Calculates the Boltzmann partition function Z = Σexp(−Eᵢ/kT) for a two-level system and the probability of each energy state. For a two-level system with energy gap ΔE = kT, populations differ by factor e ≈ 2.72 — NMR exploits the tiny excess population in the lower energy spin state.
Inputs
E1 Ev
Capacity to do work (J or kWh). Conserved — converts between forms but total stays constant in a closed system.
E2 Ev
Capacity to do work (J or kWh). Conserved — converts between forms but total stays constant in a closed system.
G1
Reference formula or conversion factor shown for context.
G2
Reference formula or conversion factor shown for context.
T K
Thermal state of the substance. Check whether the formula needs Celsius, Fahrenheit, or Kelvin (K = °C + 273.15).
Results
partition function Z
The type of mathematical function or operational classification determined by the calculation.
probability of level 1 P1
The measured or computed level on the applicable scale.
probability of level 2 P2
The measured or computed level on the applicable scale.
mean energy ⟨E⟩ (eV)
Arithmetic average — sum divided by count. Simple and familiar, but pulled by outliers. If your data contains extreme values, the median may be more representative.
Z = Σ gi·e^(−Ei/kBT)
Reference formula or conversion factor shown for context.