Carnot Efficiency Calculator
Calculate the maximum theoretical efficiency of a heat engine (Carnot efficiency) and the maximum COP for heat pumps and refrigerators.
How Carnot Efficiency Is Calculated
The Carnot cycle defines the theoretical maximum possible efficiency of any heat engine operating between two temperature reservoirs. No real engine can exceed this limit — it sets the upper bound of thermodynamic performance.
Carnot Efficiency Formula:
η = 1 − (T_cold / T_hot)
Where:
- η (eta) = efficiency (0 to 1, or 0% to 100%)
- T_cold = temperature of cold reservoir in Kelvin
- T_hot = temperature of hot reservoir in Kelvin
- Converting: K = °C + 273.15
Worked Example: A steam turbine operates with steam at 550°C and exhausts at 45°C:
- T_hot = 550 + 273.15 = 823.15 K
- T_cold = 45 + 273.15 = 318.15 K
- η = 1 − (318.15 / 823.15) = 1 − 0.3865 = 0.6135 = 61.35%
In practice, real steam turbines achieve 35–45% due to friction, heat losses, and irreversibilities.
Efficiency Reference by Engine Type:
- Car gasoline engine: 20–35%
- Diesel engine: 35–45%
- Combined-cycle gas turbine: 55–62%
- Nuclear steam plant: 30–35%
- Carnot limit for typical car: ~60%
Key Insight: To maximize efficiency, maximize the temperature difference. A 10°C drop in the cold reservoir temperature improves efficiency more at low temperatures than at high temperatures. This is why power plants use large cooling towers.