Calculator
Formula Used
Background corrected concentration:
C₀c = C₀ − Cᵦ
Cₜc = Cₜ − Cᵦ
Total first order black carbon loss rate:
k = ln(C₀c ÷ Cₜc) ÷ t
Half life:
t½ = ln(2) ÷ k
Deposition loss rate:
kdep = k − ACH
Deposition velocity:
vdep = kdep × room volume ÷ surface area
How to Use This Calculator
- Measure indoor black carbon after the source stops.
- Enter the first reading as C₀.
- Enter the later reading as Cₜ.
- Subtract a background value using the background field.
- Enter the elapsed time and its unit.
- Add air exchange rate if known.
- Enter room volume and surface area.
- Press calculate to view the loss rate and exports.
Example Data Table
| Test case | C₀ | Cₜ | Cᵦ | Time | ACH | Volume | Surface | Approx. k | Approx. vdep |
|---|---|---|---|---|---|---|---|---|---|
| Room decay test | 2800 | 900 | 80 | 2 h | 0.30 | 60 | 150 | 0.600 h⁻¹ | 0.120 m/h |
| Candle source test | 5200 | 1200 | 150 | 1.5 h | 0.50 | 45 | 110 | 1.047 h⁻¹ | 0.224 m/h |
| Filtered room test | 1800 | 400 | 50 | 3 h | 0.40 | 85 | 210 | 0.526 h⁻¹ | 0.051 m/h |
Indoor Black Carbon Loss Rates in Chemistry
Why Loss Rates Matter
Indoor black carbon is a useful marker for combustion particles. It can come from traffic, cooking, candles, diesel exhaust, or smoke. Once it enters a room, its concentration usually falls over time. The fall may happen because clean outdoor air replaces indoor air. It may also happen because particles attach to walls, ceilings, furniture, or filters.
Decay Model
This calculator treats the measured decay as a first order process. That means the loss rate is proportional to the corrected concentration. The method works best after the source has stopped. It also works best when the room air is well mixed. A fan can improve mixing during a controlled test. The background value is subtracted from both readings. This helps isolate the removable black carbon signal.
Removal Pathways
The total loss rate includes every removal pathway. Air exchange is one part. Deposition is another part. Filtration can be included if the measured concentration decays while the device is operating. When an air exchange rate is entered, the tool estimates the remaining deposition rate. This value should be read as an estimate, not a direct laboratory constant.
Reading Half Life
Half life is often easier to understand than a rate constant. It shows how long the corrected concentration takes to fall by one half. A high loss rate gives a short half life. A low loss rate gives a longer half life. The calculator also reports an equivalent clean air delivery rate. This is the room volume multiplied by the total loss rate.
Measurement Quality
Good measurement practice matters. Use the same instrument for both readings. Keep windows, doors, fans, and filters in the intended test state. Record the start and end time carefully. Avoid adding new indoor sources during the decay period. Check that the final corrected value is lower than the initial corrected value.
Using the Results
These results can support indoor air studies, exposure models, and ventilation checks. They can also compare rooms or test conditions. The numbers should be interpreted with field notes. Temperature, humidity, surface loading, and particle size can affect real loss behavior. Use repeated tests when decisions need strong evidence. Clear reporting also helps later review. Save inputs with units. Note instrument averaging time. Keep raw data nearby. Small documentation steps reduce confusion during method checks later.
FAQs
What is indoor black carbon?
It is a carbon-rich particle marker from combustion. Common sources include traffic exhaust, cooking smoke, candles, biomass burning, and diesel engines.
What does loss rate mean?
Loss rate shows how quickly corrected black carbon concentration decreases indoors. A higher value means faster removal from air.
Why subtract background concentration?
Background correction removes the non-decaying baseline. It helps isolate the black carbon portion that actually changed during the test.
What is a first order decay model?
It assumes the removal speed depends on the current corrected concentration. This model is common for well mixed indoor air tests.
What is deposition velocity?
Deposition velocity estimates how fast particles move from air to indoor surfaces. It uses deposition rate, room volume, and surface area.
Can filtration be included?
Yes. If a filter runs during the decay test, total loss includes filtration. Separate filtration needs extra test design or device data.
What if final concentration is higher?
The calculator will reject that case. A higher final value means a new source, poor mixing, changing background, or measurement error may exist.
Are results suitable for research reports?
They can support reports when inputs are documented. Use repeated trials, calibration records, and field notes for stronger scientific interpretation.