Question

An automobile tire is filled to a gauge pressure of 195 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 55°C.

(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

Answer 1

(a)

Given that,

Gauge pressure at 20 oC = 195 kPa

Ti = 20 + 273 = 293 K

Tf = 55 + 273 = 328 K

Absolute pressure at 20oC temperature,

P = 195 + 101.3 = 296.3 kPa

At constant volume,

P' = P*(T' / T) (from ideal gas equation)

P' = 296.3 * (328 / 293)

P' = 331.69 kPa

gauge pressure of the air in the tire,

P = 331.69 - 101.3 = 230.39

P = 230.39 kPa

(b)

Final volume, V' = V + (10/100)*V = 1.1V

From ideal gas equation,

P'V' / Tf = PV / Ti

Pressure P' = (PV / Ti) / (V' / Tf)

gauge pressure,

P' = 198.44 kPa