# Why is exhaust stroke isochoric in otto cycle?

Please help me clarify this simple concept. In otto cycle, after the power stroke, the gas expands adiabatically and during the exhaust stroke why is the volume of the gas constant? Doesn't the volume of the gas change after the exhaust valve is open? Is the volume considered constant because the temperature of the gas drops quickly at the end of the power stroke? If so, how does the temperature of the gas drop so quickly in such small time interval? I am confused, please help me. Thank you!

• Isochoric is an idealization. The plot here is closer to reality. It was produced by directly measuring the pressure and volume during the cycle marinesite.info/2020/04/… Commented Nov 24, 2022 at 19:02

Doesn't the volume of the gas change after the exhaust valve is open?

Yes it does, for the real Otto cycle which is an irreversible open system. But it does not for the reversible closed system model of the cycle.

The ideal reversible model of the Otto cycle does not include the intake or exhaust strokes because it is a closed thermodynamic system model of the cycle. Instead of thermal energy being lost along with mass in the exhaust stroke for an open system, it is shown as heat rejected at constant volume for the reversible closed system model. See the PV diagram of the ideal reversible cycle.

For reference I have included arrows to represent the intake and exhaust strokes of a real open system cycle which are not normally shown for the reversible closed system model. This has no impact on the net work done, since there is no net work done for the combination of the exhaust and intake strokes both of which occur at the same constant external pressure and the same increase and decrease in volume. All the thermal energy lost during the real exhaust stroke is accounted for as heat rejected at constant volume for the reversible cycle model.

Hope this helps.

• You wrote: "Instead of thermal energy being lost along with mass in the exhaust stroke for an open system, it is shown as heat rejected at constant volume for the reversible closed system model." What would be the difference between "thermal energy being lost along with mass in the exhaust stroke" as you wrote or "heat rejected along with mass in the exhaust stroke", which you did not write? Commented Nov 25, 2022 at 11:49
• @hyportnex no difference in the amount of energy, just the mechanism by which the energy crosses the boundary between the system and surroundings. For the (actual) open system it is internal energy of the mass of gas that leaves the system. For the closed system it is energy transfer due solely to temperature difference, I.e., “heat” Commented Nov 25, 2022 at 13:25
• So you are making a linguistic distinction between two physical situations, convection vs. conduction. (1) If the engine's exhaust stage was by diffusion ("exhaustion"?) how would you call the amount of thermal energy carried away or is it heat only when carried by phonons and not "real" particles? (2) If your coordinate system is now with the convected exhaust gas in which the gas is stationary does that change the language as regards the gas is concerned, not the engine that is left behind, but the gas; what does the gas have now? I am confused. Commented Nov 25, 2022 at 16:06
• @hyportnex I’m not sure I understand your comments. But are you suggesting that the exhaust stroke of an IC engine is heat transfer by convection? Commented Nov 25, 2022 at 17:28
• In the sense of dictionary.com: "ORIGIN OF CONVECT 1880–85; back formation from convected < Latin convect(us) past participle of convehere to carry together (see con-, vector) + -ed2"; in this sense the "it" that stays unnamed is being carried away by exhaust particles, molecules, etc. So given the average velocity of the exhaust particles there is a rate of energy transfer from the IC to air. Now observe the energy transfer in the reference frame that moves along at the speed of the average exhaust COM, how would you call that "it" that is being transferred? Commented Nov 25, 2022 at 17:49