# Is it Possible to have Adiabatic Processes other than $PV^\gamma$ for the ideal Gas?

Is it possible to represent an adiabatic process for an ideal gas by a formula other than $PV^\gamma=Const$?:

Relevant Considerations:

We always need to connect a pair of arbitrary points/states $A:(P_1,V_1)$ and$B:(P_2,V_2)$ on the P-V indicator diagram to define the Internal Energy function(U)

If the two points do not lie on some $PV^\gamma=Const$, we may think of some abrupt process connecting the two states. Such a process cannot be represented by a continuous curve on the diagram since the intermediate states are non-equilibrium states. Pressure will not have a unique value wrt the system for such processes.It will be different from point to point.We have a pair of points A and B without any curve connecting them

Now we connect the points A and B by an arbitrary "continuous" path on our diagram(on paper) and select close discrete points on it. The consecutive "close" discrete points may be connected by abrupt adiabatic "processes" as described previously. Therefore in the pragmatic sense we can have an arbitrary quasi-static "adiabatic" path connecting the points A and B : The "close" points ie physical; states,will lie on a curve different from $PV^\gamma=Const$

[In the physical/practical implementation of the $PV^\gamma=Const$ curve we do consider/implement a chain of discrete equilibrium states]

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