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There are several well-studied cycles, like the Carnot, Otto, etc., among infinitely many. But, what happens when we also consider the costs of driving the system through a particular cycle? How does it change our analysis?

More precisely, how is the system of interest together with another system that changes 'the environmental conditions', like providing contact with a heat bath or isolating it from the rest of the universe etc., for the system of interest analyzed, rigorously?

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closed as unclear what you're asking by Chemomechanics, John Rennie, Jon Custer, GiorgioP, A.V.S. Mar 10 at 13:22

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One never worries about the cost of using a Carnot cycle because it is not a practical cycle and is never actually used. Its mainly used to show the theoretical upper limit of any actual heat engine cycle.

One of the reasons it is impractical is that all the processes need to be reversible, which means they need to be carried out infinitely slowly (quasi-statically). So while the Carnot cycle is the most efficient possible heat engine cycle in terms of work output divided by gross heat input, the rate at which it can do work (output power) would be extremely low.

Someone once said putting a Carnot engine in your car would give you fantastic fuel economy, but pedestrians would be passing you by!

ADDENDUM

My answer above applied to your question before you edited it and made it a broader question.

I’m not sure that there is a simple answer to the first paragraph of the edited question. There are so many variables and you would need to include not only cost, but cost benefit ratios, the demands of a particular application and so forth. Personally, I don’t have enough practical background to address them. But it does appear that niels nielson has such experience so I would defer to his answer. (Chester Miller, maybe you can contribute as well if you are reading this)

But the second paragraph brings up some other aspects of the Carnot cycle that limit its practicality, in addition to the power output limitations I already mentioned. To name just two:

  1. For a piston/cylinder engine closed system operating in a Carnot cycle, how does one, practically speaking, insulate the cylinder for the adiabatic processes and then have it removed for the isothermal processes? My recollection is the thermodynamic model of the Otto cycle (car engine) models the compression stroke as a reversible adiabatic compression. In reality it is adiabatic due to rapid compression and not insulation. Such rapid compression would not meet the quasi-static requirements of a reversible cycle.

  2. For a steam Carnot cycle application, you need to compress a combination of vapor and liquid mixture to raise the temperature of the working fluid to the boiler temperature and pressure. I believe in practice this is difficult to do. By comparison, in a Rankine cycle the compressor deals only with bringing saturated liquid up to the boiler pressure and is therefore more practical.

Hope this together with niels nielsen's answer helps

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In the idealized analysis of the suitability of a particular thermodynamic cycle (Brayton, Otto, Stirling, etc.) for a particular application, the overall process is straightforward, and consists of several steps. In practice, though, the process is simpler than this; I'll describe both paths.

First, the designer determines what the hot source and cold sink temperatures will be. This will vary, depending on whether the cycle is to be driven by a combustion process, a geothermal source, etc., and whether the process is closed or open. The Carnot cycle is then invoked, so as to conveniently furnish an upper bound on the efficiency of the overall process, independent of the process details.

Second, the designer then takes the desired power output specification for the application (for example, the megawatt (thermal) rating of the power plant) and divides this number by the efficiency upper bound. This establishes a lower bound for the heat input rate of the process, and permits the designer to estimate the lower bound of the overall size of the heat input, work extraction, and heat rejection processes needed to support the desired power rating.

Third, the designer then looks at the characteristic process scale (set by step 2) and estimates for each possible thermodynamic process the practicality of each i.e., whether or not a (for example) Stirling cycle can be applied.

In practice, however, this is not how it's done. If the designer knows that the plant will be of megawatt scale and running on coal as the heat source, then (s)he also knows that the coal will be used to boil water into steam and drive an expansion process using a turbine, which then establishes all the rest of the big-picture design criteria for the plant.

If the plant is to be driven by natural gas and has a power rating in the tens-of-kilowatts range, then the designer knows to choose an otto-cycle prime mover, which again establishes all the big-picture plant requirements; if it's in the megawatt range, then the answer is a water-injection natural gas boiler on an open cycle, and so forth.

Or, if the required output of the plant is the generation of propulsive thrust instead of shaft horsepower and weight is to be minimized, then the right answer is a brayton cycle running on kerosene.

To summarize: The design criteria that are handed to the design engineer will almost always dictate which thermodynamic cycle (s)he will have to specify, based on knowledge of the current state-of-the-art and common practice.

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