Quick Question- carnot efficiency

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    Carnot Efficiency
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SUMMARY

The discussion centers on the calculation of Carnot efficiency in engines utilizing multiple heat reservoirs. It is established that one cannot simply average the temperatures of the hot and cold reservoirs to determine T(hot) and T(cold). Instead, a weighted average must be employed, taking into account the flow rates and heat capacities of each reservoir. This approach ensures accurate efficiency calculations, particularly when there is a significant disparity in flow rates, as illustrated by the example of 99% flow from a 400K reservoir and 1% from a 1000K reservoir, which would yield an inflated efficiency if a simple average were used.

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trelek2
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Suppose an engine uses multiple heat reservoirs:

When calculating the carnot (maximum possible efficiency) is it valid to simply take the average of the temperatures of the hot reservoirs from which the heat is extracted as T(hot) and the average of the temperatures of the heat sinks to which heat is rejected as T(cold)??
(regardless of the amounts of energy Q rejected/extracted from each of the reservoirs)
 
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I think you'd have to do a weighted average, based on flow rates and heat capacities or how they mix.

Put it this way if you have 99% flow from 400K reservoir and 1% from 1000K
using a average temp of 700K would give an unrealistically high efficieny.

This is all assuming I've undersood your original question correctly.
 
I agree with xxChrisxx; it all depends on how much heat is being removed from each reservoir per cycle.
 

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