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I am looking over the Otto Cycle on this MIT website and it says at one point "the processes from 1 to 2 and from 3 to 4 are isentropic" in reference to the expansion and compression of the piston. I understand however that the compression and expansion in an internal combustion engine is quite violent and quick. And according to wikipedia "Throughout an entire reversible process, the system is in thermodynamic equilibrium, both physical and chemical, and nearly in pressure and temperature equilibrium with its surroundings." However this isn't the case for our expansion and compression is it? the pressure and temperature of our expansion/compression is not in equilibrium? It also says "reversible processes are extremely slow (quasistatic)". But once again, our expansion/compression isn't slow at all?

I've noticed, there are many processes that seem to be described as isentropic that from what I can tell are not in equilibrium with their environment throughout and are not quasistatic (my book for example says pumps, turbines, nozzles, and diffusers perform isentropic operations)? So through what justifications are these approximations made?

The main reason I ask this question is because I am attempting to calculate the pressures in a gun barrel, and I have seen the process described as isentropic (adiabatic and reversible) but for the same reasons as the Otto cycle, cannot understand how this would apply. The gun barrel acts similar to a rapidly expanding piston. Ignition, rapid expansion of gases against bullet (piston), then bullet (piston) leaves and the gases diffuse rapidly into the atmosphere. How is this reversible or quasistatic in any way? If anyone has an idea regarding the gun barrel and what process it is that would be appreciated as well.

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The Otto cycle shown on the MIT website is a reversible idealization of the internal combustion cycle, not the actual cycle, which is an irreversible cycle since, among other things, the compression and expansion occurs rapidly instead of quasi-statically as required for a reversible cycle.

The idealization simply gives us an upper limit for the maximum possible efficiency of the Otto cycle if it in fact could be carried out reversibly. In the same manner, isentropic (reversible adiabatic) pumps and turbines are idealizations of real pumps and turbines, providing an upper limit to their maximum possible efficiency.

Finally, the Carnot cycle is an idealization of a reversible cycle that gives us an upper limit to the efficiency of any cycle operating between two fixed temperatures.

Hope this helps.

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