# How to interpret the Otto Cycle PV diagram?

AFAIU this is the practical Otto cycle with the added isobaric stroke for when the piston intakes and expells through the valves.

However, there's one thing I don't understand: AFAIK, PV diagrams assume constant particle number N. But when the valves are open, that is no longer true. Indeed, what sparked this question was thinking that the intake process is certainly an isobaric expansion when the valve is open, but it is also isothermal as it is air in thermal equilibrium with the outside. It is rather that we have a larger and larger number of particles filling the cylinder, right? Am I missing something?

• you are over-thinking this. pv diagrams for steam or gas turbine cycles aren't closed, it's for a mass going through the system. Nov 2, 2023 at 13:12

Nothing in your logic is wrong, in my understanding, but I'm not sure what your question or issue is.

PV diagrams assume constant particle number

Yes, there is an unchanging fluid mass during stages 1-2-3-4-1 as the system is closed.

the intake process is certainly an isobaric expansion when the valve is open, but it is also isothermal

Sure, but it's irrelevant to the cycle itself. In stage 0-1, the system is pulling in fluid from the outside world. Frankly, whatever happens to that fluid before the system closes is outside the scope of the diagram.

we have a larger and larger number of particles filling the cylinder

Yes, that's the case. Likewise, during stage 1-0 we have an expulsion of fluid from the system.

• Thanks for the answer. I later figured that if N is not conserved, then there's no reason for points 0 and 1 to have different temperature. To be perfectly clear, maybe a 3D plot would be needed with N as another variable. I guess this is just the projection onto the PV plane of that 3D plot Nov 2, 2023 at 17:26
• Right, a third axis of Temperature would make sense. As with all of engineering, we have to make some assumptions to move forward! Nov 2, 2023 at 17:35
• Also the heat rejection 4–1 and constant pressure 1–0 is an approximation modeling the single act of expelling the burned hot gas. If you look at a real indicated PV chart from a real engine running. the 4 corner shape here has rounded edges Nov 2, 2023 at 17:46