I've heard Nitrogen holds its pressure regardless of temperature changes and due to slightly larger molecule size it does not escape the tire. Is it a good idea to fill Motorcycle tires with Nitrogen?
And can we mix Nitrogen with regular compressed air in tires?
Most of the claims made for filling tires with nitrogen are either complete bunk, or are based on misunderstandings of physics.
If you are filling your tires with air, you are already filling them with 78% nitrogen, so yes, it mixes fine with air.
Now as for the temperature and pressure relationships ... All gases which are at pressures well above their corresponding boiling points (oxygen, nitrogen, carbon dioxide, argon all fit this description under normal atmospheric conditions) follow something called the ideal gas law with extreme accuracy: PV=nRT where P=absolute pressure, V= volume, N=number of moles of gas (basically related to the amount of gas that we are talking about), R is a universal constant, T=absolute temperature. The inside of a tire is a fixed volume and once you have closed that tire valve, it is also a fixed mass (i.e. fixed number of moles). So then P = T multiplied by a constant, i.e. the absolute pressure is proportional to the absolute temperature. It doesn't matter what the gas is. Oxygen, nitrogen, doesn't matter.
There is one constituent of normal air that we have not discussed ... Water.
Water is NOT far enough away from its normal boiling temperature for the above equation to hold true. In fact, at normal ambient temperatures, it can exist as both a gas and a liquid (but hopefully not a solid, unless you are riding in winter). When water changes state from liquid to gas, there is an enormous increase in its volume. If this is happening inside a fixed volume, this translates to a larger-than-gas-law-predicts change in its pressure. The vapor pressure of water is very strongly dependent on temperature.
Compressed air coming out of a normal ordinary air compressor ... contains water that was condensed out of the air.
Nitrogen coming out of a gas cylinder ... does not. So the advantage of using nitrogen coming from a gas cylinder is really that it doesn't contain water.
Compressed air that has gone through an air dryer (industrial air compressors often have this, to avoid having water cause trouble in their system) ... will have the same effect.
But ... If you lubricated your tire beads with a soap and water solution in order to help seat the bead ... guess what; you just introduced some liquid water to the system which wipes out all foreseeable advantage of using either dry nitrogen or dry compressed air.
Nitrogen molecules "bigger" than oxygen molecules? No, not appreciably so; not enough to make an appreciable difference in this application. Your tires are not made of selective membrane material (used in oxygen purifiers - to help old folks breathe when their lungs don't work well enough any more).
"So why do aircraft use nitrogen" ... because aircraft tires are subject to very heavy heat loads on landing, and nitrogen removes a potential fire/explosion source! And the inflation pressure required on tires for a Boeing 747 might be a little above what a normal shop air compressor can do.