(a) The pressure rise in the tyre is 149 kPa. (b) The mass of air that must be bled off is 17 g.
(a) Calculate the pressure rise.
Since the volume is constant but the pressure and temperature are changing, this is an example of Gay-Lussac's Law:
#color(blue)(bar(ul(|color(white)(a/a) P_1/T_1=P_2/T_2color(white)(a/a)|)))" "#
We can rearrange the above formula to get
#P_2=P_1 × T_2/T_1#
A gauge pressure (
Your data are:
The new pressure is 460.1 kPa.
The pressure rise is
(b) Calculate the mass of air to be bled off.
For this calculation, we can use the Ideal Gas Law:
#color(blue)(bar(ul(|color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#
We can re-write the Ideal Gas Law as
You would have to bleed off 17 g of air.