Question regarding the Otto cycle

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ehabmozart
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Why is the heat rejection process in an otto cycle is at constant volume. Let us say that the exhaust and intake stages in the actual cycle are the last two strokes of the cycle. In the ideal cycle, it seems to me that they merge those two stages into one stage which is heat rejection and constant volume. Why is it so?

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There are 2-stroke and 4-stroke Otto cycles. At the bottom of the power stroke in each version of the Otto cycle, an exhaust port or an exhaust valve opens, and the hot gases in the cylinder expand quickly out of the cylinder.

It may not be truly a constant volume situation in real engines, but for the purposes of analysis using the ideal cycle (with emphasis on the ideal), it's close enough.
 
The heat rejection process is actually done outside of the engine.

The exhaust gases are rejected in the atmosphere. You should look at the atmosphere as a huge radiator that is so large compare to the addition of the exhaust gases that it can be assumed to be at constant volume. And because the atmosphere is so large compare to the engine displacement, the cooling (or pressure drop) is almost instantaneous from the point of view of the engine.

Then the intake stroke feeds itself from the «other end» of the atmosphere, where the gases have cooled down, ready to repeat the cycle.

The ideal Otto cycle defines a closed system. An engine working with such a cycle would need no valves and have its piston stopped at TDC until the gas inside is heated up (say by an external heat source) and once it would be at BDC it would stay there until the gas has cooled down to its initial pressure & temperature.

An actual engine has an open cycle ... unless you include the atmosphere as the heat exchanger!