An automobile tire is filled to a gauge pressure of 175 kPa when its temperature

Question

An automobile tire is filled to a gauge pressure of 175 kPa when its temperature is 20 degree C. (Gauge pressure is the difference between the actual pressure and atmospheric pressure.) After the car has been driven at high speeds, the tire temperature increases to 52 degree C. 1) (a) Assuming that the volume of the tire does not change, and that air behaves as an ideal gas, find the gauge pressure of the air in the tire. kPa (b) Calculate the gauge pressure if the volume of the tire expands by 10%. kPa

Explanation / Answer

Solution: Initial actual pressure within the tire = (175 + 101.325) kPa = 276.325 kPa as atmospheric pressure is 101.325 kPa.

(a) If the volume of the tire does not change and the gas inside behaves as ideal; it will obey the relation: P1/T1 = P2/T2, so we get actual pressure, P2 = 306.5 kPa and the gauge pressure will be (306.5

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