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Carnot Cycle & Heat Engine Calculator

Carnot Engine Efficiency

Carnot Efficiency Formula:
η = 1 - T_c/T_h = (T_h - T_c)/T_h
Where: η = efficiency, T_h = hot reservoir temperature (K), T_c = cold reservoir temperature (K)
This represents the maximum theoretical efficiency for any heat engine.
Common Temperature Examples:
Steam turbine: T_h ≈ 873K (600°C)
Automobile engine: T_h ≈ 773K (500°C)
Room temperature: 293K (20°C)
Refrigerator: T_c ≈ 273K (0°C)

Note: Carnot efficiency is theoretical maximum - real engines are less efficient.

Heat Engine Work & Energy

Heat Engine Relations:
W = Q_h - Q_c (Work = Heat absorbed - Heat rejected)
η = W/Q_h = (Q_h - Q_c)/Q_h
Q_c/Q_h = T_c/T_h (for Carnot cycle)
COP_heat = Q_h/W (Coefficient of Performance for heat pump)
Typical Engine Efficiencies:
Gasoline engine: 25-30%
Diesel engine: 35-40%
Steam turbine: 35-45%
Gas turbine: 35-40%
Fuel cell: 40-60%
Electric motor: 90-95%

Refrigerator & Heat Pump

Refrigeration Cycle Formulas:
COP_ref = Q_c/W = T_c/(T_h - T_c) (Coefficient of Performance - Refrigerator)
COP_hp = Q_h/W = T_h/(T_h - T_c) (Coefficient of Performance - Heat Pump)
COP_hp = COP_ref + 1
W = Q_h - Q_c (Work input required)
Typical COP Values:
Home refrigerator: 2-4
Air conditioner: 2.5-4
Heat pump: 3-5
Commercial freezer: 1-2

Note: Higher COP means more efficient operation

Entropy & Carnot Cycle Analysis

Entropy and Carnot Relations:
ΔS = Q/T (Entropy change)
ΔS_universe ≥ 0 (Second Law of Thermodynamics)
For Carnot cycle: ΔS_total = 0 (reversible process)
For real engines: ΔS_total > 0 (irreversible process)
Carnot Cycle Processes:
1. Isothermal expansion (T_h)
2. Adiabatic expansion
3. Isothermal compression (T_c)
4. Adiabatic compression

Key Property:
Net entropy change = 0 for complete cycle