An automobile tire is filled to a gauge pressure of 198 kPa when its temperature

Question

An automobile tire is filled to a gauge pressure of 198 kPa when its temperature is 20°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°C. Please answer part b.

(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.

ANSWER: 230 kPa

(b) Calculate the gauge pressure if the volume of the tire expands by 10%.

Explanation / Answer

here

P1*V1/T1 = P2*V2/T2 -->> P2 = P1*[V1/(1.1*V1)]*T2/T1

which is simply 230/1.1 = 209 kPa

and then the gauge pressure should be 209 - 198 = 11 kPa.

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