THE IDEAL GAS LAW FORMULA might help explain why different gases expand at virtually the same rate as their temperature increases.
A gas may be completely described by its makeup, pressure, temperature, and volume. Where P is the pressure, V is the volume, n is the number of mols of gas, T is the absolute temperature, and R is the Universal Gas Constant,
P V = n R T
This formula is the "Ideal Gas Law Formula." Although there is no such thing as an ideal gas the formula is pretty accurate for N2, CO2, and oxygen as we assume that the gas molecules are point masses and the collisions of the molecules are totally elastic. (A completely elastic collision means that the energy of the molecules before a collision equals the energy of the molecules after a collision, or, to put it another way, there is no attraction among the molecules.) The formula becomes less accurate as the gas becomes very compressed and as the temperature decreases but here "very compressed" pressures are well above even the highest tire pressures and "decreased temperatures" are extremely cold, too cold for tires. There are some correction factors for both of these factors for each gas to convert it to a Real Gas Law Formula, but the Ideal Gas Law is a good estimation of the way N2, CO2 and "air" should react through temperature changes.
What does all this mean? It simply means that "air", nitrogen vapor, and CO2 vapor should all react pretty much the same within normal tire pressures (0-120 PSI) and temperatures.
Above is from
this site which will tell you more than you ever wanted to know about nitrogen in tires.
Bottom line - it's a waste of money.My question is why 80 PSI cold. Have you weighed the RV and checked an inflation chart? Over inflated tires ride harder and are more susceptible to road hazard damage.