When a car is in motion, the temperature of the tyre rises due to increases in the kinetic energy of the air molecules inside the tyre. Assuming air to be ideal gas, the equation of state is given by
PV = n RT
∴ Change in the state of the system is given by
∆ PV = ∆ n RT ……(1)
Since there is no change in volume or composition, we can rewrite equation (1) as V∆ p = nR ∆ T
Since temperature rises during motion, ∆T is positive. Therefore, ∆P is also positive implying that pressure inside tyre increases when the car is in motion.