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

where

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.