Why does the air pressure inside the tires of a car increase when the car is driven?
The tyres become heated due to friction between the tyre and the road increasing the temperate of the tyre.
For the car to move, there has to be friction between the tyre and the road. Otherwise the car will go nowhere.
Hence a moving car has to do work against this friction. This work results in the transfer of energy to the tyres as heat.
If we consider the tyre to have a volume which is fixed (an approximation as the rubber provides some flexibility in volume) then the pressure law states that "for a fixed mass at constant volume, the pressure is directly proportional to the temperature (in Kelvin)." Hence the increase in temperature will result in an increase in pressure.
In molecular terms, molecules in the tyre collide with the tyre wall resulting in a force, and therefore, pressure on the tyre wall. The increase in temperature increases the kinetic energy, and hence the speed, of the air molecules in the tyre. The increased speed of the molecules will increase the number of collisions per second with the tyre wall. This in turn results in an increased force, and therefore increased pressure on the tyre wall.