Short Answer
Z = Σ e^(−βEᵢ) is the best answer.
Thermodynamics questions usually test sign conventions, state variables, or what is being held constant. Before calculating, decide whether the system is exchanging heat, doing work, or both.
Z = Σᵢ e^(−βEᵢ) where β = 1/(k_BT); all thermodynamic properties can be derived from Z.
Why This Answer Is Correct
This is a Hard-level question in Thermodynamics. The prompt is really testing whether you can connect the concept to its defining physical relationship instead of picking a nearby-but-wrong term.
Write the system boundary first. Many thermodynamics mistakes disappear once you know what counts as heat, work, and internal-energy change.
Choices At A Glance
- A. Z = Σ e^(βEᵢ)
- B. Z = Σ e^(−βEᵢ)
- C. Z = ln(W)
- D. Z = −kT ln(Ω)
When similar options appear on an exam, eliminate the ones that break the core law, use the wrong units, or confuse a definition with a consequence.
Topic Snapshot
Topic: Thermodynamics
Difficulty: Hard
Best next move: Re-state the governing law in your own words, then solve one more example from the same topic before moving on.