Disproving Carnot's Theorem: Is There an Error in My Thinking?

In summary, the conversation discusses the efficiency of Carnot's engine compared to other engines and its ability to drive another engine as a refrigerator. The conclusion is that Carnot's theorem is disproved because a non-reversible heat engine cannot be reversed to make a refrigerator. The proof can be found in the book.
  • #1
phymath7
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TL;DR Summary
I was going through the proof of carnot theorem given in the book 'Heat and thermodynamics ' by Zemansky(seventh edition ,page 174).Here the proof was conducted by considering that the efficiency of the carnot engine is less than the other arbitrary engine.The other engine is driving the reverse carnot refrigerator .That leads to a contradiction hence carnot's theorem is proved.
But if I would assume that the efficiency of the carnot's engine is greater than the other engine and the carnot engine is driving the other engine backward as a refrigerator ,that would lead to the same contradiction hence disproving carbot's theorem! Is there something wrong I have done? Perhaps.Please point me out.
 
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  • #2
Could you show the proof in the book?
 
  • #3
Lnewqban said:
Could you show the proof in the book?
Screenshot_20230205-235624_OneDrive.jpg
 
  • #4
Ok,I have got it.The main point is that the carnot engine being a reversible engine can be reversed to make a refrigerator.But we can't reverse a non-reversible heat engine to make a refrigerator hence my assumption was incorrect.
 
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FAQ: Disproving Carnot's Theorem: Is There an Error in My Thinking?

What is Carnot's Theorem?

Carnot's Theorem states that no heat engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs. The efficiency of a Carnot engine is determined solely by the temperatures of the hot and cold reservoirs and is given by the formula \( \eta = 1 - \frac{T_C}{T_H} \), where \( T_H \) and \( T_C \) are the absolute temperatures of the hot and cold reservoirs, respectively.

Why is it challenging to disprove Carnot's Theorem?

Disproving Carnot's Theorem is challenging because it is a fundamental result derived from the second law of thermodynamics. This law is well-supported by extensive experimental evidence and theoretical reasoning. Any attempt to disprove the theorem would require either identifying a flaw in the second law or demonstrating a physical process that consistently violates it, both of which have not been observed in practice.

Could there be a misunderstanding in the application of Carnot's Theorem?

Yes, misunderstandings often arise from misapplying the conditions under which Carnot's Theorem holds. The theorem assumes idealized conditions, such as reversible processes and no dissipative effects like friction or turbulence. Real-world engines are subject to various inefficiencies and irreversibilities that Carnot's idealized model does not account for, which can lead to confusion if not properly considered.

Is it possible to create a more efficient engine than a Carnot engine?

According to the second law of thermodynamics, it is not possible to create an engine more efficient than a Carnot engine operating between the same two thermal reservoirs. Any claim of a more efficient engine would require extraordinary evidence and would likely imply a need to revise our understanding of thermodynamics, which has been robustly validated over centuries.

What should I do if I think I have found a way to disprove Carnot's Theorem?

If you believe you have found a way to disprove Carnot's Theorem, it is crucial to rigorously test and validate your findings. Peer review and replication of results by independent researchers are essential steps. Ensure that all assumptions and conditions align with the principles of thermodynamics, and consider consulting with experts in the field to identify any potential errors or overlooked factors in your reasoning.

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