Every winter my car’s tire pressure warning light comes on, even though no air actually escapes. As we learned in class, a drop in temperature of a gas is proportional to a drop in pressure, as the molecules lose internal energy. I decided to calculate the temperate drop required to make my pressure warning light come on for any given tire. A quick google search showed me that the pressure light comes on when the pressure (assuming gauge pressure) drops below 25% of the recommended psi, which is 31 psi, or 2.11atm.
25% of 31 = 23.25 psi = 1.58 atm
P1 = P2 à 2.11 atm = 1.58 atm àT2 = 29.8OC
T1 T2 40oC T2
Therefore I expect my tire pressure light to come on when the temperature drops below approximately 29 degrees celsius.