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Thermodynamic Cycles

Carnot · Brayton · Otto · combined · COP

Efficiency vs Ratio

Brayton η=1−PR^(−(γ−1)/γ); Otto η=1−CR^(−(γ−1)). Curve marks the operating point.

Carnot Limit

η=1−T_L/T_H — the hard ceiling.

Combined Cycle

η=η_top+η_bot−η_top·η_bot.

Refrigerator / Heat Pump COP

Carnot COP_ref=T_L/(T_H−T_L); HP=T_H/(T_H−T_L).
Formula reference

Carnot η=1−T_L/T_H (Kelvin). Brayton η=1−PR^(−(γ−1)/γ). Otto η=1−CR^(−(γ−1)).

Combined η=η₁+η₂−η₁η₂. COP_ref =T_L/(T_H−T_L), COP_HP =T_H/(T_H−T_L)=COP_ref+1.