Serway & Jewett — The Kinetic Theory of Gases: Problem 15.

You are working for an automobile tire company. Your supervisor is studying the effects of molecules striking the inner surface of the tire due to their thermal motion. He gives you the following data from a recent experiment. The air in a tire on a parked car was measured to have a gauge pressure of \(P_i = 1.65 \text{ atm}\) on a day when the temperature was \(T = 6.5^\circ\text{C}\). The car was then driven for a while and then measurements were taken again. The gauge pressure in the tire was then \(P_f = 1.95 \text{ atm}\) and the interior volume of the tire had increased by \(5.00\%\). (a) Your supervisor asks you to determine by what factor the rms speed of the air molecules had increased from the first measurement to the second. (b) He also hints at a proposal he is going to make to replace air in tires with argon. Will this change the factor by which the average speed of the molecules changes in the conditions described?