Carnot Efficiency Calculator
Carnot Efficiency
η = 1 - (T_cold / T_hot)
Maximum possible efficiency for a heat engine (ideal case)
About This Calculator
Carnot Efficiency Calculator is designed to reduce manual errors and give repeatable outputs when you need quick, reliable answers.
Calculate the maximum theoretical efficiency of a heat engine operating between two temperatures using the Carnot cycle formula. Used in thermodynamics coursework, engine analysis, and power plant engineering.
If your workflow expands, pair this calculator with Ideal Gas Law Calculator and Heat Transfer Calculator to cross-check assumptions and build a stronger analysis chain.
Formula
η_Carnot = 1 − (T_cold / T_hot), where temperatures are in Kelvin. Maximum efficiency is achieved only by a theoretically perfect (reversible) Carnot engine. Real engines always have lower efficiency due to friction and irreversibilities.
Example Calculation
The worked example below demonstrates how the input fields translate into the final output. Use it as a quick validation pass before entering your own numbers.
- hot temperature (K): 600
- cold temperature (K): 300
Explanation of Results
Result Interpretation
η = 1 − (300 / 600) = 1 − 0.5 = 0.50 = 50%. This means even a perfect heat engine between 600 K (327°C) and 300 K (27°C) can convert at most 50% of heat to work. The other 50% must be rejected to the cold reservoir — a fundamental thermodynamic limit, not an engineering limitation.
FAQ
What is Carnot efficiency?
Carnot efficiency is the maximum possible efficiency any heat engine can achieve when operating between a hot source (T_hot) and cold sink (T_cold). It equals 1 − T_cold/T_hot (temperatures in Kelvin). No real engine can exceed this — it's a thermodynamic law, not an engineering challenge. Real engines achieve 30–45% of Carnot efficiency.
Why can't heat engines reach 100% efficiency?
The second law of thermodynamics requires that some heat must be rejected to a cold reservoir — you can never convert all heat to work. Even a perfect Carnot engine wastes heat proportional to T_cold/T_hot. To approach 100% efficiency, T_cold would need to approach absolute zero (0 K), which is physically unattainable.
How do real engines compare to Carnot efficiency?
Modern coal power plants achieve ~33–40% thermal efficiency (vs Carnot ~60%). Combined-cycle gas turbines reach ~60% efficiency (close to their Carnot limit). Car gasoline engines achieve ~25–35% thermal efficiency. The gap from Carnot is due to friction, heat losses, and irreversible processes inherent in real systems.
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See Also
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