What Is the Carnot Efficiency Formula for Engine Calculations?

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SUMMARY

The Carnot efficiency formula for engine calculations is defined as η = 1 - (T_c / T_h), where T_c is the cold reservoir temperature and T_h is the hot reservoir temperature. In the discussed scenario, with temperatures of 500K and 300K, the thermal efficiency calculates to 0.4 or 40%. Given that the engine receives 200 calories from the hot reservoir, it rejects 120 calories to the cold reservoir, confirming the relationship between input and output energy in a Carnot engine. This formula is essential for understanding the maximum efficiency achievable by heat engines operating between two thermal reservoirs.

PREREQUISITES
  • Understanding of thermodynamics principles
  • Familiarity with heat engines and their operation
  • Knowledge of temperature scales (Kelvin)
  • Basic algebra for solving proportional equations
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  • Study the derivation of the Carnot efficiency formula in detail
  • Explore real-world applications of Carnot engines
  • Learn about other types of heat engines and their efficiencies
  • Investigate the impact of temperature differences on engine performance
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Students of thermodynamics, mechanical engineers, and anyone interested in the principles of heat engine efficiency will benefit from this discussion.

brilyn
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Is there a formula used to solve engine problems? For example a carnot engine is operated between two heat reservoirs at temperatures of 500K and 300K. If the engine receives 200 cal from the reservoir at 500K in each cycle. How many calories does it reject to the reservior at 300K?
This seems like it should be very easy but it's something we never went over in class. I know is receives more from the hot than it rejects so would I set up a proportional equation and take 200/500 then multiply by 300? this gives me 120cal... Let me know if I'm on the right track or if there is a formula to use Thanx
 
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I'm not sure if this will help but the thermal efficiency of a Carnot engine is 1- T_c/T_h
 
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