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?
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.
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.