Suppose I have two points on a PV graph labeled as A and B both having same pressures (that is the process is isobaric) and the volume of A is less than that at B. How can we rigorously prove that there exists a thermodynamic reversible process and a thermodynamic irreversible process which both start and end at A and B respectively.

CONTEXT:- I originally came about this question when I was finding the value of entropy for an irreversible process from A to B knowing the value of heat exchanged in the reversible process. I now realize that entropy is a state function and all I need to do is prove the existence of a reversible path between the two points A and B in order to say that the entropy change for the required irreversible process is equal to that of the reversible one

  • $\begingroup$ Are you asking us to specifically identify an isobaric reversible path and an isobaric irreversible path between the same two end points? It isn't clear what you are asking. $\endgroup$ May 2, 2020 at 12:07
  • $\begingroup$ Yes I want u to prove that generally for any two random points with a general process $\endgroup$ May 2, 2020 at 12:10
  • $\begingroup$ But for isobaric, right? $\endgroup$ May 2, 2020 at 12:20
  • $\begingroup$ Umm yes ...I would like to know for other processes too actually $\endgroup$ May 2, 2020 at 12:22
  • $\begingroup$ Ik for example that u can't have a reversible adiabatic path and irreversible adiabativc path with the same endpoint $\endgroup$ May 2, 2020 at 12:23

1 Answer 1


Here's my show at it. Vertical cylinder of gas with a piston of mass m siting on top.

Reversible process: Cylinder initially at temperature T1. Heat cylinder by putting it in contact with a continuous sequence of ideal reservoirs of gradually increasing temperatures, running from T1 to T2.

Irreversible process: Cylinder initially at temperature T1. Heat cylinder by putting it in contact with single reservoir of temperature T2 (and let system equilibrate).

  • $\begingroup$ Is there no proper mathematical proof of it? $\endgroup$ May 2, 2020 at 14:10
  • $\begingroup$ I mean someone can similarly prove that there exists an irreversible adiabatic and reversible adiabatic with same endpoint (which does not happen) $\endgroup$ May 2, 2020 at 14:11
  • $\begingroup$ For the adiabatic case, that is, of course, as you say, impossible. But, for the isobaric case, it is possible. Just carry out the processes that I described. What is your problem about that? $\endgroup$ May 2, 2020 at 14:18
  • $\begingroup$ Carry out the processes is not mathematical though...and I can't perform those processes .I want to provide a proof theoretically $\endgroup$ May 2, 2020 at 14:58
  • $\begingroup$ I can't understand what you are asking. Are you asking to see the 1st and 2nd laws of thermodynamics applied to the two processes to determine the heat flows, entropy changes, etc? I'm very confused. $\endgroup$ May 2, 2020 at 15:36

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