Question

A human adult breathes in approximately 0.50L of air at $1atm$ with each breath. If an air tank holds $10L$ of air at $200atm$ . How many breaths the tank will supply?

Answer 1

Hint:
The number of breaths that will be supplied can be found by finding the product of volume and pressure of one breath. The number of breaths that can be obtained from the tank depends on the volume and pressure of the tank. The number of breaths will always be restricted by the volume or pressure of the tank.
Formula used:
$PV = nRT$
Where $P$ is the pressure, $V$ is the volume of the gas, $n$ is the number of moles, $R$ is the gas constant and $T$ is the temperature.
For this question we will consider $n$ to be the number of breaths.

Complete answer:
The question first mentions the volume and pressure of one breath. The tank has a particular volume from which the adult can take a breath. To find the answer we will take the ratio of one breath to maximum number of breaths. We will consider the maximum number of breaths to be $x$ .
Therefore, the equation will be as follows,
$\dfrac{{{P_1}{V_1}}}{{{P_2}{V_2}}}$=$\dfrac{{{n_1}RT}}{{{n_2}RT}}$
Where, ${P_1}$ is the pressure of one breath = $1atm$
${P_2}$ is the pressure of tank = $200atm$
${V_1}$ is the volume of one breath = $0.50L$
${V_2}$ is the volume of the tank = $10L$
${n_1}$ = $1$
${n_2}$ = $x$
Therefore, the equation will now look like this,
$\dfrac{{0.50}}{{2000}} = \dfrac{1}{x}$
To find the variable, we must now take the reciprocal of the above equation so we can get the following equation:
$\dfrac{{2000}}{{0.50}} = x$
Further dividing leads to the value of the variable which will now be:
 $x = 4000$
Therefore, the number of breaths an adult can take will be $4000$ considering the circumstances where in the pressure of the tank is $200atm$ and volume is $10L$ .

Note: It is important to remember that only after finding the volume and pressure present in one breath only then can we find the total number of breaths that are possible from the tank.
In case there is a change in temperature between the two situations then the number of breaths will also change. But in this we will consider the process to take place in an isothermal condition since there is no change mentioned.