Question

A human adult breathes in approximately 0.50 $dm^3$ of air at 1.00 bar with each breath. If an air tank holds 100 $dm^3$ of air at 200 bar, how many breathes (in order of $10^4$) the tank will supply?

• A. 4.0
• B. 0.4
• C. 40.0
• D. 0.04

Answer 1

Answer: (A)

4.0

Answer 2

At constant temperature, the amount of gas is proportional to the product of pressure and volume ($PV$). The total amount of gas available from the tank is proportional to $P_{tank} \times V_{tank}$. The amount of gas consumed per breath is proportional to $P_{breath} \times V_{breath}$. The number of breaths ($N$) is the ratio of the total amount of gas to the amount per breath: $N = \dfrac{P_{tank} \times V_{tank}}{P_{breath} \times V_{breath}}$

Given: $P_{breath} = 1.00 \, bar$ $V_{breath} = 0.50 \, dm^3$ $P_{tank} = 200 \, bar$ $V_{tank} = 100 \, dm^3$

$N = \dfrac{(200 \, bar) \times (100 \, dm^3)}{(1.00 \, bar) \times (0.50 \, dm^3)}$ $N = \dfrac{20000}{0.50}$ $N = 40000$

The question asks for the number of breaths in order of $10^4$. $40000 = 4.0 \times 10^4$. Thus, the number of breaths is 4.0, when expressed in units of $10^4$.