Question

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

(a) What would be the pressure at this temperature?

(b) How many litres of air measured at ${47}^{\circ }C$ and pressure of $1atm$ should be let out to restore the tyre to $3atm$ at ${47}^{\circ }C$?

Answer 1

Given V=10 litre, P=3 atm, T=290k

(a) After driving V=10 litre, P=? T=320K

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

or $\frac{3}{290}=\frac{P_2}{320}$

or $P_2=\frac{320\times 3}{290}=3.31atm$

(b) At ${47}^{0}C$

Now volume is to be taken out so that tyre is left at a pressure this air will occupy V litre

$P_1{V}_1=P_2{V}_2$ (temperature is ${47}^{0}C$)

$0.310\times 10=1\times V_2$

$V_2=3.1$ litre .