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Nitrogen's benefit in road tires is rather oversold, and mostly by companies who can make a profit by selling you nitrogen. All gases obey the same gas law: PV=nRT. And if the amount of gas is constant, then PV/T=constant. And if volume is constant as it is inside a tire on average, then P/T = constant. So as temperature (in absolute degrees) goes up, pressure goes up. As temperature goes down, pressure goes down which is why TPMS sensors go off in the cold to tell you to add pressure, because pressure actually went down with the temperature. Nitrogen is no different than air. Air is made up of over 75% nitrogen, then oxygen, then a few other gases. All of these gases obey the same gas law. The only time nitrogen might make a difference is if there is a lot of moisture in the air inside the tire. The amount of moisture in saturated air depends on the temperature. If there is a condition where the moisture in water form vaporizes, it adds to the pressure, but this is a very slight effect, and would only ever be noticed by professional racers or experienced track drivers who could tell the difference of 0.5 psi in a tire. Very few drivers can tell that when pushing a car at the limit. And then this is only a problem if the air is not dried as it should be from a proper tire filling station. If there is no moisture in the air, then nitrogen will act exactly the same as air in a tire. The only other claim to fame is that pure nitrogen will oxidize the inside of the tire less than air, since there is no oxygen. If you drive your tires for 500,000 miles, this might, might make a difference. And some people think that the size of the molecules means that pure nitrogen might leak less over many, many months. I have never seen any conclusive test that validates any benefit for nitrogen for regular car use except the benefit of nitrogen vs moist air in terms of slight pressure variations. If you are racing professionally, then nitrogen makes sense, plus you carry N2 bottles to the track for other uses.

If you search for publications from even tire companies on the benefit or lack of benefit to nitrogen use in tires, you will see that while there is nothing wrong with using pure nitrogen in tires, there is very little need for it vs air. Extracting nitrogen from air takes energy which would be better saved for more useful purposes.
 

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Some info here on partial pressures and Dalton's law: http://www.bae.uky.edu/~snokes/BAE549thermo/psychrometrics.htm

And I had saved this post a while back from user pisgahchemist on eng-tips:

"as the temperature of a gas increases, then the pressure of the gas increases, but it stays a gas. A gas won't condense as the temperature increases while the volume remains constant. Consider the combined gas law: P1*V1/T1 = P2*V2/T2. If we assume that V is constant (the volume of the tire may increase by a percent or two, but for our purposes, the volume remains constant) then P1/T1 = P2/T2 which is a direct proportion: as T increases, P increases. Suppose that at 20C (293K, 68F) the absolute pressure of the water vapor in the tire is 1.00 psi, which is what it would be if the air were saturated in water vapor. Then at the temperature where the tire is operating, let's say 100C (373K, 212F), the vapor pressure will be 1.27 psi absolute, well below the 14.7 psi where liquid water and water vapor are in equilibrium at 100C. (The 1.00 psi is determined by assuming that a tire has an absolute pressure of 44 psi (30 psi guage + 14 psi atmospheric) which is about 3 times atmospheric pressure. Using a table of vapor pressures, we can determine that the equilibrium pressure of water vapor at 20C is 0.340 psi before compression.) The new pressure of the water vapor in the hot tire is calculated from:
P2 = P1 * T2 / T1 = 1.00 psi * 373 K / 293K = 1.27 psi
Therefore, we can conclude that simply raising the temperature would never cause water vapor to condense.

A compressor works by mechanically forcing a gas into a smaller volume which increases the pressure:
P2 = P1 * V1 / (V2 ) where P is inversely proportional to V. As V decreases, P increases.
If the volume is small enough and the resulting pressure great enough, then it is possible for some of the water vapor in the air to condense to form liquid water, and release heat. The heat energy that is released is the energy of motion (kinetic energy) originally possessed by the water molecules in the gaseous state. The kinetic energy of molecules in the liquid state are much less than the kinetic energy of gas molecules. And it is this difference in energy that shows up as a small amount of temperature increase in the compressed air.

But the majority of the heat energy that causes the compressed air to be hot comes from doing work on the gas by compressing it. The energy that is applied to the gas shows up as an increase in kinetic energy which of course is proportional to temperature. The air which is emitted by the compressor is still mixed with water vapor since only a fraction condenses. If the compressor is any good at all, the air goes through a dryer of some description which either allows the water vapor to combine with a desiccant (often calcium chloride), or be condensed by a refrigerator, which is the way that a household dehumidifier works.

The bottom line is that you will never have liquid water forming inside a tire that is being operated at an elevated temperature."
 
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