We measure the pressure in an automobile tire early in the morningwhen the tempe

Question

We measure the pressure in an automobile tire early in the morningwhen the

temperature is 60?F. We read 35.1 psi (lb/in2 ) on the pressuregauge. This is the

pressure with respect to atmospheric pressure. To obtain theabsolute pressure of the air

in the tire we must add to this the pressure of the atmosphere. Onthat day, the

atmospheric pressure is 0.87 × 10 raised to the 5thpower Pa. Later in the day, the temperature is

71.8?F but the atmospheric pressure isunchanged. What will we read (psi) on

the pressure gauge if we measure the pressure in the tire then?Assume that the volume

of the tire remains the same.

Explanation / Answer

at the lower temp T1 (=288.7K), the pressure is P1 = Patm + P where Patm = .87 x 10^5 Pa P = 35.1 psi = 242000 Pa at the higher temp T2 (=295.26K), the total pressure P2 is givenby P2/P1 = T2/T1 >>> since volume remains the same P2 = (295.26/288.7)(242000+87000) = 336476 Pa tire pressure = 336476 - 87000 = 249476 Pa = 36.18 psi

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