Why do you need to add air to your tires when the temperature drops? The temperature inside and outside of the tire is the same (let's assume that you aren't currently driving, and your car has been sitting for a few hours). I understand that the absolute pressure of the tire drops, because P=nRT/V but why doesn't that apply to the outside atmosphere as well?
What I don't understand is why relative pressure of the tire (to the atmospheric temperature) doesn't remain the same. I'm thinking that it might have something to do with the weight of the car, or that the atmosphere doesn't exactly have a fixed volume. Any insight would be much appreciated!