Calculation actual efficiency problem

AI Thread Summary
The discussion revolves around calculating the actual and maximum theoretical efficiencies of a heat engine that takes in 1030 J of energy at 1000 K and exhausts 585 J at 250 K. The maximum efficiency, derived from the Carnot efficiency formula, is calculated to be 75%. The actual efficiency is determined by the useful work output, which is 445 J, leading to an efficiency of approximately 43%. Participants confirm the calculations and clarify the formulas used for both efficiencies. The thread concludes with a clear understanding of how to derive both efficiency values.
astru025
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Homework Statement



A heat engine takes in 1030 J of energy at 1000 K and exhausts 585 J at 250 K. What are the actual and maximum theoretical efficiencies of this heat engine?

Homework Equations



For maximum efficiency I got 75 % by taking 1 - (250K / 1000K). For actual efficiency the equation is W/ Q or work out / heat in.

The Attempt at a Solution



I am not sure where to start on this problem and any help would be very nice!
 
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The max efficiency is the Carnot efficiency which you seem to have right (I think).

As for the actual efficiency...
For actual efficiency the equation is W/ Q or work out / heat in.

Correct.

If 1030 J goes into the engine and 585J comes out of the exhaust how much is used elsewhere by the engine, presumably doing useful work?
 
445 j?
 
astru025 said:
445 j?
Yes.
 
So if 1030J goes in and only 445J comes out in the form of useful work the efficiency is ?
 
445 J / 1030 J = 43 % thanks very much!
 

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