Polytropic Equation: Is Temperature Constant?

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SUMMARY

The discussion centers on the polytropic thermodynamic process and the equation pv^n=c. It is established that temperature is not constant in a polytropic process, which is distinct from isothermal (n=1) and adiabatic (n=γ) processes. The equation is applicable to quasistatic processes involving simple compressible gas systems, and it does not necessitate negligible heat transfer. The derivation of the equation is questioned, with references made to "Thermodynamics" 5th Edition by Wark, indicating a need for clarity on its formulation.

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Is temperature constant in a polytropic thermodynamic process? The equation pv^n=c leads me to believe so. But logic tells me otherwise. Its not isothermal or adiabatic. Did they derive this equation from using log transforms when analyzing gas experiments?
 
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A polytropic process does not require the heat transfer to be negligible. The process is following a relationship between equilibrium states. The equation is restricted to a quasistatic process for a simple compressible gas system.

The above is taking from "Thermodynamics" 5th Edition by Wark. Page 664
 
But how did they come up with the equation pV^n=c?
I can find any derivation for that equation. I'm trying to understand how the equation was formed.
 
jaredokie said:
But how did they come up with the equation pV^n=c?
I can find any derivation for that equation. I'm trying to understand how the equation was formed.
People noted that, for an isothermal process, n=1 and for an adiabatic process, n=γ. So they figured that, if the temperature is controlled properly, there can be other processes which satisfy a p-v equation of the specified mathematical form. They coined the term "polytropic" to refer to such processes.
 

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