A student comes to school by a bicycle whose tire is filled with air at a pressure 240 kPa at `27^(@)`C. She travels 8 km to reach the school and the temperature of the bicycle tire increases to `39^(@)`C. What is the change in pressure in the tire when the student reaches school?

Explanation

We can take air molecules in the tire as an ideal gas. The number of molecules and the volume of tire remain constant. So the air molecules at `27^(@)C` satisfies the ideal gas equation `P_(1)V_(1)=NkT_(1)` and at `396^(@)C` it satisfies `P_(2)V_(2)=NkT_(2)`.
But we know
`V_(1)=V_(2)=V`
`(P_(1)V)/(P_(2)V)=(NkT_(1))/(NkT_(2))`
`(P_(1))/(P_(2))=(T_(1))/(T_(2))`
`P_(2)=(T_(2))/(T_(1))P_(1)`
`P_(2)=(312K)/(300K)" "240" "10^(3)Pa=249.6kPa`