Calculating Heat Discharge in a Steam Engine: Efficiency and Work Rate Analysis

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SUMMARY

The discussion focuses on calculating heat discharge in a steam engine operating at half of its theoretical maximum efficiency. The correct formula for heat discharge (QL) is derived from the relationship QH = W/emax, where emax represents the maximum efficiency. Given that the engine operates at 50% efficiency, the heat discharged per second is calculated as QL = QH - W, resulting in a discharge of 1 J/s. The theoretical maximum efficiency is defined as 1 - TL/TH.

PREREQUISITES
  • Understanding of the Carnot efficiency formula
  • Basic principles of thermodynamics
  • Knowledge of heat engine operation
  • Familiarity with the concepts of work and heat transfer
NEXT STEPS
  • Study the Carnot cycle and its implications on engine efficiency
  • Explore the relationship between heat input and work output in thermodynamic systems
  • Learn about the calculation of heat discharge in various types of heat engines
  • Investigate the impact of temperature differences (TL and TH) on engine performance
USEFUL FOR

Students of thermodynamics, mechanical engineers, and anyone involved in the design or analysis of heat engines will benefit from this discussion.

kasse
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Homework Statement



If a steam engine operates at half of its theoretical maximum efficiency, and does work at a rate of W J/s, calculate how much heat is discharged per second.


The Attempt at a Solution



emax = W/QH (Carnot)

emax = W/2QH

--> QH = W/emax

Wrong answer. What is my mistake?
 
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kasse said:

Homework Statement



If a steam engine operates at half of its theoretical maximum efficiency, and does work at a rate of W J/s, calculate how much heat is discharged per second.

The Attempt at a Solution



emax = W/QH (Carnot)

emax = W/2QH

--> QH = W/emax

Wrong answer. What is my mistake?

Theoretical max would be equal to 1, 50% would be the actual efficiency = .5 =W/QH=1/2. Heat discharged would be QL which equals QH-W. If the engine is operating at 50% efficiency, half the heat input will go to shaft work, the other half will be discharged. So this engine would discharge 1 J/s. BTW, theoretical max. for a heat engine is 1-TL/TH.
 

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