The efficiency of a Carnot engine

[brianeyes88677]

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.

 

[DrClaude]

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.

 

[brianeyes88677]

Misspelling :"But I can 'prove' that any engine has the highest efficiency through this method."

 

[brianeyes88677]

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?

 

[jbriggs444]

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.

 

[brianeyes88677]

It is a proof by contradiction.

Why we take the Carnot engine as standard? I can do the same proof with any other engine.

 

[jbriggs444]

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?

 

[DrClaude]

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.