Carnot efficiency is a fundamental concept in thermodynamics, representing the maximum possible efficiency that any heat engine can achieve when operating between two temperature reservoirs. This theoretical limit was formulated by the French physicist Sadi Carnot in 1824 and is based on the principle that the efficiency of a heat engine depends only on the temperatures of the hot and cold reservoirs, not on the specific working substance or material used in the engine. Harvard University professors and many thermodynamicists agree that Carnot efficiency is independent of the nature of the working substance in a heat engine, which has important implications for our understanding of thermodynamic cycles and their practical applications.

Scientific Basis of Carnot Efficiency

The Carnot cycle, which serves as the foundation for Carnot efficiency, consists of two isothermal processes (heat absorption and heat rejection) and two adiabatic processes (no heat exchange). The efficiency of a Carnot engine is given by the formula:

η=1−TCTH\eta = 1 - \frac{T_C}{T_H}η=1−TH​TC​​

where:

• η\etaη is the Carnot efficiency,
• TCT_CTC​ is the absolute temperature of the cold reservoir,
• THT_HTH​ is the absolute temperature of the hot reservoir.

This formula shows that the efficiency depends only on the temperatures of the two reservoirs. The key point here is that the working substance (the material or gas used in the engine, such as steam, air, or a refrigerant) does not appear in the equation. Thus, the theoretical maximum efficiency of the engine is determined purely by the temperatures at which the engine operates, not by the characteristics of the substance inside the engine.

Practical Implications

From a practical standpoint, this insight means that no matter what working substance is used in the heat engine, the theoretical efficiency is the same as long as the engine operates between the same two temperature reservoirs. For example, whether a Carnot engine uses helium, hydrogen, or steam as its working substance, its maximum efficiency will always be limited by the temperatures of the heat sources, not the specific properties of the substance.

However, while the Carnot efficiency sets the upper limit, real engines do not achieve this ideal efficiency due to various losses, such as friction, heat leakage, and irreversibilities in the working substance's behavior. In real-world applications, the choice of the working substance does play a significant role, as it affects factors such as the specific heat, thermal conductivity, and compressibility, which influence the engine's overall performance and practicality.

Why the Working Substance Does Not Affect Carnot Efficiency

The reason Carnot efficiency is independent of the working substance can be understood by considering the idealized nature of the Carnot cycle. In an ideal Carnot engine, the working substance undergoes reversible processes, meaning there are no losses due to friction or turbulence. The efficiency depends solely on the ratio of the temperatures of the hot and cold reservoirs because the Carnot cycle assumes that heat can be completely transferred from the hot to the cold reservoir without any entropy generation within the system. This assumption abstracts away the specific characteristics of the working substance, focusing only on the temperature differences.

In practice, the real-world efficiency of heat engines is governed by other factors that are more directly related to the working substance, such as the material's thermal properties, phase transitions (e.g., boiling or condensation in steam engines), and the practicality of maintaining stable, reversible cycles. These factors lead to deviations from the Carnot limit, but they do not change the theoretical calculation of maximum efficiency.

Conclusion

While it is clear that the working substance plays a crucial role in the performance and design of real heat engines, the Carnot efficiency itself remains independent of the substance used. The fundamental limitation of a heat engine's efficiency, according to Carnot's theorem, is determined solely by the temperature difference between the heat reservoirs. Therefore, researchers and engineers can optimize the design of real-world engines by considering the characteristics of the working substance, but when calculating the maximum possible efficiency for any given temperature difference, the nature of the working substance does not affect the Carnot efficiency. This concept is central to understanding thermodynamic cycles and serves as a benchmark for evaluating the performance of practical heat engines.

Carnot efficiency is independent of the working fluid, which means that physical concepts can exist without physical entities. Talking so much is just nonsense. No one can go against common sense.

Bo Miao Shafeea Khalaf Alsharaa & ResearchGate Community

Dear Bo and Shafeea,

Thank you for engaging in this stimulating discussion on the fundamentals of thermodynamics. I appreciate the depth of your insights and would like to contribute by presenting findings from my recent research, which challenges traditional interpretations of the Second Law of Thermodynamics and offers novel perspectives on entropy and the arrow of time.

Reevaluating the Second Law of Thermodynamics

The Second Law posits that the entropy of an isolated system tends to increase over time, leading to the concept of irreversibility in natural processes. However, in my paper, "Entropy is Constant & Arrow of Time is T-Symmetric," I demonstrate that for open systems—those exchanging energy and matter with their surroundings—entropy can remain constant under specific conditions. This finding suggests that the traditional view of ever-increasing entropy does not universally apply, particularly in open systems where dynamic interactions occur.

Implications for Heat Engine Efficiency

Regarding the Carnot efficiency, which defines the maximum possible efficiency of a heat engine operating between two temperature reservoirs, traditional thermodynamics asserts that this efficiency is independent of the working substance. This principle has been foundational in understanding heat engines. However, my research indicates that when considering open systems with constant entropy, the characteristics of the working substance and its interactions with the environment can influence the system's overall behavior. This perspective opens avenues for reexamining how working substances might affect efficiency in practical applications, potentially challenging the notion that Carnot efficiency is entirely independent of the working substance.

Addressing the Arrow of Time

The concept of the arrow of time, which refers to the unidirectional flow of time from past to future, has long been associated with the Second Law and increasing entropy. In my research, I propose that time symmetry can be restored in open systems with constant entropy, effectively resolving the arrow of time paradox. This groundbreaking insight suggests that under certain conditions, processes could be reversible, and the distinction between past and future becomes less pronounced. This challenges the conventional understanding of time's unidirectional progression and has profound implications for physics and our perception of temporal dynamics.

Conclusion

While traditional thermodynamics has provided a robust framework for understanding energy and entropy, my research invites a reevaluation of these principles, especially concerning open systems. The constancy of entropy in such systems and the implications for the arrow of time suggest that our current understanding may be incomplete. I encourage further exploration and discussion on these topics to advance our comprehension of thermodynamic processes and the fundamental nature of time.

I look forward to your thoughts and any further discussion this may inspire.

Best regards,

Sandeep Jaiswal

Carnot efficiency is independent of the working fluid, and there are physical concepts that can be separated from physical entities. The following is a detailed analysis:

Thermal engine system: pistons, containers (geometric boundaries), heat sources (energy boundaries), etc. are all centered around the working fluid, and calculating thermal power conversion is studying the working fluid. The Carnot efficiency is independent of the working fluid, and is detached from physical entities, becoming a concept suspended in the air.

2. This statement is incorrect. The formulas for entropy and Carnot efficiency that follow are incorrect. The entire second law of thermodynamics is incorrect.

3. Pay attention to the second point, don't think that inventing the concept of entropy is omnipotent.

Bo Miao ,

I think the problem is dQh is a function of Th and Tc and dV or dP, not Th only.

Entropy can be calculated using Boltzmann equation in Carnot engine where every point has absolute value thus impossible to be paradoxical. Changing gas medium does affect the value of entropy but they cancels out to have no effect on efficiency.

BTW, Carnot engine is an ideal engine meaning any real world engine using different fuel and design will have different efficiency.

Jixin

You are avoiding the question that Carnot efficiency is not related to the working fluid, which means that the physical concept (Carnot efficiency) is detached from the physical entity (working fluid). Please refer to the previous post for a detailed discussion. In addition, the second law of thermodynamics only plays a role in piecing together data in practical thermodynamic calculations. Resulting in inaccurate final results.

Yes. That is the definition of ideal, meaning not real. It is then applied back to various of fluid and nothing strange happens. It is a pretty precise approximation. That is the reason in 200 years we are approaching the Carnot efficiency but will never get it.

After 100 years of try, say using steam, mathane, natural gas, gasoline… many many engine design All yielding slightly smaller efficiency.

Your point and the textbook point are totally different. Carnot engines by definition is an ideal engine so nothing to do with real fluids anymore.

Jixin

It's not a problem with ideal concepts, it's a problem with your understanding of thermodynamics. You can go back and take a look at the textbook. The second law of thermodynamics cannot be solved through verbal explanation.

It cannot be solved by Carnot cycle because it is a cycle have nonspontaneous process. actually all stocks are reversible. I.e. no total entropy change. 2nd law is for spontaneous processes thus you have picked a wrong example to derive 2nd law. 2nd law deals with both reversible and irreversible processes and usually people focus on spontaneous in the statement.

Carnot efficiency is not related to the working fluid, which means that the physical concept (Carnot efficiency) is detached from the physical entity (working fluid). The second law of thermodynamics cannot violate common sense. This mistake is that the calculation of thermal work in the second law of thermodynamics is incorrect. As for irreversible and reversible thermodynamic calculations, they are irrelevant.

Here is a very good video that will help understanding entropy and second law while learning thermodynamics:

https://www.youtube.com/watch?v=DxL2HoqLbyA

You should keep those videos and watch them slowly!

Carnot efficiency is not related to the working fluid, which means that the physical concept (Carnot efficiency) is detached from the physical entity (working fluid). The second law of thermodynamics cannot violate common sense. This mistake is that the calculation of thermal work in the second law of thermodynamics is incorrect.

Bo Miao Sandeep Jaiswal Jixin Chen & ResearchGate Community

• Dear Bo and Sandeep Jaiswal,
• Reevaluating the Second Law of Thermodynamics The notion that entropy can remain constant in open systems is a compelling area of investigation. While the Second Law posits that entropy in isolated systems tends to increase, open systems—which exchange energy and matter with their surroundings—can indeed exhibit dynamic behaviors that deviate from this principle. However, the constancy of entropy in such systems is contingent on specific conditions, such as achieving a dynamic equilibrium between incoming and outgoing flows. This equilibrium is rare and context-dependent, making it more of an exception than a general rule. Therefore, asserting that the Second Law "does not universally apply" necessitates a precise delineation of the conditions under which this claim holds.
• Heat Engine Efficiency and Carnot's Principle The challenge to Carnot efficiency based on the influence of the working substance is an intriguing perspective. Carnot's formulation assumes an idealized, lossless system and asserts that the maximum efficiency of a heat engine depends solely on the temperatures of the reservoirs, not the working substance. While real-world systems often deviate from these ideal conditions due to factors like viscosity and thermal conductivity, concluding that the working substance fundamentally alters Carnot efficiency would require rigorous experimental and theoretical evidence. Until such evidence is provided, Carnot's efficiency remains a cornerstone of thermodynamic theory, serving as a theoretical upper limit rather than a practical guarantee.
• The Arrow of Time and Restoring Time Symmetry The suggestion that time symmetry can be restored in open systems with constant entropy is a fascinating proposition. The arrow of time is deeply rooted in the statistical nature of entropy increase, as articulated by the Second Law. If a system can maintain constant entropy over time, it raises profound questions about the relationship between time's unidirectional flow and entropy. However, it is essential to distinguish between the philosophical and physical interpretations of time's arrow. Any proposed restoration of time symmetry must align with empirical evidence and the foundational principles governing irreversible processes in macroscopic systems.
• Conclusion Your research presents a thought-provoking challenge to conventional thermodynamic principles, particularly regarding open systems. While these ideas hold the potential to expand our understanding, the conclusions require robust mathematical modeling, experimental validation, and alignment with established physical laws. I look forward to engaging further and exploring the specific methodologies and results from your work.

Now let's discuss the relationship between Carnot efficiency and working fluid. Don't interfere with this issue by bringing downstream problems (be careful not to digress).

Carnot efficiency is not related to the working fluid, which means that the physical concept (Carnot efficiency) is detached from the physical entity (working fluid). The second law of thermodynamics cannot violate common sense. This mistake is that subsequent calculations of thermal work based on the second law of thermodynamics are also incorrect.

Dear Bo Miao,

Your arguments are interesting; however, what you propose requires more than just an image. Perhaps you could provide more details about the system you are presenting, as well as the experimental or theoretical conditions and the detailed development you have carried out to reach the conclusions you are presenting?

Thank you for your attention and interest. My goal is to encourage everyone to use basic physics and logic methods to study thermodynamics. Similarly, supporters of the second law of thermodynamics can provide detailed explanations. The second law of thermodynamics is a conjecture based on finite experience. The mistake is very basic and goes against common sense. The pursuit of science is logical, empirical, and mathematical.

Galileo explained the errors of Aristotle's theory of falling bodies in just a few words, and now it's time for the second law of thermodynamics. I believe in overturning the second law with the least amount of language. The Second Law and Aristotle's theory of falling bodies are both relatively low empirical understandings with numerous problems. You can refer to the first post on the topic for details.