Answer:
[tex]T_{f} = 312.348\,K\,(39.198\,K)[/tex]
Explanation:
Let assume that gas inside the automobile tire behaves as an ideal gas. Due to the absence of leakages, the number of moles remains constant during the trip. Air temperature can be found by using the following relation:
[tex]\frac{P_{o}}{T_{o}}=\frac{P_{f}}{T_{f}}[/tex]
Final temperature is cleared with the expression:
[tex]T_{f} = \frac{P_{f}}{P_{o}}\cdot T_{o}[/tex]
[tex]T_{f} = \frac{220\,kPa}{210\,kPa}\cdot (298.15\,K)[/tex]
[tex]T_{f} = 312.348\,K\,(39.198\,K)[/tex]
