Indoor Air Quality Questions and Answers

Answer: A

Correct answer: 1.5 air changes per hour

The air exchange rate is the ventilation flow divided by the volume:

\[ \frac{90}{60} = 1.5\ \mathrm{h^{-1}} \]

The units confirm it: cubic metres per hour over cubic metres leaves per hour, so the rate is a frequency rather than a flow. Its reciprocal is the nominal time constant - here forty minutes - which is the period in which the concentration would fall to \( e^{-1} \) of its value after a source stopped.

Answer: B

Correct answer: \( 0.2 \ \mathrm{mg/m^3} \)

At steady state the rate in equals the rate out, so with clean supply air:

\[ C = \frac{G}{Q} = \frac{20}{100} = 0.2\ \mathrm{mg/m^3} \]

Note what does not appear: the room volume. Volume governs how quickly the steady state is reached, not what it is - a large room takes longer to reach the same concentration. Only the source strength and the ventilation flow determine the eventual level.

Answer: C

Correct answer: \( 0.24 \ \mathrm{mg/m^3} \)

Ventilation dilutes towards the outdoor concentration, not towards zero, so the indoor level is the outdoor value plus the contribution of the indoor source:

\[ C = C_{out} + \frac{G}{Q} = 0.04 + \frac{30}{150} = 0.04 + 0.20 = 0.24\ \mathrm{mg/m^3} \]

The distractor 0.20 omits the outdoor term. That term is what limits how much ventilation can achieve: no amount of outdoor air can bring the indoor concentration below what the outdoor air already contains.

Answer: D

Correct answer: \( 30 \ \mathrm{m^3/h} \)

The required flow is the generation rate divided by the permitted excess concentration:

\[ Q = \frac{G}{\Delta C} = \frac{0.018}{0.0006} = 30\ \mathrm{m^3/h} \]

An excess of 0.0006 by volume is 600 parts per million, which with a typical outdoor value of about 400 gives an indoor level near 1000 ppm - the figure commonly used as a ventilation guideline. The calculation is what lies behind that number rather than any direct toxicity of carbon dioxide.

Answer: A

Correct answer: \( 135 \ \mathrm{m^3/h} \)

Flow is the air exchange rate multiplied by the volume:

\[ Q = nV = 3 \times 45 = 135\ \mathrm{m^3/h} \]

This is the inverse of the earlier calculation and the two are worth practising together, since specifications are written both ways - a code may require so many air changes per hour, while a fan is selected on cubic metres per hour. The volume is what converts between them.

Answer: B

Correct answer: 30 minutes

After the source stops, the concentration decays exponentially with time constant \( \tau = 1/n \):

\[ \tau = \frac{1}{2} \ \mathrm{h} = 30\ \mathrm{minutes} \]

which is by definition the time to fall to \( e^{-1} \), about 37 per cent, of the initial value. The relation is what a tracer gas decay measurement exploits in reverse: fitting an exponential to the recorded decay gives the slope, and the slope gives the air exchange rate.

Answer: C

Multiply the recirculation flow \( 50 \times 4 = 200 \) by the single pass efficiency of 0.8. Recirculating filtration adds to the dilution the outdoor air already provides, but only for contaminants the filter actually captures.

Answer: D

With a fixed source the steady concentration is inversely proportional to the ventilation rate. In practice increasing ventilation can also increase the pressure difference that draws radon in, so the gain is often less than the simple calculation promises.

Answer: A

Correct answer: \( 4.0 \ \mathrm{mg/m^3} \)

At steady state:

\[ C = \frac{G}{Q} = \frac{60}{15} = 4.0\ \mathrm{mg/m^3} \]

The room volume of 30 m\(^3\) is not needed - it governs how quickly this level is reached, not the level itself. The low ventilation rate is what produces the high concentration: at 60 m\(^3\)/h the same appliance would give 1.0 mg/m\(^3\), which is why unvented combustion in a poorly ventilated kitchen is dangerous.

Answer: B

Correct answer: One eighth of the original

Six years is three half-lives:

\[ \frac{6}{2} = 3 \qquad \left(\frac{1}{2}\right)^{3} = \frac{1}{8} \]

The distractor "one third" divides the years by the half-life and inverts, treating the decay as linear. The exponential decline is why formaldehyde from new pressed wood is worst when the material is new, and why the problem diminishes over years without any intervention - though warmth and humidity both accelerate the release.