The recent cold weather and speaking of thermodynamics in class got me thinking about how thermodynamics impacts our daily lives. A common example of the effect of thermodynamics is the change in tire pressure from summer to winter. How much does the pressure in a car tire change as the temperature changes from summer to winter?
To find out, I used the following model: the car tires were filled on a nice summer day (temperature 27 C). The car being used in this model is a Mini Cooper and, according to Firestone’s website, its ideal tire pressure is about 35 psi. Assuming no loss in air mass or volume and using the ideal gas law (pv = nkT), the change in air pressure from summer to winter (temperature -1 C) can be calculated without necessarily knowing the volume of air in the tires (shown below).
P(s)V = nkT(s)
P(s)/T(s) = nk/V
P(w)/T(w) = nk/V
Because the air mass and volume don’t change n, k and V are constants.
P(w)/T(w) = P(s) / T(s)
P(w) = P(s) T(w)/ T(s)
P(s) = 35 psi * 1Pa/1.5 * 10^-4 psi = 241317 Pa
T(s) = 27 C + 273 = 300 K
T(w) = -1 C +273 = 272 K
P(w) = 241317( 272) / 300 = 218,794.08 Pa
This can be used to show that a tire looses 22, 522.92 Pa (P(s) -P(w)) in tire pressure from summer to winter