How to Determine Temperature of Heat and Cold Reservoirs in a Carnot Cycle?

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SUMMARY

To determine the temperatures of the heat and cold reservoirs in a Carnot cycle with a 90-degree Celsius differential and 28% efficiency, one can utilize the Carnot efficiency formula: Efficiency = 1 - (Q out / Q in). Given the temperature difference, the relationship T(hot) - T(cold) = 90 must be established. By rearranging the efficiency equation, the temperatures can be calculated directly from the known efficiency and temperature differential.

PREREQUISITES
  • Understanding of Carnot cycle principles
  • Familiarity with thermodynamic efficiency calculations
  • Knowledge of temperature scales (Celsius and Kelvin)
  • Basic algebra for rearranging equations
NEXT STEPS
  • Study the Carnot cycle and its implications in thermodynamics
  • Learn how to derive temperature relationships from efficiency equations
  • Explore practical applications of Carnot efficiency in real-world systems
  • Investigate the impact of temperature differentials on system performance
USEFUL FOR

Students studying thermodynamics, engineers working with heat engines, and anyone interested in understanding the principles of efficiency in thermal systems.

eliassiguenza
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Homework Statement


All i want to know is how do i find the temperature of my heat and cold reservoir, given that they have a 90 degree celsius/kelvin differential and a 28% efficency.


Homework Equations


Efficency= Work out/ Work in = 1- Q out/Q in


The Attempt at a Solution


I been thinking all night and couldn't sleep well over this, i know how to get efficency but it seems a tricky question, how ever i was thinking of just calculating the heat and work for many diferent temperatures with 90 degrees differential and then see what happens?
Anyone has a better idea? I feel very reluctant of making so many calculations...
 
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How else does one express the carnot efficiency in terms of the temperatures of the hot and cold reservoirs?

They told you that T(hot)-T(cold) = 90.
 
yeah! got that one thank you very much! I thought about it straight away after posting it! thanx
 

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