 For the Otto cycle, we are trying to adapt a spark ignition internal combustion reciprocating engine into an idealized model And we'll start by considering the four strokes of a four stroke engine This is gonna be the best drawing ever by the way Okay, imagine I have two valves here one for intake one for exhaust and For the beginning of my process here the exhaust valve is closed the intake valve is open And the piston is moving down so from top dead center to Bottom dead center. We are calling this the intake stroke Then Then we are sealing the cylinder That is both valves are in the closed position And we move the piston up This is compressing the gas and the gas here is referring to the air that's in the engine and also the fuel Because the fuel was mixed with the air prior to intake to the cylinder This is the compression stroke Then we are Producing power So at the very top dead center Disclaimer here. It's not actually top dead center, but we're modeling it in an ideal way At top dead center ish that spark plug fires which ignites the fuel and we are assuming in our Autocycle that that combustion happens instantly so quickly in fact that the piston doesn't have a chance to move and Then as a result of now being hot the air is going to push against the piston and move it down That's our power stroke lastly the exhaust valve is going to open the piston will move up and We will get all of that gas at least some of it out so that we can intake again Make sense. So those four strokes are intake compression power exhaust In my gas powered engine in my car These are just repeated over and over and over again in a two-stroke engine You are actually using both sides of the piston. So while it's going down It is also Compressing the area underneath the piston in this four stroke discussion We were talking about the gas being on this side only So intake brings in an air fuel mixture compression compresses the air fuel mixture Then between compression and power the spark plug fires Combusting all the fuel Instantaneously for the purposes of our analysis then that hot mixture of air and whatever products are left after combustion Push against the piston moving it down producing some power and then we are moving the piston back up to exhaust that mixture of air and exhaust gases so that we can bring in a fresh air fuel mixture again intake compression power exhaust our Auto cycle is going to start by ignoring intake and exhaust all together We are focusing only on compression and power and in fact We are going to break it up into pieces to make it a little bit easier to model our Auto cycle begins with just Compression and then We have a process Where we will analyze the heat addition caused by the combustion And then we'll have a process where we have expansion and produce power And then we will have a process that completes the loop We have compression We have combustion we have Expansion and then we have the hypothetical process that encompasses the Exhaust the cooling and the re-intake So we're calling this the cooling process or heat rejection if you prefer and In the combustion process the piston doesn't move. We just have you know fire here Which we are treating as being External heat addition in the expansion process. We have work out and then in our cooling process We are assuming that The exhaust gases get exhausted. They are allowed to mingle with the atmosphere long enough to cool back down to their initial conditions And we bring them back in and all of that happens for free Instantly so the combustion process is isochoric the cooling process is isochoric They are considered to be isochoric because they happen very very quickly So quickly that the piston doesn't have a chance to move for our compression and expansion processes We are assuming that those happen as ideally as possible and Ideal compression and expansion is modeled as being isentropic Therefore the four processes of our auto cycle are as follows One to two is isentropic compression two to three Is isochoric heat addition Three to four is isentropic expansion And then four to one is isochoric heat rejection and the relevant parameters to the auto cycle are displaced volume Compression ratio and the number of cylinders trial abbreviate as n Lastly because the auto cycle only occupies half of Of what the piston cylinder arrangement is actually doing If you are calculating the power output of an actual engine Let's say one that is operating at 2000 rpm Then you only get 1000 auto cycles per minute Does that make sense because there's an auto cycle happening and then there's the quote waste of time on quote While you are exhausting the gases bringing in fresh gases and then you have another auto cycle So in a 2000 rpm our engine, you're only getting 1000 auto cycles What that means is if you're calculating a power output you would take your mass inside the engine multiplied by your specific network out That would give you number of kilojoules or amount of energy per auto cycle Then you would multiply by the number of auto cycles per time unit So if we imagine that we were working this in kilojoules per kilogram and we multiply by a number of kilograms then we would multiply by Rotational speed let's say 2000 rpm's and Then we would multiply by one auto cycle per two revolutions and The way that this works is because the energy that you get over here is per auto cycle So auto cycle and auto cycle cancel This would give you power output So I realize I'm mixing the symbols here with numbers. Let's try an actual example. Say that you had an engine that was oh 2000 rpm had four cylinders each cylinder had 0.5 kilograms of air And each auto cycle was producing 400 kilojoules per kilogram That's a network out then you would take 0.5 kilograms per cycle times the number of cycles times the specific network out That's 400 kilojoules per kilogram and then you multiply by 2000 revolutions per minute and And then you multiply by one auto cycle for two revolutions and You remember that this 400 kilojoules per kilogram is per auto cycle and you're left with kilojoules per minute So if you multiply by one minute is 60 seconds, you would get kilojoules per second, which is a kilowatt Calculating the power output of a reciprocating engine Is easiest to do if you just piece together what you know don't think of it as a single equation