## Engineering Question #4990

Jeff, a 36 year old male from Calgary asks on April 19, 2010,

I'm having a debate with a friend about the supposed benefits of filling your tires with Nitrogen gas. The major claim seems to be that N2 is less thermally expansive than normal air, so your tires will not increase or decrease pressure as much when temperatures change. I remember the Ideal Gas Law (PV=nRT), but the value of R, the ideal gas constant, seems to be a "close enough" approximation of how most gasses behave. I've read that most diatomic gases behave pretty much identically under the normal range of temperature and pressure we're talking about, but I can't find a difinative answer if pure nitrogen has different thermal expansion properties vs normal air (assume 78% nitrogen, 21% oxygen, 1% argon). To really put this to bed, I need a specific value of R for all three gasses. Any thoughts?

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### John Jones answered on April 20, 2010

Short answer: there is no advantage to filling the tires with nitrogen; the thermal expansion of nitrogen is not significantly different from that of air.

Longer answer: the ideal gas law, pV=nRT, is indeed just an approximation, but to tailor it to the behaviour of real gases, you don't just tweak the value of R, you use the more accurate van de Waals equation:

(p+n2a/V2)(V-nb) = nRT

where the parameters a and b reflect the deviations of a given real gas from ideal behaviour. If a and b are both zero, the gas will behave as an ideal gas.

For nitrogen, a = 1.408 and b = 0.039; for oxygen, a = 1.378 and b = 0.032

For comparison, for CO2 a = 3.6 and b = 0.04, while for helium, a = 0.034 and b = 0.023.

The conclusion we draw from this is that, while neither nitrogen nor oxygen is quite ideal, their deviations from ideality are almost identical; thus the expansion coefficient of pure nitrogen will be almost identical to that of air.

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