Thermodynamics and Statistical Physics
Core concepts
Know the first law ΔU = Q − W (sign conventions matter) and the second law in both Kelvin–Planck and Clausius forms. Entropy change is ΔS = ∫dQ_rev/T, and irreversibility means ΔS_universe ≥ 0. Master the ideal gas law, the equipartition theorem (½kT per quadratic degree of freedom), and the Maxwell–Boltzmann distribution. For cycles, efficiency η = W/Q_in, with the Carnot limit η = 1 − T_c/T_h for temperatures in kelvin. Statistical ideas: microstates versus macrostates, Boltzmann factor exp(−E/kT), and the partition function Z = Σ exp(−E_i/kT), from which all thermodynamic quantities follow.
Traps
Always convert to kelvin-Carnot efficiency questions with Celsius answers are a classic distractor. Distinguish isothermal (ΔU = 0 for ideal gas, Q = W) from adiabatic (Q = 0, PV^γ constant) processes. Entropy of the system can decrease if the surroundings gain more. Reversible versus irreversible paths to the same endpoints give the same ΔS but different Q and W. For diatomic gases, count five degrees of freedom (three translational plus two rotational) at ordinary temperatures.
Worked example
A Carnot engine operates between 500 K and 300 K. Its efficiency is 1 − 300/500 = 0.40, so 40% of heat input becomes work. Rule of thumb: for any heat engine, η = 1 − Q_c/Q_in, and equality with the Carnot expression holds only for reversible operation.