Greetings all, this is my first post. I’m attempting to solve a problem regarding different octane fuels for a combustion engine and how pressure from a turbo can influence the Auto Ignition Point (Temperature where a fuel can ignite before reaching its proper cylinder position). The items of interest here are going to be pressure, temperature, and volume. My first thought was to turn to the ideal gas law but no matter which way I turn I can’t seem to find an answer to properly convey that certain octane fuels have a certain max amount of psi you can feed pre-ignition before it can reach the auto ignition point. Math is below.

PV=nRT

What I know:

Auto Ignition Temp of 93 Octane = 280C or 553.15K

Auto Ignition Temp of Ethanol = 365C or 638.15K

My work:

First I want to find how many moles can fit inside of a single cylinder of a 2.5 liter engine 4 cylinder engine. 2.5L/4 = .625L.

Assuming when the pressure is in the downward position the atmospheres = 1

Temperature for this example when the cylinder is downward = 311.15K

So plugging information into the equation we get

1*.625L = n* .082(L?atm?K?1?mol?1) * 311.15K = 0.0244960669114967 mole

Now when the cylinder is completely in the up position the volume decreases from .625L to 0.05 L. I want to figure out what make pressure we can have given the moles we just calculated for since it won’t change.

P(atm) *.05L=0.0244960669114967 * .082(L?atm?K?1?mol?1) * 553.15K = 22.2219 atm

22.2219 atm = 326.57 psi.

Since the volume decreased 12.5 times, we can assume the pressure inside the cylinder if starting at 1 atm would increase to 12.5 atm or 183.75psi.

326.57 psi – 183.75psi = 142.82 psi. So what I get is that basically this fuel will never achieve the ability to detonate until ~143 psi which is not the case. Usually 22psi is the limit you can go before you start entering dangerous territory. What am I doing wrong? I know this is calculated for a perfect world but its not anywhere near what I know is the right answer. What am I doing wrong?