Question

Before taking a trip, you check the air in a tire of your automobile and find it has a pressure of 33 lb in^-2 on a day when the air temperature is 17°C (about 63oF). After traveling some distance, you find that the temperature of the air in the tire has risen to 46°C (approximately 115°F). What is the air pressure in the tire at this higher temperature, expressed in lb in^-2?

Answer 1

We can use ideal gas equation to solve this problem.

PV = nRT since considering tyre elasticity (very high) we can ignore volume change.

Hence V,n,R are constants

1 lbf/in2 = 0.068046 atm; 1 atm = 14.695975 lbf/in2

33 lbf/in2 = 2.245518 atm; 17^oC = 17 + 273.15 = 290.15 K; 46^oC = 319.15 K

P1 / P2 = T1 /T2

P1 = (T1 / T2 ) x P2

P1 = [(319.15 K) / (290.15 K)] x 2.245518 atm

P1 = 2.46995371256 atm

P1 = 2.46995371256 x 14.695975 = 36.298378011 lbf/in2

The air pressure in the tire at this higher temperature = 36 lbf/in2   (2 sig fig)

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