Question #0a30f
1 Answer
(a) The pressure rise in the tyre is 149 kPa. (b) The mass of air that must be bled off is 17 g.
Explanation:
(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 (
or
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)|)))" "#
Since
We can re-write the Ideal Gas Law as
or
Since
You would have to bleed off 17 g of air.