THERMODYNAMIC CYCLES

Heat-engine cycles convert thermal energy to work; refrigeration cycles do the opposite using work input. Carnot is the upper-bound efficiency η = 1 - Tc/Th between hot and cold reservoirs. Otto (gasoline IC engine) efficiency η = 1 - 1/r^(γ-1) depends on compression ratio r. Diesel adds heat at constant pressure: η = 1 - (1/r^(γ-1))·(rc^γ - 1)/[γ(rc - 1)]. Brayton (gas turbine) η = 1 - 1/rp^((γ-1)/γ) depends on pressure ratio rp. Vapor-compression: COP = Qc/W_in.

• η_Carnot = 1 - Tc/Th
• η_Otto = 1 - r^(1-γ)
• η_Brayton = 1 - rp^((1-γ)/γ)
• COP_R = Qc / W_in
• COP_HP = Qh / W_in = COP_R + 1

References & StandardsCengel "Thermodynamics" Ch. 9-11, ASHRAE Fundamentals Ch. 2

Use for first-pass cycle analysis and component sizing in engines, turbines, refrigerators, heat pumps. Compute ideal efficiency or COP, then derate for real-component irreversibilities (compressor isentropic efficiency 0.7-0.85, turbine 0.85-0.92). For refrigeration, COP_real ≈ 0.4-0.6 × COP_Carnot at typical evaporator/condenser temperatures.