An automobile tire is filled to a gauge pressure of 161 kPa when its temperature

Question

An automobile tire is filled to a gauge pressure of 161 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 57 C 1) (a) Assuming that the volume of the tire does not change, and that air behaves as an tdeal gas, find the gauge pressure of the air in the tire. kPa Submit You currently have O submissions for this question. Only 5 submission are allowed. You can make 5 more submissions for this question. 2) (b) Calculate the gauge pressure if the volume of the tire expands by 10%. kPa Submit You currently have O submissions for this question. Only 5 submission are allowed. You can make 5 more submissions for this question.

Explanation / Answer

For part (1), first convert gauge pressure to absolute pressure and °C to K.

P1 = (101.3 + 161) = 262.3 kPa
T1 = 273 + 20 = 293K
P2 = ???
T2 = 273 + 57 =330 K.
V1 = V2 (volume unchanged);

P1/T1 = P2/T2;

P2 = (P1/T1)*T2 = (262.3/293)*330

= 295.42 kPa. From this subtract 101.3 you get approx 194.12 kPa as the gauge pressure.

For part (2) use the ideal gas law equation and substitute V2 = 1.1*V1 since the volume has increase by 10%.
P1*V1/T1 = P2*V2/T2

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

which is simply 295.42/1.1

= 268.545 kPa and the gauge pressure should be 268.454-101.3

= 167.245 kPa

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