A car tyre has an internal volume of 2.2 × 10^-2 m^3. One day when the car has b

Question

A car tyre has an internal volume of 2.2 × 10^-2 m^3. One day when the car has been left standing and the temperature is 18 °C, the tyre overpressure (i.e. the amount by which the pressure in the tyre is above atmospheric pressure) is found to be 3.1 × 10^5 Pa. The car is then driven down a motorway, after which the overpressure in the tyre is found to have risen to 3.3 × 10^5 Pa.

(a) What mass of air would have to be let out of the tyre to reduce the pressure to its original value of 3.1 × 10^5 Pa? (Assume that the temperature of the air inside the tyre remains constant during this process.)

(In answering this question you may assume the air in the tyre behaves as an ideal gas, a constant atmospheric pressure of 1.0 × 10^5 Pa, and the average molar mass of air to be 2.9 × 10^-2 kg mol^-1.)

Explanation / Answer

a) ideal gas, we have PV=nRT. so n=PV/RT. assume that T and V is unchanged. so we have. n2-n1=(P2-P1)*V/RT=0.18(mol). so mass m=0.18*2.9e-2=5.3e-3(kg)

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