Physics · Advanced university
Partition function of a two-level system · formula reference
Ground energy is zero with degeneracy 1; the excited level has degeneracy g. Energies are measured from the ground state.
Formula
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 example
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
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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