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Carnot Efficiency Formula:
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The Carnot efficiency formula represents the maximum possible efficiency that any heat engine can achieve operating between two temperature reservoirs. It establishes the theoretical upper limit for thermal efficiency based on the second law of thermodynamics.
The calculator uses the Carnot efficiency formula:
Where:
Explanation: The formula shows that efficiency increases as the temperature difference between the hot and cold reservoirs increases. Maximum efficiency (100%) is only theoretically possible when the cold reservoir is at absolute zero.
Details: Carnot efficiency serves as a benchmark for real heat engines. No real engine can exceed this theoretical maximum, and practical engines typically achieve significantly lower efficiencies due to various irreversibilities and losses.
Tips: Enter both temperatures in Kelvin. Ensure T_h > T_c for meaningful results. The calculator will compute the maximum theoretical efficiency as a percentage.
Q1: Why can't real engines achieve Carnot efficiency?
A: Real engines have irreversibilities like friction, heat loss, and finite temperature differences that prevent them from reaching the theoretical maximum.
Q2: What are typical Carnot efficiency values for real systems?
A: For steam power plants, Carnot efficiency might be 60-70%, but actual efficiency is typically 30-40%. Internal combustion engines have even lower practical efficiencies.
Q3: Why must temperatures be in Kelvin?
A: The ratio T_c/T_h must be calculated using absolute temperature scales to maintain thermodynamic consistency and avoid negative efficiency values.
Q4: Can efficiency be greater than 100%?
A: No, Carnot efficiency cannot exceed 100% as this would violate the second law of thermodynamics. Values range from 0% to approaching 100% asymptotically.
Q5: How does this relate to refrigerator efficiency?
A: The same temperature ratio appears in the coefficient of performance (COP) for refrigerators and heat pumps, but in different forms.