Tire Pressure Warning

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 = 29.8^OC

T₁    T₂             40^oC          T₂

Therefore I expect my tire pressure light to come on when the temperature drops below approximately 29 degrees celsius.

References

http://www.aa1car.com/library/tpms_warning_light.htm