Answer:
T₂ = 280.17 K
Explanation:
Here, we can use the equation of state to find the final temperature of air in tires. Equation of State is written as follows:
[tex]\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}[/tex]
Since, the volume is constant.
Therefore,
[tex]V_{1} = V_{2} = V\\\\\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}\\\\T_{2} = \frac{T_{1}P_{2}}{P_{1}}[/tex]
where,
T₂ = Final Temperature of Air in Tire= ?
T₁ = Initial Temperature of Air = 270.734 K
P₁ = Initial Pressure of Air = 454.518 KPa
P₂ = Final Pressure of Air = 470.361 KPa
Therefore,
[tex]T_{2} = \frac{(270.734\ K)(470.361\ KPa)}{454.518\ KPa}[/tex]
T₂ = 280.17 K
