# Where can I find an online reference explaining temperature, volume and pressure relationship?

Without assumptions. Every reference I find has lots of assumptions like “ideal gas” or “temperature remains constant” etc. No reference I found would even tell you even how much volume air would have as you continued to pressurize it in a piston. Temperature doesn’t remain constant, phase changes do occur, gasses are not perfectly ideal, etc. I am looking for correct answers not simplified ones!

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## 10 Answers

Try from here?

http://en.wikipedia.org/wiki/Ideal_gas_law

Your remarks on the volume if continued pressure in a piston, I don’t understand.

In the case of a piston, the volume is a direct consequence of the piston movement. Pressure and temperature then change as a consequence.

“In a piston, the volume is a dict consequence of the piston movement.” <—So how do I understand the piston movement? For instance if I have 1e5 Newtons of force on a piston described by some unnamed variables and I increase that to 1e12 Newtons what happens and why? “Ideal Gas Law” describes on ideal gasses so it is an incorrect answer for anything but a very narrow set of inputs.

I’m not sure the equation you’re hoping to find exists. The ideal gas law relates all three of these variables. I understand you don’t like the assumption of idealism, but if I recall correctly, most gases we encounter are close enough to being ideal that this equation serves as a good approximation.

If I recall my last chemistry class right (it’s been awhile, forgive me) there is another equation P1V1/T1 = P2V2/T2. That’s basically saying that if you have one data point for each P/V/T for the gas you’re interested in, the proportion will remain the same. But in order to calculate any one variable of P2/V2/T2, you need to know the other two. To my recollection this equation does not require that the gas be ideal.

The piston has a surface with which it pushes on the gas as a consequence of the force applied to the piston. This force equals the force generated by the pressure of the gas on that surface, else the piston would move.

So from the force on the piston you can calculate the pressure resulting in the cylinder.

From the pressure you can calculate the resulting volume and temperature combination of the cylinder. And yes… at one moment you need to decide to treat air as if it is an ideal gas and keep temperature changes in mind.

“at one moment you need to decide to treat air as if it is an ideal gas” <—If in the practical real world air was an ideal gas my air compressor wouldn’t have a water drain on the bottom of it. This is just one counterexample of the non-ideal gas air requiring real-world modifications to equipment due to its non-ideal nature in practical real-life situations.

Indeed… There is hot air, cold air, well and poorlycooled cylinders, moist air, dry air…. Etc.

@Mariah @Mariah Thank you both but none of these equations take into account things like work performed by the piston, phase changes, heat loss/gain through container, etc. I don’t think I could begin to accurately model a real-world device. This question I am asking is a HARD question but I still suspect their are resources which address it.

I’m going to make a recommendation…rather than trying to find a mathematical equation, try simulation software. VenSim is a good one. Now that I understand the level of complexity you’re looking at, I can see you’re probably going to end up with high order differential equations if you want to do this mathematically.

Simulation software will let you use math equations to model the individual facets that you do understand mathematically (work and heat transfer are described by equations, for example), but will model the complex system, which is a conglomerate of all of these more simple subsystems, numerically rather than analytically. It will still be an approximation as it will use Riemann sums to solve the integrals, but on good simulation software you can set the precision of the sums (at the expense of calculation speed) to get a good approximation.

Good luck.

@Mariah Thank you very much. I will check out VenSim. I already spend thousands per month on electricity doing some statistics. I have never done any mechanical modeling but I do have a pet project which motivates me to learn.

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