# Max PSI Before a Certain Temperature is Reached

Tags:
1. Jun 4, 2015

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?

2. Jun 4, 2015

### MrAnchovy

You are ignoring the fact that the gas inside the combustion chamber heats up as it is compressed. Wikipedia has a fairly relevant entry.

3. Jun 5, 2015

You are correct however since we are looking for the max pressure we can aquire before the auto ignition temp of when 93 octane can ignite without spark (553.15K), we input this into the equation to find what pressure would allow this to be heated to this temperature. Good input but the final temperature is a constant in the regard of this testing. Anyone else have any input to help me out?

4. Jun 5, 2015

I think where I'm having trouble is the timing aspect of an engine. Essential you can adjust when the spark actually happens during the compression cycle to maximize the pressure/force against the piston it achieve greater power output. If you spark the fuel/oxygen mixture earlier it allows it a larger time to expand the controlled explosion in the cylinder increasing pressure. Taking that out I'm assuming that the spark is only happening when the cylinder is in the upright position. I think I may have found where my experiment stops because I have no idea how to even go about finding out information past the ideal gas law.

5. Jun 5, 2015

### Staff: Mentor

That sounds like a question whose answer should be found in textbooks or tutorialsa out Otto Cycle engine design. Have you searched for those?

6. Jun 5, 2015

### MrAnchovy

That's funny because I've never heard of the law of conservation of temperature. The law of conservation of energy on the other hand says that when you do work against a gas to compress it, the temperature of the gas goes up. The pressure at TDC is therefore much greater than the intake pressure times the compression ratio.

7. Jun 5, 2015