Does tire pressure follow the "Gas Law" ?

OK kids, today's science lesson is about the stuff we inflate our tires with. If you don't want to take the lesson simply skip to the "Bottom Line."

If you took engineering, chemistry or perhaps some other science class in school, you might remember something called the "Ideal Gas Law"  PV=NRT.  I covered the formula in THIS post, and the resultant "Rule of Thumb" is that for every 10°F increase or decrease in temperature the pressure in your tires will increase or decrease by 2% . Now we need to be careful and remember that some may be discussing passenger tires where 2% of 36 psi is rounded to mean 1 psi change for 10°F change but I am discussing tire pressures that may range from 45 psi to 130 psi so percentage is more accurate.

But that formula is based on basic scientific theory of a dry gas used in a non-expandable container.

The first "fly in the ointment" is that most people are inflating their tires with compressed air and air is a combination of different gases such as 78.084% Nitrogen, 20.946% Oxygen, 0.934% Argon 0.03769% other gases such as  CO2 , Neon, Helium, Methane, Krypton, and Hydrogen. Note the concentrations of these trace gases along with various "pollution" changes over time so the specific percent varies slightly. Wikipedia has the details if you are interested.

The other major variable is the percent moisture. Water vapor varies between 1% and 5% depending on temperature and geographic location. It also varies based on the process of compressing air and the quality of maintenance the air compressor receives. In general the percent of water vapor will be raised in an air compressor, so unless special procedures are taken you are going to end up with a few percentage points of water vapor. Making this even more complex is that the effect of moisture on your tire pressure varies with temperature. This can range from less than 1 psi to almost 5 psi. I have a post on how you can make the air you use to inflate your tires "dryer" if you feel that is important.

In the equation the V stands for volume and since tires do expand a little bit as the pressure goes up and inflation gas isn't 100% dry or 100% of any one gas but a mixture of Oxygen, Nitrogen and other trace gases, these facts have an effect on how close to PV=NRT you will get with your tires.

Remember that even if you pay to "fill" your tires with Nitrogen you will never reach 100% nitrogen as there are always some other gases mixed in. In some experiments I have seen that the best you can reasonably expect to get would be about 95 to 98% N2.

Another problem is to know the actual temperature of the gas inside your tire. Most people have either an external TPM sensor or use an IR gun to measure the temperature of the tire and mistakenly assume that is the temperature of the gas inside the tire. About the only time you might obtain an accurate reading of tire inflation air temperature is many hours after last moving the tire and hours of storage in a constant temperature room so both in internal and external temperature is the same.

In an effort to get closer to the actual numbers I decided to try and do a quick experiment using an internal TPMS and an External TPMS on my Class-C motorhome. I ran into a number of problems.

Some of these problems include the fact that external sensors did not completely "wake up" in the first minute of operation so I was not able to easily get a zero point temperature reading.

Also we need to accept that despite claims to the contrary, TPM sensors are not calibrated laboratory grade instruments so they introduce some error into the experiment. Next we need to consider that external sensors are only providing the temperature of the metal in the sensor body which is affected by the outside air temperature. This will usually result in a cooler temperature reading than the actual temperature of the gas inside the tire.

I did collect some data but with all the variation I was able to identify I felt the experiment did not deliver any meaningful data. I did see variations in pressure readings between the internal and external sensors over time but the numbers were inconsistent.

What does all this mean?

BOTTOM LINE
1. Reality is much more complex than nice controlled laboratory experiments
2. Tire inflation pressure does vary with tire temperature and the pressure does increase as the temperature increases.
3. Dryer inflation gas will have less variation of pressure than "wet" inflation gas.
4. In my opinion none of the above observations is significant enough to change the "Rule of thumb" that we can expect our tire pressure to vary by about 2% for every change of 10°F.
5. We all need to remember that not every change or difference that is measurable is meaningful
6. Best advice I can give is not to get your shorts in a bunch about inflation.


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Why does my tire lose pressure? Simple and Technical answers

 As people get ready to start traveling again, some are discovering that their RV tires have lost inflation pressure over the past few months while it was parked. There are a number of possible contributors to a loss of pressure.

Some of these have been covered in my posts on leaking valve cores or metal valve O-Rings or possibly punctures or even rim corrosion. This post will cover just two of the possible causes. permeation and Temperature change.

The simple answer is that tire pressure will change about 2% for every 10°F change in temperature.

The complex answer and mathematical proof follows:

1. Normal pressure loss due to gas permeation. This is basically what happens when the molecules of gas "leak" or travel through the rubber of a tire. New passenger and LT tires sold to "Detroit" have to pass tests and meet a specification of a loss rate of less than 1% or 2% per month when averaged over a number of weeks or months, with different companies having different specs depending on the application. TBR (Truck-Bus-Radial) tires as seen on Class-A RVs will have similar performance goals. Low Cost import tires sold at "Billy-Jo-Bob's Cheep Tire Emporium and Bait Shop" may not have any such spec so might lose pressure faster because of the use of lower cost inner-liner rubber. This topic could be an entire post of its own but is quite technical and is not based on just the molecule size of Oxygen.

2. Tire inflation pressure is directly proportional to tire temperature. The "Ideal Gas Law" is a good approximation of what really happens. The general terms of the Ideal Gas Law are PV=NRT
 P is the Absolute pressure, not gauge pressure, measured in pascals
V is the air Volume measured in cubic meters. While tires do change a little bit in volume the difference is not meaningful for the purposes of this discussion.
N is the amount of gas in the air chamber in moles. For the purposes of this discussion, we can ignore this number as we are not changing the amount of gas in the tire when we are comparing the pressure difference just due to temperature difference.
R is the ideal, or universal, gas constant. R for dry air is 287.1 for N2 296.8 and for O2 259.8 for water vapor it is 461.5 so you can see that moisture in your inflation gas can significantly affect the Pressure/Temperature ratio a change from air (79%N2) to 95% N2 is not significant for the purposes of this discussion. I did a post on how to make your own "air dryer" so you can approximate the properties of dry air or dry Nitrogen.
T is the absolute temperature in degrees kelvin.

After discarding the inconsequential terms we really end up with is a simple ratio P2/P1 = T2/T1 and we can even ignore the conversion of psi to pascals as the ratio of pressure is the ratio of temperature in degrees Kelvin. Sorry we do need to use Kelvin but you don't need to do a conversion as you will soon see.

Lets see how this woks out
If P1 is 100 psi and if  T1 is 70°F or 294.261°K and if the temperature drops to 60°F or 288.706 °K we can solve for P2/P1 =  288.706/294.261 which leaves us with the ratio ot the two temperatures as 0.9811 so we had a 2% drop in pressure for a 10°F drop in temperature

30°F would be 272.039/294.261 = 0.92448 or 8% drop in pressure for a 40°F drop in temperature from 70°F to 30°F.

You may see various web pages such as this one from TireRack or Wikipedia saying 1psi for each 10°F change but you need to remember that this information is based on the assumption that the "normal" inflation is about 35 psi in a passenger tire.

What temperature for CIP "cold inflation pressure - Part two

The following is based on a couple posts I made on an RV forum but wanted to share with the rest of my readers

I had posted my comments on the thread from my Aug 25 post on CIP in the hopes of clarifying questions about adjusting inflation for various changes in ambient temperature, but there have been comments that indicate the need for more details when talking about tire temperature so here is a bit more info on the topic.

+++++++++
We really have two different but related temperatures to consider.

One set of temperatures is the external set. This would be the "Ambient" temperature of the air around us and the temperature of the road surface.
 The other and much more important temperature is the temperature of the tire structure.

Now with the correct instruments, it is possible to measure the temperature of the tire structure. This is done at test tracks and at race tracks using a small needle probe that sticks into the tire rubber 1/8" to 1/2" deep depending on the tire type & size and gives a reading the engineers use to make adjustments to race car suspension or to tire pressures. Since good & accurate tire "Needle Pyrometers" cost a couple hundred bucks, few individuals have them. Some think a simple IR gun from Harbor Freight is OK but all that does is give the approximate surface temperature of a tire which is always cooler than the important internal structural temperature. Rubber is an insulator so heat does not move through a tire structure from hot to cool very well so you can mislead yourself if you only use surface temperature. The IR gun is fine for conductive materials such as metal in a hub or brake drum.

Heat is generated at the molecular level not from belts rubbing against each other. This heat moves slowly from the hottest location (belt edges) to cooler surfaces. There is the surface of the air chamber and the surface on the outside of the tire.

The air on the inside of the tire gets warmed from the heat transfer from the inside surface of the tire. This air is also cooled by transfer to the metal wheel and the turbulence inside the tire means the temperature of the inflation gas (air) is fairly uniform.

The inside temperature is related to the outside temperature in that cooler outside temperature allows faster heat transfer from inside to outside so the inside temperature will be a little lower when the outside is lower but not in a 1:1 relationship.

Tire pressure will increase as described by Boyle's Law PV=NRT. I did the math proof in my blog post of March 13 2014 .

So after all that we are left with the facts that:

1. A tire generates heat based on deflection (tire inflation & load) and rate of deflection (speed)
2. More deflection due to more load or less inflation or both, results in more heat in the tire structure.
3. More speed means greater generation of heat. This is one reason tires have speed ratings.
4. If you lower the CIP you will generate more heat and this will hurt the rubber and eventually weaken it.
5. With sufficiently low inflation or sufficiently weakened rubber the heat will increase at a faster rate than it can flow out of the tire structure and can go into "run-away" increase which can result in a sidewall flex failure or "Blowout" due to shorter term low inflation or possibly a belt separation due to long term heating and weakening of the belt rubber.

I hope this clarifies and answers any additional questions.

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