Carbon Dioxide and Electromagnetic Radiation
Jerry A. Bell
Simmons College, Professor of Chemistry (emeritus)
American Chemical Society, Senior Scientist (retired)
Wisconsin Initiative for Science Literacy, Faculty Associate
j_bell@acs.org
jerryalanbell@gmail.com
Background
The left-hand curve in this graphic shows the
distribution of electromagnetic radiation (light)
from a surface at the temperature of the sun, about
5800 K. You can see that the peak of the curve is
in the visible region of the spectrum. As is obvious
from our everyday observation, the Earth’s
atmosphere is transparent to visible light.
The right-hand curve in the graphic shows the
distribution of electromagnetic radiation (infrared
light) from a surface at about the temperature of
the Earth. Most of the gases in Earth’s atmosphere
are transparent to infrared light, but some minor
components, notably carbon dioxide, CO2, absorb strongly at some infrared wavelengths.
Energy from the sun’s light passes through the atmosphere and is absorbed by and warms the
surface. The warmed surface radiates infrared energy back toward space and some of this energy
is absorbed by carbon dioxide, water vapor, and other minor gases in the atmosphere. These
gases re-emit the energy in all directions, thus reducing the amount that escapes to space. The
result is that some of the energy leaving the surface is “trapped” and the planet is warmer than it
would be if these gases were not part of the atmosphere. This is usually called the “greenhouse
effect.” You can learn more about the energy balance between the sun and the Earth and the
mechanism of the greenhouse effect in the American Chemical Society Climate Science Toolkit,
www.acs.org/climatescience. [1]
In this activity, we will examine the interaction of carbon dioxide with electromagnetic radiation
(light).
Materials
Lecture experiment:
two 10- or 12-ounce plastic cups. Transparent cups are best for making it clear to the class
that nothing “visible” changes during the activity, but they are not required.
four large steel washers that will lie flat on the bottom of the cups
70-watt (or higher) floodlight in a reflector lamp with a device that holds it so that its light is
directed straight down into the two plastic cups sitting side-by-side. A utility lamp with a
spring clip for attachment at a work site works well and can be attached to the upright of
a ring stand or other vertical rod/pole to hold the lamp.
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two temperature probes and associated computer/data logging device. Ideally, the output of
the probes should be projected for the entire class to observe. Alternatively, thermometers
read by volunteers calling out the readings every 30 seconds or so could be used, but are
not as “dramatic” and have greater thermal lag.
cardboard or poster board shield/baffle to place in front of the apparatus to avoid audience
distravtion when the light is on before the observations begin
1- or 2-L beaker or equivalent container such as a 1- or 2-L soda bottle with top cut off
heaping teaspoon of baking soda, sodium hydrogen carbonate
about 100 mL of vinegar, dilute acetic acid
about 20-25 mL water to add to the cups
sheet of light cardboard or plastic to cover the beaker
safety goggles for experimenter(s)
Procedures, Observations, and Questions
To prepare for the experiment place two steel washers in the bottom of each cup, add 10-12 mL
water, and arrange the cups side-by-side several inches below the floodlight, so that each will get
the same amount of illumination. (The experiment does not require the washers, but they add
mass that stabilizes the cups so they are not tipped over by the temperature probes.) Place one of
the temperature probes in each cup supported in such a way that they are not against the washers
but near the bottoms of the cups. It’s OK if the probes are leaning against the sides of the cups.
Turn on the light and monitor the temperatures in the cups as they warm up to see that the
temperatures are approximately the same. Adjust the position of the cups, if necessary, to get the
temperatures equal within 1 C or better. Place the light shield in front of the set up, so the light
does not bother the observers during the 15-20 minutes it may take for the temperatures to
become constant (or only very slowly changing).
1. Remove the light shield and begin projecting temperature vs. time curves for the two probes.
(a) What is the temperature in each cup?
(b) What observations can you make about the contents of each cup? Is there any significant
difference between the contents? Explain your responses.
2. Put the baking soda in the 1- or 2-L container and add the vinegar. As bubbles subside. cover
the container to contain its gaseous contents.
(a) What do you observe immediately? After several seconds, what do you observe?
(b) How would you describe the gaseous contents of the container? What do you think the
gas(es) is(are) in the container? Explain.
3. Pour the gas from the container into one of the cups under the light source. Be careful not to
pour any of the liquid into the cup.
(a) Describe what happens to the temperatures in the cups over the next few minutes.
(b) Is there any significant difference between the temperatures? If so, what is the difference
and how would you interpret it?
(c) What observations can you make about the contents of each cup? Is there any significant
difference between the contents? Explain your responses.
(d) Propose a molecular-level explanation/model for these observations. What is the
evidence/justification for your model?
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Discussion
The reaction of sodium hydrogen carbonate with acetic acid produces CO2 gas. This causes the
mixture to foam up, displace the air in the container, and leave it mostly filled with CO2 and
water vapor. CO2 is denser than air, so it can be poured from the container into one of the cups
under the light source. Water vapor from the container may also accompany the CO2, but has no
affect on the result; the cup is already saturated with water vapor from its added water.
Before CO2 is added to one of the cups, they are at about the same constant temperature and have
reached an energy balance with the light source. The cups are gaining energy from the visible
and infrared radiation from the light source and losing energy as infrared radiation and by
conduction to their surroundings because they are warmer than the surroundings. The gains and
losses for each cup balance, so their temperatures remain about constant.
When CO2 is added to one of the cups, its energy balance is upset. The CO2 gas molecules in the
cup now absorb infrared energy from the light source and emission from the warmed cup and
vibrate more rapidly. Collisions with other molecules transfer some of this energy to the other
molecules making them move more rapidly. The faster movement is observed as an increase in
the temperature of the gas in the cup (and the cup itself as the gas transfers some of its energy to
the cup).
After a few minutes, the extra motion and convection in the cup stir the gases enough and the
CO2 disperses into the surrounding air. As CO2 is lost from the cup, the gas in the cup absorbs
less and less infrared energy and its temperature returns to the previous energy-balanced value.
Not the Atmospheric Greenhouse Effect
Sometimes, references to this experiment suggest that it demonstrates the atmospheric
greenhouse effect that keeps the Earth warm enough to have evolved life as we know it and is
now causing excessive warming of the planet as human activities (mainly fossil fuel burning) are
increasing the amount of CO2 in the atmosphere. [2] Although absorption of infrared energy by
CO2 (and other greenhouse gases that include methane, water vapor, nitrous oxide, and
halogenated hydrocarbons) is required for the greenhouse effect, it is a combination of
absorption and emission of this energy by the gases that is the basis of the mechanism for the
energy-trapping atmospheric greenhouse effect (see below).
A major difference between the greenhouse effect and the experiment here is the concentration
of the greenhouse gas. Greenhouse gases are a minor component of Earth’s atmospheric gases;
they make up much less than one percent of dry air. (Water vapor can be a higher percentage of
humid air, but its concentration varies widely over the surface of the planet and is highly
dependent on the temperature.) In the experiment here, the concentration of CO2 in the cup to
which it is added can approach one hundred percent (although it is probably somewhat less).
When most of the molecules in the gas can absorb infrared energy and distribute this energy
among the motions of the rest of the molecules, the bulk of the gas warms up, as observed in this
experiment. In our atmosphere, relatively few molecules absorb the infrared energy emitted by
the sun-warmed planet, so their transfer of energy of motion has little effect on the bulk
temperature. It is the redirection of the radiated infrared energy from essentially all outgoing to a
scattering in all directions that “traps” energy and keeps the planet warmer than it otherwise
would be (and causes it to warm further with more of the absorbing gases present).
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A Simple Model of the Atmospheric Greenhouse Effect
{This discussion is from the ACS Climate Science Toolkit [1] => Atmospheric Warming => A
Single-Layer Atmosphere Model.}
Arrhenius and his 19th century predecessors proposed that absorption of radiant energy by
Earth’s atmospheric gases is responsible for warming its surface. What we introduce here is a
model that illustrates the fundamental mechanism for atmospheric warming. This model is based
on electromagnetic radiation absorption and emission properties of black bodies. The emissions
from high and low temperature objects that act very much like black bodies (the sun and the
Earth) are shown on the first page. The detailed analysis of this emission by Max Planck led to
his quantum hypothesis at the beginning of the 20th century, but this detail is unnecessary for our
model here. We will need earlier results on the total energy per unit area emitted by a black
body, which is T4, where  is the Stefan-Boltzmann constant, 5.67·10–8 W·m–2·K–4, and T is
the Kelvin temperature of the object.
A problem involved in introducing this model is that most of us have little knowledge or
intuition about the behavior of low-temperature black bodies. The radiation they emit is invisible
and we have essentially no direct experience of phenomena related to their properties (although
the above experiment demonstrates infrared absorption by an atmospheric gas, carbon dioxide,
which is an important component of the model). Thus, it sometimes requires extra effort to
develop a sense of how the model works.
Any body (solid, liquid, or gas) at any temperature above zero Kelvin emits thermal radiation.
The emissivity at a specified wavelength is the ratio of the amount of energy emitted by the body
to the amount of energy emitted by a black body at the same temperature. Emissivity is often
symbolized by  (Greek lowercase epsilon). Emissivities range from 0 (no emission) to 1 (for a
black body). A body with an emissivity less than
unity and the same at all wavelengths is called a grey
body, by comparison with a black body that has unit
emissivity at all wavelengths. This figure compares
the emission from a black body (full area under the
top black curve) at 280 K to the emission from a grey
body with an emissivity of 0.80 at the same
temperature (the area under the lower grey curve)
over the same frequency range.] .
The total energy emitted by a grey body is equal to
the energy emitted by a black body at the same temperature multiplied by the emissivity, T4.
Atmospheric aerosols, tiny aerosol particulate matter suspended in the atmosphere, are a pretty
good approximation to grey bodies. [The term “grey body” has nothing to do with the visible
color of a body, but is used only by comparison to a “black body” when considering emission
and absorption of thermal IR radiation. A grey body may appear to be any color. For example,
for the purposes of our model here, we take the varicolored surface of the Earth (on average) as a
black body, but it is probably better described as a grey body with a very high emissivity.]
Grey bodies, like black bodies, absorb electromagnetic radiation. The absorptivity of a grey body
is the ratio of the amount of energy absorbed by the body to the amount of energy absorbed by a
black body at the same temperature. Note that the definition of the absorptivity is parallel to the
definition of emissivity. If the components of a grey body, the particles and molecules in a
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sample of an atmospheric aerosol, for example, are in thermal equilibrium, then the emissivity
and absorptivity for thermal radiation must be equal. If the emissivity and absorptivity were not
the same, the sample could spontaneously develop cooler and warmer regions, which violates the
second law of thermodynamics. Since the emissivity and absorptivity are the same for a grey
body in thermal equilibrium, we will use the same symbol, , for both emissivity and absorptivity
in the single-layer model for the atmospheric warming mechanism illustrated in this figure.
The energy from the sun (shown at the left in the figure) that the surface absorbs is given by the
expression (1 – )Save. Save is the average incoming solar energy per unit area of the Earth, 342
W·m–2, and  is the Earth’s albedo, 0.30, which accounts for the fraction of the total incoming
radiation that is reflected away, as shown in the figure. The warmed surface emits radiation as a
black body at a temperature of Tp. The total energy emitted per unit area is Tp4.
In this model, the atmosphere is represented by a single homogeneous layer of gases in thermal
equilibrium at temperature Ta acting as a grey body with an emissivity and an absorptivity given
by . The figure shows that the atmosphere absorbs part of the energy emitted by the warmed
surface. The amount of energy absorbed, Tp4, is governed by the atmospheric absorptivity.
The remainder of the radiation from the surface, (1 – Tp4, passes unabsorbed through the
atmosphere and into space outside the atmosphere. A grey body, like a black body, emits in all
directions. This is represented in the figure by atmospheric emission both in toward the surface
and out into space. The amount emitted in any direction is given by the expression for emission
per unit area from a grey body, Ta4.
At the steady state when the temperatures are constant, incoming solar radiation energy absorbed
by the Earth must be balanced by outgoing radiation from the surface and atmosphere. The
equation representing the planetary energy balance is:
(incoming)
(1 – )Save = (1 – Tp4 + Ta4
(outgoing)
(1)
Similarly, for a constant atmospheric temperature, the energy it absorbs must equal the energy it
emits. The equation representing this equivalence is:
(absorbed)
Tp4 = 2Ta4
(emitted)
(2)
Solving this equation for Ta4 gives:
Ta4 = (1/2) Tp4
(3)
Note that the temperature of the atmosphere will always be lower than the temperature of the
surface. We can substitute for Ta4 in the planetary balance equation (1) and solve for Tp.
(1 – )Save = (1 – Tp4 + (1/2) Tp4
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(1 – )Save = Tp4 [(1 –  + (1/2)]
Tp4 = [2 (1 – )Save]/(2 – 
Tp = {[2 (1 – )Save]/(2 – 
A plot of Tp as a function of emissivity,  gives this graph
for the single-layer atmosphere model. If the emissivity and
absorptivity are zero, no radiation from the surface will be
absorbed. This is identical to the energy balance for Earth
acting as a black body in the absence of atmospheric
greenhouse gases, for which the planetary temperature is
calculated to be 255 K, just as in this graph. At this
temperature, all the water on the planet would be frozen and
life, as we know it, could not exist.
If the emissivity and absorptivity are unity, the atmosphere is
a black body and all radiation from the surface is absorbed.
For this model, the graph shows that the surface temperature for  = 1 is 303 K. In this case, the
atmospheric temperature is:
Ta = (1/2)1/4 Tp = 0.841  (303 K) = 255 K
That is, the atmosphere emits outward into space as a black body at 255 K, just as it must to
balance the incoming solar energy absorbed by the planet. (These conclusions should come as no
surprise, since the limiting conditions are built into the model.)
The average temperature of the surface of the Earth is about 288 K. For the single-layer
atmosphere model, the graph shows that this temperature would correspond to an atmospheric
emissivity of about 0.8. Thus, the model succeeds in its main purpose, demonstrating how an
atmosphere that absorbs and re-emits some of the radiation from a planet’s surface results in a
surface that is warmer than if there were no atmosphere.
Numerical values related to the properties of this single-layer model of the atmosphere must be
taken with a large grain of salt. Since these are consistent with the observed properties of the
Earth system, the model captures the essence of the physical processes governing atmospheric
warming, but is totally unrealistic in assuming a uniform atmosphere that absorbs and emits like
an ideal grey body. A more realistic model has to take into account that the atmosphere is not
uniform, but changes in both pressure and temperature with altitude. The greenhouse gases
absorb and emit at only some infrared wavelengths, not smoothly like a grey body. Much more
detailed calculations are possible, with actual atmospheric properties and the results match
observational data from radiation leaving the top of the atmosphere and from the downward
radiation at the surface. See the ACS Climate Science Toolkit. [1]
References
1. American Chemical Society Climate Science Toolkit (www.acs.org/climatescience).
2. Manfred Adelhelm and Ernst-Gerhard Hohn, “A Simple Demonstration of the Greenhouse
Effect,” J. Chem. Educ., 1993, 70(1), 73-74.
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