The tire is inflated (while cold) to a volume of 11.8 l and a gauge pressure of 36.0 psi (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.) at a temperature of 12.0 ∘c. while driving on a hot day, the tire warms to 65.0 ∘c and its volume expands to 12.2 l. what is the pressure in the tire after warming on a hot day?
Gauge pressure = total pressure – atmospheric pressure
Total pressure = gauge pressure + atmospheric pressure
Total pressure initially in 11.8 liter volume = 36.0 atm + 14.7 atm = 50.7 atm. Kelvin temperature = 12 + 273 = 285 K
Use the combined gas law to determine the total Pressure in volume of 12.2 liters. Kelvin temperature = 273 + 65 = 338 K
P1V1/ T1 = P2V2/ T2
50.7 atm(11.8 liters)/ 285 K = P2(12.2 liters)/338 K
P2 = 50.7(11.8) (338) / 285(12.2)
P2 = 58.2 atm
Total pressure = 58.2 atm
If one wanted the Gauge Pressure then
Gauge pressure = 58.2 atm – 14.7 atm = 43.5 atm
