# Proving Carnot efficiency is maximum and conditions

• C_Pu
In summary, the standard proof for the Carnot efficiency states that coupling a supposedly more efficient engine to a Carnot refrigerator would violate the second law. However, some discussions on stackexchange suggest that this argument only applies to the reversible Carnot engine and the two-isotherm two-adiabatic cycle is simply for conceptualization. There is confusion about whether this argument can be applied to any arbitrary efficiency.
C_Pu
The standard proof to show carnot efficiency cannot be exceeded is to couple a supposedly more efficient engine to a carnot refrigerator, and show that it would violate second law. However, isn't it true that we can make the same argument with any arbitrary efficiency?

Some discussions on stackexchange regarding this topic say the key point is only carnot engine is reversible which makes this line of argument specific to carnot efficiency. They also suggested the two-isotherm two-adiabatic carnot cycle is only for easier conceptualization of a reversible cycle.

Can someone clarify all this confusion please?

C_Pu said:
However, isn't it true that we can make the same argument with any arbitrary efficiency?
Could you clarify what you mean by that? (And also what you mean by "Carnot efficiency.")

## 1. What is Carnot efficiency and why is it important?

Carnot efficiency is a measure of the maximum possible efficiency of a heat engine, which is a device that converts heat energy into mechanical work. It is important because it sets a theoretical limit on the efficiency of any heat engine, and understanding it can help improve the design and performance of real-world engines.

## 2. How is Carnot efficiency calculated?

Carnot efficiency is calculated by dividing the difference in temperature between the hot and cold reservoirs by the temperature of the hot reservoir. This can be expressed as the ratio of absolute temperatures or as a percentage. For example, if the hot reservoir is at 600 K and the cold reservoir is at 300 K, the Carnot efficiency would be 50% or 0.5.

## 3. What are the conditions for maximum Carnot efficiency?

The conditions for maximum Carnot efficiency include having a reversible process, operating between two fixed temperature reservoirs, and having no energy losses due to friction or other inefficiencies. In other words, the heat engine must be operating at its maximum theoretical efficiency with no external factors affecting its performance.

## 4. Why is a reversible process necessary for maximum Carnot efficiency?

A reversible process is necessary because it ensures that the system is in thermal equilibrium at all times, meaning that there are no energy losses due to heat transfer between the system and its surroundings. This is essential for achieving the maximum theoretical efficiency of a heat engine.

## 5. Can Carnot efficiency ever be exceeded?

No, Carnot efficiency cannot be exceeded. It is a fundamental limit based on the laws of thermodynamics and the principles of heat transfer. While real-world heat engines may not achieve the maximum Carnot efficiency, it cannot be exceeded by any practical means.

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