You inflate your car tires to a gauge pressure of 2.43 atmospheres at a temperature of 24 degrees C. After driving a couple of miles the temperature of the tire increases by 46 degrees C. What is the new gauge pressure to the nearest hundredth of an atmosphere? What fraction of the air would you have to let out of the tire in order for the pressure to return to its original value?

Answer 1

The ratio of final to initial ABSOLUTE temperature is 319/297 = 1.0741

Absolute pressure increases by the same ratio, so the final absolute pressure is (2.43+1)*1.0741 = 3.663
The final gauge pressure is 2.663 atm. Remember that absolute pressure is always 1 atm more than gauge pressure.

PV = nRT
P/(nT) = constant

To return to original pressure P, n*T must remains the same, so the amount of gas (n) must be multiplied by a factor 1/1.0741 = 0.931
That would require releasing 6.9% of the gas in the tire