Answer : The temperature of the air in the tire is, 341 K
Explanation :
Gay-Lussac's Law : It is defined as the pressure of the gas is directly proportional to the temperature of the gas at constant volume and number of moles.
[tex]P\propto T[/tex]
or,
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]
where,
[tex]P_1[/tex] = initial pressure = 198 kPa
[tex]P_2[/tex] = final pressure = 225 kPa
[tex]T_1[/tex] = initial temperature = [tex]27^oC=273+27=300K[/tex]
[tex]T_2[/tex] = final temperature = ?
Now put all the given values in the above equation, we get:
[tex]\frac{198kPa}{300K}=\frac{225kPa}{T_2}[/tex]
[tex]T_2=340.9K\approx 341K[/tex]
Therefore, the temperature of the air in the tire is, 341 K