Calculation actual efficiency problem

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Homework Help Overview

The problem involves a heat engine that takes in energy and exhausts a portion of it, prompting a discussion on calculating both actual and maximum theoretical efficiencies. The context includes thermodynamics, specifically the principles governing heat engines and efficiency calculations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the concept of maximum efficiency, referencing the Carnot efficiency formula. There are attempts to clarify the calculation of actual efficiency based on the work done by the engine. Questions arise regarding the interpretation of energy input and output, as well as the calculation of useful work.

Discussion Status

The discussion has progressed with participants confirming calculations and exploring the relationship between energy input, output, and efficiency. Some guidance has been provided regarding the equations involved, and there is a focus on understanding the definitions of actual versus theoretical efficiency.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information available for discussion. There is an emphasis on ensuring clarity in the definitions and calculations related to efficiency.

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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