Question

A car tyre has a volume of 10 litres when inflated. The tyre is inflated to a pressure of 3 atm at ${17}^{0}C$ with air. Due to driving the temperature of tyre increases to ${47}^{0}C$.

(a) What would be the pressure at this temperature?
(b) How many litres of air measured at ${47}^{0}C$ and pressure of 1 atm should be let out to restore the tyre to 3 atm at ${47}^{0}C$?

Answer 1

Given

$\left(a\right)P_1=3atm$

$T_1={17}^{o}C=290k$

$V_1=10C$

$P_2=?$

$T_2={47}^{o}C=320k$

for a constant volume

$\frac{P_1}{P_2}=\frac{T_1}{T_2}$

$P_2=\frac{P_1{T}_2}{T_1}$

$\frac{3\times 320}{290}=3.31atm$

$\left(b\right)$ pressure to be restored $=3atm$

decrease in pressure $=3.31-3$

$=0.31atm$

Let $V$ be the volume that is let out

$\therefore$ at constant temperature

$P_1{V}_1=P_2{V}_2$

$0.31\times 10=1\times V$

$V=3.1L$