Using the temperature-pressure relationship, why you should check your tire pressure when the temperature changes?
Gas pressure is directly proportional to Kelvin temperature, so when the temperature of the air drops, the pressure in a tire will drop as well.
Here are some numbers to back this up.
Which can be rearranged to give
Lets say the temperature changes from 5°C to-25°C (we had a situation similar to this only a few weeks ago in Winnipeg, where I live). Expressed in Kelvin, this is a change of 278 K to 248 K.
The resulting change in pressure (expressed as a fraction) would be
So, this is better than a 10% drop in pressure within a tire. Not enough to make it go flat, but enough to cause it to wear improperly and waste fuel.