# Definition of polytropic process

Being a student I was learnt that polytropic process is a process with constant heat capacity:

$$\frac{\delta Q}{\delta T}=C.$$

It is rather straightforward to derive that for ideal gas this expression implies

$$pV^n=\text{const}, (*)$$

with $$n=\frac{C-C_p}{C-C_V}.$$

Therefore I was very surprised that the wikipedia page (https://en.wikipedia.org/wiki/Polytropic_process) devoted to the polytropic process defines it through the expression (*). However it seems that for non-ideal gas the path (*) does not correspond to any interesting conserving quantity.

My question: when the term "polytropic process" was initially introduced and what meaning it had at that time?

• Comments are not for extended discussion; this conversation has been moved to chat. – ACuriousMind Mar 16 '17 at 1:26

Looking through literature I have found the answer to my question. The term "polytropic" was firstly introduced by German physicist and engineer G. Zeuner probably about 1866. The starting point for him was indeed

"Verhalten des Gases unter der Voraussetzung dass die dem Gase zugeführte beziehungsweise entzogene Wärmemenge der Temperaturänderung direct proportional ist"

("Behavior of the gas provided that the amount of heat supplied to or withdrawn from the gas is directly proportional to the temperature change")

"Technische Thermodynamik", Erster Band, Leipzig, 1900, p. 147.

From this definition using the equality $d Q = c\,dT$ he derived for the ideal gas the equation

$$pv^n=\text{const}$$

which he had named "polytropic curve".

However in the above cited book the author treated all gases as ideal (though the Van der Waals equation was according wikipedia published already in 1873). Therefore both definitions were in fact equivalent.

In the following time the "constant heat capacity" definition of polytropic process persisted also in English speaking countries until at least middle of the last century.