Question

An open flask containing air is heated from $300\text{K}$ to $500\text{K}$. What percentage of air would escape into the atmosphere if the pressure is kept constant?

• A. 80
• B. 40
• C. 60
• D. 20

Answer 1

The correct option is B 40

According to Charle's law,
$V\propto T$ at constant pressure
Initial volume of air $V_1=V$
Initial temperature $T_1=300K$
Final temperature $T_2=500\text{K}$
Final volume $V_2=?$

At constant pressure, $V_1{T}_2=V_2{T}_1$
$\therefore V_2=\frac{V_1{T}_2}{T_1}=\frac{V\times 500}{300}=\frac{5V}{3}$
Hence, the volume of air increased due to the increase in temperature. In order to maintain constant pressure, some volume of air must escape.
$\therefore$ Volume of air escaped
= final volume - initial volume
$=\frac{5V}{3}-V=\frac{2V}{3}$

$\therefore$ % of air escaped
$=\frac{\text{volume of air escaped}}{\text{total final volume of air}}$

$=\frac{\frac{2V}{3}}{\frac{5V}{3}}\times 100=40\%$