I'm a geophysicist and I can tell you that Nitrogen in your tires will absolutely make a significant difference in mileage and tire life
. Of course, that's assuming your car is a perfect sphere in a vacuum. You're right, the dryness is the only benefit.
You could calc it out using the gas law if you're a loser:
PV = nRT
P is the pressure (SI unit: pascal)
V is the volume (SI unit: cubic meter)
n is the number of moles of gas
R is the ideal gas constant (SI: 8.3145 J/(mol K))
T is the thermodynamic temperature (SI unit: kelvin).
Personally, I'd fill with regular air and spend my lonely Saturday nights contemplating this much more complex equation instead:
Girls = time + money
and, time = money
Therefore, Girls = money^2
Money = root [evil]
Therefore, Girls = (root [evil])^2 = evil.