Question

An automobile tire has a maximum rating of 38.0 psi (gauge pressure). The tire is inflated (while cold) to a volume of 11.8 L and a gauge pressure of 36.0 psi at a temperature of 12.0 °C. Driving on a hot day, the tire warms to 65.0 °C and its volume expands to 12.2 L. Does the pressure in the tire exceed its maximum rating? (Note: the gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.)

Answer 1

Im = 38.0 psi Pig - 36.0 psi Plabs Pig & P, atm P = 36.0 + 14.7 = 50.7 psi T = 12 + 273 = 285k V = 11.8L P2 = ? V2 = 12.2L T2 = 65+273 = 338k PV = P2 V2 T2 50.7 X 11.8 = P27 285 338 P2 = 58.15 psi Pag = P2 – 14.7 Pag = 58.15 - 1407 = 43.45 psi > 38 psi pressure in tire is gueter than maumum value .