Question

An ideal gas effuses from two different vessels $A$ and $B$ under identical conditions. $A$ has circular orifice while $B$ has square orifice. Calculate ratio of rate of effusion in $A$ to that in $B$ if radius of circle = $2$ times diagonal of square.

• A. $8\pi :1$
• B. $1:8\pi$
• C. $1:4\pi$
• D. $4\pi :1$

Answer 1

The correct option is B $1:8\pi$

Rate of effusion $\alpha$ density

$\alpha$ mass volume

$\alpha$ mass Area $\times$ Thukas

$\frac{R_A}{R_B}=\frac{AreaB}{AreaA}$

$=\frac{(side{)}^2}{\pi \times (Radius{)}^2}$

Radius $=2\times$ diagonal

$=2\times$ side $\sqrt{2}$

$d^2=5^2+5^2$

$d^2=25$

$d=5\sqrt{2}$ $\frac{R_A}{R_B}=\frac{(side{)}^2}{\pi \times 4\times 2\times side}$

$=\frac{1}{8\pi }$