Carnot Efficiency Calculator
Calculate maximum theoretical efficiency of heat engines using Carnot cycle thermodynamics
Carnot Cycle Analysis
Temperature of the heat source
Temperature of the heat sink
Carnot Cycle Results
Hot Reservoir
Cold Reservoir
Thermodynamic Ratios
Carnot Cycle Formula
Efficiency: η = (T_h - T_c) / T_h × 100%
Calculation: η = (373.1 - 298.1) / 373.1 × 100% = 20.10%
Note: Temperatures must be in Kelvin for calculations
Real-World Applications
Steam Power Plant
Max η = 69.7%
T_h = 550°C, T_c = 25°C
Coal/gas power generation
Car Engine
Max η = 72.2%
T_h = 800°C, T_c = 25°C
Internal combustion engine
Geothermal Plant
Max η = 29.5%
T_h = 150°C, T_c = 25°C
Earth heat utilization
Solar Thermal
Max η = 55.7%
T_h = 400°C, T_c = 25°C
Concentrated solar power
Nuclear Plant
Max η = 48%
T_h = 300°C, T_c = 25°C
Nuclear reactor cooling
Refrigerator
Max η = 15.4%
T_h = 25°C, T_c = -18°C
Heat pump cycle
Carnot Cycle Reference
Efficiency Formula
η = (T_h - T_c) / T_h
Where T in Kelvin
Four Processes
- 1. Isothermal expansion (T_h)
- 2. Adiabatic expansion
- 3. Isothermal compression (T_c)
- 4. Adiabatic compression
Key Facts
- • Maximum theoretical efficiency
- • Reversible heat engine
- • Independent of working fluid
- • Depends only on temperatures
Understanding the Carnot Cycle
What is the Carnot Cycle?
The Carnot cycle represents the most efficient heat engine theoretically possible between two thermal reservoirs. It consists of four reversible processes that extract work from heat transfer between reservoirs at different temperatures.
The Four Processes
- 1. Isothermal Expansion: Gas expands at constant high temperature T_h
- 2. Adiabatic Expansion: Gas expands and cools to T_c (no heat transfer)
- 3. Isothermal Compression: Gas compressed at constant low temperature T_c
- 4. Adiabatic Compression: Gas compressed and heated to T_h
Why Carnot Efficiency?
Maximum Efficiency: η = (T_h - T_c) / T_h
Temperature Ratio: η = 1 - T_c / T_h
Work Output: W = η × Q_h
Heat Rejected: Q_c = Q_h - W
Practical Limitations
- Reversibility: Requires infinitely slow processes
- Perfect Insulation: No heat losses to surroundings
- Ideal Components: Frictionless, lossless operation
- Time: Would take infinite time to complete cycle
Real vs. Theoretical Efficiency
Steam Power Plants
Carnot efficiency up to 70%, but actual efficiency around 35-40% due to real-world limitations
• High-pressure steam (550°C)
• Condenser cooling (25°C)
• Friction and heat losses
Car Engines
Carnot efficiency around 72%, but actual efficiency only 25-30% in real engines
• Combustion temperature (800°C)
• Exhaust temperature (25°C)
• Incomplete combustion
Refrigerators
Coefficient of Performance limited by Carnot cycle, actual COP much lower
• Room temperature (25°C)
• Freezer temperature (-18°C)
• Compressor inefficiencies