Question

During one of his adventure, Chacha chaudhary got trapped in an underground cave which was sealed two hundred year back. The air inside the cave was poisonous, having some amount of carbon monoxide in addition to $O_2$ and $N_2$. Sabu, being huge could not enter into the cave, so in order to save chacha choudhary he started sucking the poisonous air out of the cave by mouth. Each time, he filled his lungs with cave air and exhaled it out in the surroundings. In the mean time fresh air from surrounding effused into the cave till the pressure was again one atmosphere. Each time Sabu sucked out some air, the pressure in the cave dropped to half of its initial value of one atmosphere. If the initial sample of air from the cave contain $5\%$ by volume $CO$.
If the safe level of $CO$ in the atmosphere is less than $0.001\%$ by volume how many times does Sabu need to such out air in order to save Chacha chaudhary.

Answer 1

Answer: 13

Vol. of $CO$ left $=\frac{\text{ Initial vol. of }CO}{2^n}$
$n=$ Number of sucking time
$0.001=\frac{5}{2^n}$
$2^n=5000$
$n\times \log 2=\log 5+\log 10^3$
$n=13$ times