🔥 Classical Thermodynamics & Carnot Cycle
Carnot Heat Engine Efficiency Calculator
Compute the maximum theoretical thermodynamic efficiency ($\eta_{\text{carnot}} = 1 - \frac{T_C}{T_H}$), mechanical work output ($W$), rejected heat ($Q_C$), and heat pump $\text{COP}$.
🏭 Steam Power Plant (550°C ➔ 30°C)
⚡ Gas Turbine (1200°C ➔ 400°C)
⚛️ Nuclear Reactor (300°C ➔ 25°C)
🌊 OTEC Cycle (25°C ➔ 5°C)
Thermal Reservoirs
kJ
Maximum Carnot Efficiency (η_max)
63.17% Efficiency
Rejected Heat ($Q_C$)
368.3 kJ
Heat Pump COP
1.58
Refrigerator COP
0.58
💡 Carnot Cycle Formula:
$$\eta = 1 - \frac{T_C}{T_H} = 1 - \frac{303.15\text{ K}}{823.15\text{ K}} = 1 - 0.3683 = 63.17\%$$
The Second Law & The Carnot Limit
Nicolas Léonard Sadi Carnot proved in 1824 that no heat engine can be more efficient than a reversible cycle operating between two temperatures:
- Carnot Efficiency: $$\eta = 1 - \frac{T_C}{T_H} = \frac{T_H - T_C}{T_H} \quad (\text{Temperatures must be in Kelvin})$$
- Mechanical Work Output: $$W = \eta \cdot Q_H = Q_H - Q_C$$
- Heat Pump COP: $$\text{COP}_{\text{HP}} = \frac{T_H}{T_H - T_C} = \frac{1}{\eta}$$
- Refrigerator COP: $$\text{COP}_{\text{Ref}} = \frac{T_C}{T_H - T_C} = \text{COP}_{\text{HP}} - 1$$