The efficiency of a Carnot engine

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Discussion Overview

The discussion centers around the efficiency of a Carnot engine and the implications of its efficiency in relation to the second law of thermodynamics. Participants explore the reasoning behind why the Carnot engine is considered the standard for maximum efficiency and whether other engines can exceed this efficiency without violating thermodynamic principles.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions the proof that no engine can have greater efficiency than a Carnot engine, suggesting that the reasoning could apply to any engine.
  • Another participant asserts that the proof relies on the second law of thermodynamics, stating that if an engine were more efficient than a Carnot engine, it could lead to violations of this law.
  • Some participants emphasize the necessity of studying the Carnot cycle to understand the efficiency of the Carnot engine itself.
  • There is a discussion about whether coupling a more efficient engine to a Carnot refrigerator can serve as a valid proof, with some arguing it cannot.
  • A participant reiterates that the Carnot engine is taken as a standard due to its theoretical maximum efficiency, while questioning if similar proofs could be applied to other engines.
  • One participant clarifies that coupling any engine, including those less efficient than a Carnot engine, will not lead to violations of the second law, reinforcing the Carnot engine's unique status.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of certain proofs and the implications of coupling engines. There is no consensus on whether the reasoning presented can be generalized to other engines or if the Carnot engine uniquely defines the upper limit of efficiency.

Contextual Notes

Participants highlight the dependence on the second law of thermodynamics and the specific conditions under which the Carnot engine operates. The discussion reflects varying interpretations of the implications of efficiency and thermodynamic principles.

brianeyes88677
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I can't realize the proving why Carnot engine has the highest efficiency.

"Let εc be the efficiency of a Carnot engine operating between two given temperatures.If an engine X, which has an efficiency εx that is greater than εc.We can couple engine X to a Carnot refrigerator , and they make a perfect refrigerator."

But I can proof that any engine has the highest efficiency through this method.
 
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That's a "proof" that you can't have an engine with greater efficiency than a Carnot engine without breaking the 2nd law. It indeed says nothing about the efficiency of the Carnot engine. For that, you need to study the Carnot cycle and figure out what its efficiency is.
 
Misspelling :"But I can 'prove' that any engine has the highest efficiency through this method."
 
DrClaude said:
That's a "proof" that you can't have an engine with greater efficiency than a Carnot engine without breaking the 2nd law.

The question is that I can claim that any engine can't have an engine with greater efficiency than engine X (differ from a Carnot engine) without breaking the 2nd law. How can "couple another engine to it " be a proof?
 
brianeyes88677 said:
The question is that I can claim that any engine can't have an engine with greater efficiency than engine X (differ from a Carnot engine) without breaking the 2nd law. How can "couple another engine to it " be a proof?
It is a proof by contradiction. If you had another engine more efficient than a Carnot engine then you could use it to do something that violates the second law. So if the second law is valid, no more efficient engine is possible.
 
jbriggs444 said:
It is a proof by contradiction.

Why we take the Carnot engine as standard? I can do the same proof with any other engine.
 
brianeyes88677 said:
Why we take the Carnot engine as standard? I can do the same proof with any other engine.
Can you? If you have an engine that is less efficient than a Carnot engine, can you couple it to one a little bit more efficient (but still less efficient than a Carnot engine) and break the second law?
 
Just to make things clear: if you were to couple a heat engine with an efficiency greater than a Carnot engine to a Carnot refrigerator, you would see heat flow from the cold reservoir to the hot reservoir without any external supply of energy, which breaks the second law. The conclusion is therefore that no engine can have an efficiency greater than a Carnot engine. Connecting any other engine to the Carnot refrigerator, including a Carnot engine, will result in heat flowing from hot to cold, as it should. Other engines could be as efficient as a Carnot engine, but the second law sets a limit to the efficiency of a heat engine, and that efficiency is that of a Carnot engine.
 
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