ln$$\left($$$$\frac{N!}{n!\left(N-n\right)!}$$$$\right)$$

The Attempt at a Solution

 

[NateD]

The contribution to the energy and specific heat from the nuclei at temperature T would be related to the Helmholtz free energy. The Helmholtz free energy is equal to F=U-TS, where U is the necessary energy to create a system, T is the temperature, and S is the entropy of the system. The entropy of the system can be calculated using Stirling's formula: ln \Omega=ln\left(\frac{N!}{n!\left(N-n\right)!}\right), where N is the total number of nuclei and n is the number of nuclei in a particular spin state. Using the above equation, we can calculate the entropy of the system at different temperatures and plot it against the energy of the system. We can then observe how the energy and entropy of the system changes with temperature.