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In discussion under another question, it was pointed out: "Not every process is polytropic; that is just a special case when $pV^n$ is constant" Must have missed that in school.

What is a real life example of a non-polytropic process in a closed system (energy transfer yes, mass transfer no)?

How are non-polytropic processes simulated/calculated?

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The polytropic equation is derived using the ideal gas EOS, so it would probably not accurately describe a real gas in a thermodynamic process.

One way to analyze a non-polytropic process is by solving the energy balance between two states to get the temperature change of the working fluid, then using that temperature change in the equation of state to calculate the volume or pressure change. Solving the energy balance can get tedious if there are things like heat transfer and friction work though. For example, the heat transfer in a piston-cylinder expansion depends on the exposed surface area of the cylinder, which is constantly changing throughout the process. In my field, many of the terms in the energy balance are ODEs, so I end up doing a lot of numerical integration before actually solving the energy balance.

I was hoping others would chime in on this issue besides the two of us, but it doesn't look like there's a lot of interest in polytropic processes...

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  • $\begingroup$ But the way of doing it you describe - solving Energy Balances for finites steps of the process? - is how one would calculate a non-polytropic process? I only learned very basic TD, where can I leanr more about this approach? $\endgroup$ – mart Aug 24 '20 at 7:58
  • $\begingroup$ The way I described is just based on my personal experience, which covers only a narrow slice of thermodynamics. Other types of problems might do better with other solution methods. The general idea is that if you can't use some idealized (e.g. polytropic, isentropic, isothermal, etc.) relationship between P, T, and V, then you have to use some other method to relate the begin and end states of a process. At that point, you're probably specializing in some area, and the best info would probably come from journal articles or papers rather than textbooks. $\endgroup$ – Carlton Aug 26 '20 at 19:06

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