Question

The average time taken by a molecule of oxygen at $300\text{K}$ to travel a distance equal to the diameter of the earth is : (Diameter of earth $=12800\text{km}$)

• A. $5\text{hr}$
• B. $10\text{hr}$
• C. $8\text{hr}$
• D. $15\text{hr}$

Answer 1

The correct option is C $8\text{hr}$

Given,
Temperature, $T=300\text{K}$
Distance, $d=$ diameter of earth
$=12800\text{km}$
We know that, average speed
$V_{av}=\sqrt{\frac{8RT}{\pi M}}=\sqrt{\frac{8\times 8.3\times 300}{3.14\times 32\times {10}^{-3}}}\approx 445\text{m/s}=445\times \frac{18}{5}=1602\text{km/h}$
Now, average time taken to travel distance $d=12800\text{km}$
$t=\frac{d}{V_{av}}=\frac{12800}{1602}\approx 8\text{hr}$