Answer: The gauge pressure of the air in the tires is 179.5 kPa.
Solution :
Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.
The combined gas equation is,
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
where,
[tex]P_1[/tex] = initial pressure of gas = Atmospheric pressure + gauge pressure = 101 kPa + 165 kPa = 266 kPa
[tex]P_2[/tex] = final pressure of gas = ?
[tex]V_1[/tex] = initial volume of gas = [tex]1.63\times 10^{-2}m^3[/tex]
[tex]V_2[/tex] = final volume of gas = [tex]1.70\times 10^{-2}m^3[/tex]
[tex]T_1[/tex] = initial temperature of gas = [tex]0^oC=273+0=273K[/tex]
[tex]T_2[/tex] = final temperature of gas = [tex]27.3^oC=273+27.3=300.3K[/tex]
Now put all the given values in the above equation, we get the final pressure of gas.
[tex]\frac{266\times 1.63\times 10^{-2}}{273K}=\frac{P_2\times 1.70\times 10^{-2}}{300.3K}[/tex]
[tex]P_2=280.5kPa[/tex]
Gauge pressure = Absolute pressure - atmospheric pressure = (280.5 - 101) kPa= 179.5 kPa
Therefore, the gauge pressure of the air in the tires is 179.5 kPa.
