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) Assuming the volume of the tyre remains constant, what is the internal temperature of the tyre at the end of the motorway run?

(b) What is the internal energy of the air in the tyre before and after the
journey?

Explanation / Answer

a) PV=nRT. PV/T=const. so 2.2e-2*3.1e5/(273+18)=2.2e-2*3.3e5/T so T=310(K)=37(deg). b). n=PV/RT=2.2e-2*3.1e5/8.31*(273+18)=2.82(mol). so internal energy. U1=2.82*7R*(18+273)/2=23900(J). U2=2.82*7R*(37+273)/2=25400(J).

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