TS · Thermodynamics and statistical mechanics

Two engines can obey energy conservation, yet only one obeys the entropy 熵 limit on efficiency.

Prerequisites: 19, 20, 34, 35, 36.

• Apply the first and second laws with a sign convention
• Relate ensembles, Boltzmann factors and entropy
• Analyse ideal gases, heat engines and quantum statistics

State the first-law sign convention: ΔU=Q−W when W is work done by the system.

For a reversible engine between reservoirs, efficiency is bounded by 1−Tc/Th using absolute temperatures.

Boltzmann weights are exp(−E/kT). Probabilities require division by the partition function 配分函数.

Distinguish Maxwell–Boltzmann, Bose–Einstein and Fermi–Dirac assumptions. Fermions cannot share an identical single-particle state.

Use work W done by the gas as positive. The first law 热力学第一定律 is

For reversible isothermal expansion of an ideal gas, U depends only on T, so For n = 0.50 mol, T = 300 K and doubled volume, The gas expands and receives heat. The reservoir loses the same entropy in this reversible limit.

Celsius temperature ratios cannot be used in the Carnot efficiency formula.

entropy: A state quantity connected to multiplicity and reversible heat transfer.

partition function: The sum of statistical weights used to normalise probabilities.