Thermodynamic Cycles

Physics: Carnot efficiency η_C = 1 − T_C/T_H — the absolute maximum for any heat engine operating between two reservoirs; this bound follows from the second law. Otto cycle (gasoline engine): η = 1 − r^(1−γ) where r is compression ratio and γ = C_p/C_v ≈ 1.4. Diesel cycle: η = 1 − (r_c^γ − 1)/(γ·r^(γ−1)·(r_c−1)) where r_c is cutoff ratio. Kelvin-Planck statement: no engine operating in a cycle can convert heat entirely to work; Clausius: ΔS_universe ≥ 0 for any process, with equality only for reversible (Carnot) cycles.