Reversible engines with different efficiencies

In summary, all reversible heat engines have the same efficiency when operating between the same two temperature reservoirs, regardless of their construction or working fluid. This was proven by showing that any deviation from this principle would lead to a contradiction. Therefore, it is impossible to create a reversible engine that is less efficient than Carnot's, and any violation of the second law may be attributed to a less efficient engine.
  • #1
AbhiNature
18
0
Is is possible to have 2 different engines with all the following criterion?

1) Are reversible
2) Work differently (different cycles)
3) At the same working temepratures have different efficiencies.

E.g.
Working temperatures 100K and 50K.
Engine 1: Carnot's
Efficiency - 50%

Engine2: Some cycle
Efficiency - 20%

Thanks!
 
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  • #2
All Reversible Heat Engines have same efficiency when operating between the same two temperature reservoirs.

This is proved by showing that there is a contradiction, if they do not. We set the two heat engines to be compared operating between the same two heat reservoirs. Assume one is more efficient than the other. Run the less efficient one in reverse (as a refrigerator) using the fraction of the work from the more efficient engine that the less efficient engine would produce running forward. At that point there is zero net heat flow from the hot reservoir and the differential in work between the two engines is comes from the net heat removed from the cold heat reservoir. This contradicts the Carnot assumption. Thus to stay consistent:
Every reversible heat engine operating between the same two temperature reservoirs have identical efficiency. This means no matter how a reversible heat engine is constructed or what the working fluid is, its efficiency is the same as all other heat engines working from the same two temperatures.
 
  • #3
I thought so. It is as improbable to create a lesser efficient reversible engine (compared to Carnot's) as to create a more efficient reversible engine.
Whenever second law is violated, maybe, it would be due to the lesser efficient engine.
 

1. What is a reversible engine?

A reversible engine is a theoretical concept in thermodynamics that describes an ideal engine that can convert all of its input energy into work without any energy loss or waste.

2. How does a reversible engine differ from a real engine?

A reversible engine is a theoretical concept and does not exist in reality. In contrast, real engines have energy losses due to factors such as friction, heat transfer, and other inefficiencies.

3. What is the efficiency of a reversible engine?

The efficiency of a reversible engine is 100%, as it can convert all of its input energy into work without any losses.

4. Can a real engine ever achieve 100% efficiency?

No, a real engine can never achieve 100% efficiency. This is because it is impossible to completely eliminate all energy losses and waste in a real system.

5. How do different efficiencies affect reversible engines?

Different efficiencies do not affect reversible engines, as they are a theoretical concept with an efficiency of 100%. However, in real engines, different efficiencies can greatly impact their performance and energy conversion capabilities.

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