Answer: The pressure after the tire is heated to 17.3°C is 167 kPa
Explanation:
To calculate the final temperature of the system, we use the equation given by Gay-Lussac Law. This law states that pressure of the gas is directly proportional to the temperature of the gas at constant pressure.
Mathematically,
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]
where,
[tex]P_1\text{ and }T_1[/tex] are the initial pressure and temperature of the gas.
[tex]P_2\text{ and }T_2[/tex] are the final pressure and temperature of the gas.
We are given:
[tex]P_1=149kPa\\T_1=-14^0C=(273-14)=259K\\P_2=?=27.5psi\\T_2=17.3^0C=(273+17.3)=290.3K[/tex]
Putting values in above equation, we get:
[tex]\frac{149}{259}=\frac{P_2}{290.3}\\\\P_2=167kPa[/tex]
Hence, the pressure after the tire is heated to 17.3°C is 167 kPa
