Can paths of two adiabatic process intersect on a plot? This question is for both reversible and irreversible processes. There are some answers for this question on Quora, but they mostly address only for reversible adiabatic processes. Also, I want a physical interpretation of the processes that is, if they don't intersect then why don't and what it would be like, physically for a system.
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2$\begingroup$ In the previous question you speak of, it is apparent that the person who answered you understands thermodynamics much better than you. Insulting a qualified person who was trying to help you doesn’t really motivate anybody to help you again. $\endgroup$– knzhouCommented Sep 7, 2018 at 5:57
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$\begingroup$ I am sorry for I didn't mean to insult someone. And I really respect their experience. But they said some things that were contradictory to concepts mentioned in some really credible sources. I also sent them links to these sources. Point is, these things leads discussion elsewhere & it takes far to longer to get to the answer. As you can see, we didn't get to one, in the question I mentioned. $\endgroup$– shashank tyagiCommented Sep 7, 2018 at 6:28
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$\begingroup$ A system undergoing an irreversible process generally aren't in thermal equilibrium (or arbitrarily close to it) and so aren't at any point on the $PV$ diagram. Different parts of the system will in general be a different pressures, so we can't talk about the pressure and even if it happens that the system does have a single pressure, away from equilibrium pressure and volume alone are not enough to determine the state of the system, so you cannot expect to say a great deal about what the system can and cannot do until the process is finished. $\endgroup$– By SymmetryCommented Sep 7, 2018 at 9:41
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1$\begingroup$ I don't see how you can possibly say that, when all I need to do is cite one single example in which an adiabatic reversible process and an adiabatic irreversible process start out in the same initial state. By the way, I don't know whether it's appropriate to ask this, but I'm going to do so anyway: Why are you spending so much of your valuable time speculating about esoteric things like this when you could be spending it so much more productively solving actual practice problems involving adiabatic reversible and irreversible processes? $\endgroup$– Chet MillerCommented Sep 7, 2018 at 13:40
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1$\begingroup$ Serious advice here: it is a common mistake for beginner students of thermodynamics to get caught up in definitions. There are lots of complicated new words, so you end up spending all day debating the exact meaning of "irreversible quasistatic quasiequilibrium adiabatic isochore", getting the feeling that you're uncovering some deep knowledge. The reality is, it really doesn't matter. These words were made to describe real things. If you've said all this and still don't know how a car engine works, you're wasting your time. $\endgroup$– knzhouCommented Sep 9, 2018 at 4:46
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1 Answer
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To answer your first question, yes two (different) adiabatic paths can intersect in a plot. See State A in Fig 2. However, for this to be possible, at least one of them has to be irreversible. For different reversible adiabatic processes involving the same working substance, their plots cannot intersect. See Fig 1.
Now, if you could have two reversible adiabatic processes intersect and be connected by a reversible isothermal process, there would be a violation of the second law. In that context, the answer to the linked question where both adiabatic processes are shown as reversible, would be correct. That is because both the system and the surroundings would return to their original states with no increase in entropy.
However, since at least one adiabatic process must be irreversible, then the cycle A-B-C-A shown in Fig 2 below would not violate the Kelvin-Plank statement of the second law. Recall the law states:
“It is impossible to construct a device which operates on a cycle and produces no other effect (my emphasis) than the production of work and the transfer of heat from a single body”.
The irreversible adiabatic process (Process A-B) in Fig 2 produces an increase in entropy. Thus cycle A-B-C-A does constitute some other effect than the production of work and transfer of heat from a single body, and therefore does not violate the Kelvin-Plank statement of the second law.
Hope this helps
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2$\begingroup$ Can a reversible adiabatic and irreversible adiabatic curve intersect more than once? $\endgroup$ Commented Jul 4, 2020 at 15:46
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$\begingroup$ No they can't intersect more than once. $\endgroup$– Bob DCommented Jul 4, 2020 at 16:04
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$\begingroup$ Can u give a proof as to why? $\endgroup$ Commented Jul 4, 2020 at 16:16
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1$\begingroup$ Sure. For any adiabatic process there is no heat transfer between the system and the surroundings. If two adiabatic processes intersected more than once on the PV diagram you would have a cycle in which the net work done is the area enclosed by the two curves, and yet no heat is transferred to the system. This violates the first law. For any cycle $\Delta U=0$ . For adiabatic processes $Q=0$, From first law, closed system, $\Delta U=Q-W$. Therefore, $W$ must be zero. If it isn't, it violates first law. Hope this helps. $\endgroup$– Bob DCommented Jul 4, 2020 at 17:03
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$\begingroup$ Very helpful indeed!Thank you! $\endgroup$ Commented Jul 5, 2020 at 18:20