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?

A student comes to school by a bicycle whose tire is filled with air a

1.	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?
Answer» Solution :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 `39^(@)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)xx240xx10^(3)=249.6kPa`