Calculation actual efficiency problem

In summary, a heat engine with an input of 1030 J at 1000 K and an output of 585 J at 250 K has a maximum theoretical efficiency of 75% and an actual efficiency of 43%. The actual efficiency is calculated using the equation W/Q, where W is the work output and Q is the heat input. In this case, the difference between the heat input and useful work output is 445 J.
  • #1
astru025
163
0

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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  • #2
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?
 
  • #3
445 j?
 
  • #4
astru025 said:
445 j?
Yes.
 
  • #5
So if 1030J goes in and only 445J comes out in the form of useful work the efficiency is ?
 
  • #6
445 J / 1030 J = 43 % thanks very much!
 

1. What is actual efficiency?

Actual efficiency is a measure of how well a process or system performs in comparison to its ideal or theoretical efficiency. It takes into account all factors that affect the efficiency, such as energy losses, equipment malfunctions, and human error.

2. How do you calculate actual efficiency?

Actual efficiency can be calculated by dividing the actual output of a process or system by its expected or ideal output, and then multiplying by 100 to get a percentage. The formula for actual efficiency is: (actual output / expected output) x 100.

3. What are the factors that affect actual efficiency?

The factors that affect actual efficiency can vary depending on the process or system being evaluated. Some common factors include energy losses due to friction or heat, equipment malfunctions or failures, operator errors, and variations in input materials or conditions.

4. How can actual efficiency be improved?

There are several ways to improve actual efficiency, including regular maintenance and upkeep of equipment, using more efficient processes or technologies, optimizing input materials or conditions, and providing proper training and supervision for operators.

5. Can actual efficiency be greater than 100%?

In theory, actual efficiency can be greater than 100% if the actual output exceeds the expected or ideal output. However, this is rare and usually indicates that the calculations or measurements were incorrect. In practical terms, actual efficiency is typically capped at 100% as it represents the maximum achievable efficiency for a given process or system.

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