Optical measurement of atmospheric carbon dioxide

Team members

Ta Na: Responsible for proposing and refining ideas, coordinating experimental records, documenting the experimental process, generating graphs, analyzing experimental data, drawing conclusions, making comparisons, preparing appendices, and formatting.

Cao Yuan: Responsible for refining ideas, assisting with experimental operations, writing the experimental principles section, and formatting.

Gao Yihan: Responsible for writing the research background, experimental objectives, experimental advantages and improvements, and referencing.

Qi Kaiyi: Responsible for error analysis.

Chen Yiming: Responsible for writing the research background, experimental objectives, experimental advantages and improvements, and referencing.

Idea

Climate change has already become one of the most important challenges humanity faces. Carbon dioxide, the major greenhouse gas, is 'heating up' the Earth's atmosphere as they have an absorption peak in infrared wavelengths.

This project aims to build a portable and accurate carbon dioxide concentration measurement device.

Possible measurement mechanisms

1. Spectroscopy. Carbon dioxide has absorption peaks at 15, 4.3, 2.7 and 2 μm. With a laser/source of such wavelength and the correct filter, we could judge the concentration by absorption levels. See viasala for inspiration of a potential real-time reference design.
2. Interferometry. Carbon dioxide has a slightly different refraction index for all wavelengths. By observing the change in interference patterns, we can tell if there is a change in carbon dioxide concentration due to a change in effective path length.

In the end we chose single-wavelength spectroscopy, i.e. absorbance measurement to measure the CO₂ content.

Experiment Preparation

Components

• Light source:
  • A thermal/blackbody radiation/light source that can emit EM radiation at 4 micrometers. Done with a 12W halogen lamp, mounted on an IKEA SVALLET lamp stand.

• Sensor:
  • Thermopile detectors: G-TPCO-035 / TS418-1N426: Thermopile detector with a built-in optical bandpass filter for light around 4μm wavelength for CO₂ absorption
  • multimeter

• Gas chamber:
  • airtight acrylic box surrounding all optical components (chosen)
  • metal (stainless steel) extrusion with hollow structures sealed with transparent SiO2 cover glass (chosen)
  • gas chamber with specific materials (Si/SiO2) transparent to 4 micrometer wavelength

• Power supply and micellaneous electronics:
  • banana wires

• CO₂ source:
  • bottled CO₂
  • dry ice

• to look up
  • extinction coefficient of CO₂

Experiment Principles

The experiment is based on the absorption of CO₂ of 4μm-wavelength infrared light. This absorbance is dependent on the extinction coefficient of CO₂, which is dependent on its partial pressure, and the distance the light travels. It could be described using the Beer-Lambert Law:

$$F_r=F_i\times e^{-\beta s}$$

while F_r is the flux density the thermopile detector receives, F_i is the flux density of the source, β is the extinction coefficient and s is the distance.

Yet G-TPCO-035 / TS418-1N426 does not include any kind of flux/temperature/energy to voltage conversion curve in its spec sheet. This means an assumption needs to be made for the flux density-voltage relation of the thermopile detector. We assume the flux density-voltage relation is linear (linear F-V assumaption), i.e. it follows:

$$V=k\times F_i+b$$

while k is a non-zero constant and b is a constant. Both k and b are unknown and not required to be known for our purposes. To overcome this, we designed our general experiment process as follows:

1. Pump in CO₂ and maintain its stability without turning on the light, and take the first measurement at t=0s.
2. Turn on the light, take the measurements for t=3s, 10s, 20s and 30s or else, respectively.
3. Switch off the light until properly cooled to room temperature while releasing the CO₂ gas back into the room.
4. Above entails a single experiment. Repeat measurements.

As a result, two more assumptions are made for this experiment:

1. The partial pressure of CO2, thus the extinction coefficient, remains constant during each experiment. (constant β assumption)
2. The incident flux density at each moment, i.e. t=0s, 3s etc. remains constant in each day's experiment, assuming the heating of the bulb is regular across experiments. (incident flux assumption)

It follows that within any single experiment, the difference between measurements at different moments should be proportional to the difference between F_r at respective moments, and thus proportional to the exponential term of the Beer-Lambert Law. Mathematically it writes

$$V(t)-V(0)\propto F_r(t)-F_r(0)=(F_i(t)-F_i(0))\times e^{\beta s}$$

Then, given the assumptions, $\frac{V_{C{O}_2}(t)-V_{c{o}_2}(0)}{V_{a}ir(t)-V_{a}ir(0)}=\frac{(F_i(t)-F_i(0))\times e^{-{\beta }_{C{O}_2}s}}{(F_i(t)-F_i(0))\times e^{-{\beta }_{air}s}}=\frac{e^{-{\beta }_{C{O}_2}s}}{e^{-{\beta }_{a}irs}}$ (V_CO2(t)-V_CO2(0)) / (V_air(t)-V_air(0)) = (F_i(t)-F_i(0))×e^(-β_CO2×s) / ((F_i(t)-F_i(0))×e^{(-β_air×s))} = e^(-β_CO2×s)/e^{(-β_air×s))}, which in turn gives us the experession for the measured extinction coefficient:

• β_CO2 = β_air - ln((V_CO2(t)-V_CO2(0)) / (V_air(t)-V_air(0))) / s

As literature tells that β_air = 0.535 cm^-1, we can figure out the extinction coefficient at any given moment with the presence of CO₂ with the help of a reference measurement with air. Hence the partial pressure of CO₂ can be described as:

• p_CO2 = β_CO2/123cm^-1

$$F_r(t)=\frac{A}{(r-r_0{)}^3}$$

Note that these assumptions are not perfect. Problems such as gas leakage and temperature disturbance can strongly undermine the validity of the constant β assumption, while manual control of the light source, timing and logging of the data may also undermine the accuracy of the incident flux assumption. As experiment setup upgrades, these assumptions prove to be more valid as will be shown in later parts of the page.

Experiment process

....

Experiment 1

....

Experiment setup

....

Data acquisition and analysis

....

Experiment 2

....

Experiment setup

....

Data acquisition and analysis

....

Experiment 3

....

Experiment setup

....

Data acquisition and analysis

....

Comparative studies

....