Answer
a)A person breaths about 2200g of oxygen in a day.
b)The length of each side of the tank is 2.1m.
Work Step by Step
Given:Density of air(d)=1.29$\frac{kg}{m^3}$
a)The number of breath a normal person takes in a minute in 12 breaths per minute.
So in one day,the number of breaths =$12\times60\times24\frac{breaths}{day}$=17280$\frac{breaths}{day}$.
Also,typically a person breath about $\frac{1}{2}L$ of air per breath
Now,the mass of air a person breaths in a day ,m=density.volume
m=$1.29\times\frac{1}{2}\times17280\times10^{-3}$kg [$since,1m^3=1000L$]
=11.1kg
Since ,20% of this air is oxygen,the mass of oxygen a person breaths in a day is $\frac{20}{100}\times11.1$kg=2.2kg=2200g
b)The volume of the cubical tank,v=$x^3$ ,where x=length of each side of the cubical tank
Now,the volume of air that a person breaths in a day is$\frac{1}{2}\times17280\times10^{-3}m^3$=8.64 $m^3$
If this air is stored uncompressed in a cubical tank ,then both their volumes are equal i.e,
v=8.64$m^3$
$x^3=8.64m^3$
x=$\sqrt[3] 8.64$ m
=2.1 m
Therefore,the length of each side of the cubical tank is 2.1 m.
