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In Equilibrium Thermodynamics, Adkins, it is stated that

Since equilibrium state corresponds to definite values of the system parameters, we may represent a quasistatic process by plotting...an indicator diagram.... Non-quasistatic processes should not be represented by a line on a p-V diagram.

Now I'm not sure exactly whether quasistatic is the same as reversible here? If so, it is still not quite obviois to me that any line drawn on a p-V diagram represents a reversible process? Does it have to do with the fact that, for a continuous line, and point in the line has only an infintesimally different volume/pressure values to the points either side? Still, non-reversible processes do exist, and a discontinuous jump in pressure ot volume seems unphysical; to me this suggests that any process, whether reversible ot not, would be represented by a continuous line on any parameter graph, p-V or any other...

Wikipedia's article on P-V graphs did not mention reversibility, so the statement in Adkins is leaving me stumped!

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The main problem with representing a non-quasistatic process on a $PV$ digram is that during such a process in general pressure is not homogeneous throughout the system, so you cannot assign any definite value to the variable $P$. The same is also true for temperature.

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