Question

An automobile tire having a temperature of −1.6 ◦C (a cold tire on a cold day) is filled to a gauge pressure of 22 lb/in2 . What would be the gauge pressure in the tire when its temperature rises to 45◦C? For simplicity, assume that the volume of the tire remains constant, that the air does not leak out and that the atmospheric pressure remains constant at 14.7 lb/in2 . Answer in units of lb/in2 .

Answer 1

25.8 lb/in²

Step-by-step explanation:

Gay-Lussac's law tells us that given an ideal gas of a certain mass has a constant volume, the pressure exerted on the sides of its container is directly proportional to its absolute temperature.

`(P_(1) )/(T_(1) ) = (P_(2) )/(T_(2) ) \\\\(22)/(-1.6+273.15) =(P_(2) )/(45+273.15) \\\\P_(2) = (22*318.15)/(271.55) = 25.8lb/in^(2)`