Nitrogen inflation provides a more stable pressure not because of nitrogen, but because of what is removed when using nitrogen. Fundamentally, all gases will behave the same way in terms of the effect of temperature on pressure. For each 10 degrees of temperature change, there will be a corresponding pressure change of about +/- 1.9%.
The difference with nitrogen is water. When air is put under pressure, the humidity in it condenses to a liquid and collects in the tank. When air is added to the tire, the water is transferred along with the compressed air. As the tire heats up during operation, the liquid changes to a gas, expanding and causing a much larger pressure increase.
Because nitrogen is dry, there is no water in the tire to contribute to pressure fluctuations. Since nitrogen permeates out much slower than oxygen and water vapor, pressure changes due to leakage are reduced as well.
Using the Ideal Gas Law, let’s look at the effect of a 10 degree termperature change on both a truck tire and a passenger tire inflated with a dry gas.
The Ideal Gas Law equation1 is P*V=n*R*T. For this discussion, P and T change while n, R, and V are fixed or constant. Using algebra to isolate the variables of interest, P and T, the equation becomes P/T=(n*R/V). Therefore,
Pinitial/Tinitial=(n*R/V)=Pfinal/Tfinal since n, R, and V are all constant2.
As we have shown above Pinitial/Tinitial=Pfinal/Tfinal. This can be rearranged algebraically to Pfinal=[Pinitial*(Tfinal/Tinitial)]. This allows us to calculate Pfinal by multiplying Pinitial by the ratio of Tfinal to Tinitial. Note that temperatures must be converted to Kelvin units (K) from Fahrenheit units (F) for this calculation.
In the charts below, the tires are filled at 60F to 100 psig for the truck tire and 30 psig for the passenger tire.
1 - P = pressure, T = temperature, V = volume, R = the ideal gas constant, and n = the amount of gas in the tire in moles.
2 - We assume no volume (V) change (ie. no significant stretching of the tire rubber) and we consider the amount of gas in the tire (n) to be constant because the time frame is very short compared to the time it takes for gas to permeate through the tire rubber. The ideal gas constant (R) is, by definition, constant and therefore cannot change.