# Q & A: car tires heating up

Q:
If the temperature of a car's tire increase during motion.. How does that affect air's( inside the tire ) pressure and volume?
- TariQ (age 17)
Egypt
A:
First, let me give some background for other readers.  Car tires heat up from friction during driving. The friction is largely internal friction in the rubber as it flexes. Since the air inside then heats up, it increases the product of the pressure p and volume V, following the ideal gas law pV= NkT, where N is the number of gas molecules, k is Boltzmann's constant, and T is the absolute temperature. Let's say that under intense fast  driving T increases about 10%, maybe a high estimate but a convenient number.  (It's very important here to use absolute temperature, e.g. Kelvin, not some arbitrary scale, e.g. Celsius. So here we're talking about an increase of about 30K or 30°C.) So your question is: how much of that 10% increase in pV shows up in p and how much in V?

Tires are fairly rigid, so that tends to keep V fixed. When you're filling a tire, you can see as you go from say 25 psi to 35 psi that the tire expands a little, but not by anywhere near a factor of 1.4.  So I think almost all of the increase in pV will show up in p. As a guess, for a 10% increase, maybe p will go up a little over 9%. There are now some tire sensors that detect both p and T, so someone with one of those could give more precise numbers, at least for some particular tire.

As a practical matter, this heating effect is one of the reasons that tires should be kept properly inflated. If they're under-inflated, the increased flexing causes more heating. The extra heat and the flexing itself are both damaging to the tires.

Mike W.

(published on 12/25/2012)