# How to prove the existence of a certain thermodynamic path between two points?

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

• 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. May 2, 2020 at 12:07
• Yes I want u to prove that generally for any two random points with a general process May 2, 2020 at 12:10
• But for isobaric, right? May 2, 2020 at 12:20
• Umm yes ...I would like to know for other processes too actually May 2, 2020 at 12:22
• Ik for example that u can't have a reversible adiabatic path and irreversible adiabativc path with the same endpoint May 2, 2020 at 12:23