Physics · Advanced university
Partition function of a two-level system
Ground energy is zero with degeneracy 1; the excited level has degeneracy g. Energies are measured from the ground state.
Method and conditions
Ground energy is zero with degeneracy 1; the excited level has degeneracy g. Energies are measured from the ground state.
Z = 1 + g exp(−Δ/kBT)
Worked examples
A canonical system has a nondegenerate ground level at 0 and an excited level of degeneracy 2. If Δ/(kBT)=1.4, calculate Z. Round the final result to 4 decimal places if needed.
Sum the ground weight 1 and all 2 equal excited weights exp(−1.4).
1.4932
A canonical system has a nondegenerate ground level at 0 and an excited level of degeneracy 9. If Δ/(kBT)=2, calculate Z. Round the final result to 4 decimal places if needed.
Sum the ground weight 1 and all 9 equal excited weights exp(−2).
2.218
Try it
A canonical system has a nondegenerate ground level at 0 and an excited level of degeneracy 2. If Δ/(kBT)=2.1, calculate Z. Round the final result to 4 decimal places if needed.
A canonical system has a nondegenerate ground level at 0 and an excited level of degeneracy 10. If Δ/(kBT)=0.3, calculate Z. Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 1.2449
Sum the ground weight 1 and all 2 equal excited weights exp(−2.1).
- 8.4082
Sum the ground weight 1 and all 10 equal excited weights exp(−0.3).
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