Why is the Carnot Cycle so Important?

[SUDOnym]

All reversible cyclic processes (engines) have the same efficiency: 1-T2/T1.

And Carnot demostrated this efficiency with the Carnot Cycle and went on to use this to demonstrate that this was the upper limit for efficiency.

My question is, why is it that there is such importance placed on the Carnot Cycle? ie. since all reversible processes have this same efficiency couldn't we say just take an engine whos path is:

a isobaric b isochoric c isobaric d isochoric a isobaric b isochoric c isobaric d isochoric ...and so on.

and use this engine to also demonstrate that the upper limit is 1-T2/T1? is it simply that with the carnot cycle, which is:

a isotherm b adiabat c isotherm d adiabat a isotherm b adiabat c isotherm d adiabat ... and so on

makes it easy to demonstrate this result?

 

[Drakkith]

See here. http://en.wikipedia.org/wiki/Carnot_cycle#Efficiency_of_real_heat_engines

1-T2/T1 is the efficiency of the carnot cycle, however it is NOT the efficiency of a real engine. Real engines have losses that will always make them less efficient than max.

 

[Andrew Mason]

My question is, why is it that there is such importance placed on the Carnot Cycle? ie. since all reversible processes have this same efficiency couldn't we say just take an engine whos path is:

a isobaric b isochoric c isobaric d isochoric a isobaric b isochoric c isobaric d isochoric ...and so on.

and use this engine to also demonstrate that the upper limit is 1-T2/T1? is it simply that with the carnot cycle, which is:

a isotherm b adiabat c isotherm d adiabat a isotherm b adiabat c isotherm d adiabat ... and so on

makes it easy to demonstrate this result?

In order to create a reversible cycle, all heat flow has to occur at infinitessimal temperature differences. In other words, heat flow from the hot reservoir to the system has to occur with the reservoir and system at the same temperature AND heat flow from the system to the cold reservoir has to occur with the system and cold reservoir at the same temperature. In order to get from the hot temperature to the cold temperature and vice-versa without increasing entropy, the expansions and compressions cannot involve heat flow.

So any reversible cycle must be equivalent to the Carnot cycle: isothermal (expansion), adiabatic (expansion), isothermal (compression), adiabatic (compression).

AM

 

[Curl]

My question is, why is it that there is such importance placed on the Carnot Cycle? ie. since all reversible processes have this same efficiency couldn't we say just take an engine whos path is:

a isobaric b isochoric c isobaric d isochoric a isobaric b isochoric c isobaric d isochoric ...and so on.

this cycle is highly irreversible and much less efficient than carnot's cycle

 

[PJC01]

The Carnot Cycle is important because it is a theoretical model that serves as a benchmark for the maximum efficiency that can be achieved by a heat engine operating between two temperature extremes. It is a simplified representation of a reversible heat engine, which is an idealized system that can be used to study thermodynamic processes without taking into account any real-world inefficiencies or losses.

The efficiency of the Carnot Cycle is significant because it is the upper limit for the efficiency of any heat engine operating between two temperatures. This means that no real-world heat engine can ever achieve an efficiency higher than that of a Carnot Cycle. This has practical implications in the design and operation of real-world engines, as it provides a target for engineers to strive towards and improve upon.

Furthermore, the simplicity of the Carnot Cycle makes it a useful tool for studying thermodynamics and understanding the principles behind heat engines. It allows for the derivation of important relationships, such as the efficiency equation mentioned in the content, which can then be applied to more complex systems.

While it is true that any reversible cyclic process will have the same efficiency as a Carnot Cycle, the Carnot Cycle is significant because it is the simplest and most idealized representation of a reversible heat engine. Other cycles may be more complex and difficult to analyze, making it harder to draw general conclusions about thermodynamic principles and efficiencies.

In summary, the Carnot Cycle is important because it serves as a benchmark for maximum efficiency, provides a simplified model for studying thermodynamics, and allows for the derivation of important relationships that can be applied to real-world systems.