Question

A flask containing air (open to atmosphere) is heated from $300K$ to $500K$. The percentage of air escaped to the atmosphere is nearly?

• A. $16.6$
• B. $40$
• C. $60$
• D. $20$

Answer 1

The correct option is B $40$

Assume the flask to have a volume of $VL$.

From ideal gas equation-

$PV=nRT$

Since the pressure is kept constant.

$V\propto T$

$\frac{V_1}{V_2}=\frac{T_1}{T_2}.....\left(1\right)$

$V_1=$ Initial volume $=VL$

$V_2=$ Final volume $=?$

$T_1=$ Initial temperature $=300K$

$T_2=$ Final temperature $=500K$

$\frac{V}{V_2}=\frac{300}{500}$

$\Rightarrow V_2=\frac{5}{3}V$, i.e., the gas has expanded.

Since the volume of the flask can contain only $VL$ of air, the remaining air will escape.

Amount of air escaped $=\frac{5}{3}V-V=\frac{2}{3}V$

percentage of air escaped to the atmosphere $=\frac{\left(\frac{2}{3}V\right)}{\left(\frac{5}{3}V\right)}\times 100=40\%$

Hence the required answer is $\left(B\right)40$.