Educational Technology and Change Journal

By Harry Keller
Editor, Science Education

With all of the misinformation regarding global warming or climate change, it’s hard to deliver convincing information to students. The subject has many aspects. One that receives lots of negative press is the so-called “greenhouse effect.”

The term in a misnomer because the effect of carbon dioxide, methane, and other warming gases is very different than the effect that keeps a greenhouse warm. In the latter case, it’s merely the isolation from the cold air outside of the greenhouse that creates the effect. Glass is a sufficiently good insulator to stop conductive loss of heat and certainly eliminates convective losses. However, it does not block infrared (IR) radiation and keep it from escaping.

To demonstrate this fact, you only have to paint the inside of a small foam cooler black, put a piece of glass over the top, and illuminate it with a heat lamp. A thermometer punched through the side and shielded from the heat lamp with a small piece of cardboard completes this simple experiment. I have done this experiment, and the temperature will not rise.

John Tyndall, author of “The Bakerian Lecture: On the Absorption and Radiation of Heat by Gases and Vapours, and on the Physical Connexion of Radiation, Absorption, and Conduction,” Philosophical Transactions of the Royal Society of London, Vol. 151 (1861).

The atmospheric greenhouse effect is more subtle. John Tyndall discovered the effect and published his findings in 1861, the year the United States Civil War began. His paper makes very interesting reading because it describes how he had to make his own apparatus and the nature of his measurements. Its general availability is only through our technology today. 

Many people have suggested and even insisted that CO2 in the air is in such low concentration that it could not trap heat. They miss the great thickness of our atmosphere and the strong absorption of heat radiation by CO2 and methane (CH4).

A number of experiments have been created to demonstrate the atmospheric greenhouse effect, or its absence, but almost all of them fail because they’re measuring the wrong thing. The Earth’s greenhouse effect requires that light be absorbed by land masses and oceans and then reradiated back into space. Space simply lets the IR photons pass into its vast reaches.

Consider the temperature of the land and sea. These temperatures have an effective average value of around 250K, a bit below the freezing point of water, 273K. What this means for greenhouse gas warming requires a short detour into the physics of light.

Light is an odd phenomenon that perplexed scientists for hundreds of years because it acts both as a wave and as a particle. Not until 20th-century quantum mechanics were developed was the paradox resolved. Light consists of particles, photons, with zero rest mass that act like waves in some circumstances. These particles always move at one speed, the speed of light. Yet, they have differing energies. We associate these energies with their wavelength. Short wavelengths have high energies and long wavelengths have lower energies.

In the visible part of the light (electromagnetic) spectrum, blue light has about half of the wavelength of red light and about twice the energy. Higher energies belong to ultraviolet (UV) light, x-rays, and other high-energy ionizing radiation. It’s the UV light that causes suntans and skin cancer. Light with less energy than red is infrared light. Below that, you have microwaves.

Every object emits light at some level depending upon its temperature. The light from a fire, an incandescent light bulb, and an electric stove heating element all demonstrate this fact. Less hot objects only emit longer wavelength radiation and not much of that. At about 300K, around room temperature, the peak radiation is at about 10 micrometers (microns), far into the infrared. It is this radiation that the atmosphere contains. Yet, many demonstrations and counter-demonstrations of the greenhouse effect ignore this simple fact. CO2 has a strong and broad absorption band between 10 and 11 microns corresponding to a good portion of the black body emission spectrum for the Earth’s thermal radiation.

As radiation from the Earth traverses the atmosphere, it encounters these CO2 molecules and is absorbed, causing the molecules to become warmer by increasing their rotational and vibrational energy. This energy quickly transfers to nearby molecules, mostly oxygen and nitrogen, cooling the CO2 molecule and preparing it to absorb more radiation. CO2 molecules are smaller than 10 microns, making the wavelength of the radiation the effective size of the molecules for absorption. Air contains about 2.5×10¹⁸ molecules per cubic centimeter (cc). The effective absorbing area of CO2 is around 10^-10 square centimeters. The current level of CO2 in the air is nearing 400 ppm (parts per million) or 0.4 parts per thousand, which amounts to 0.04% or a fraction of 0.0004 = 4×10^-4.

Bear with the bit of arithmetic here. Multiply the molecules of air per cc by the fraction of CO2 to get the number of CO2 molecules per cc.

2.5×10¹⁸ x 4×10^-4 = 1×10¹⁵

Given the effective absorbing area of CO2 at 10^-10 square centimeters, about 100,000 CO2 molecules will be available to absorb infrared radiation in each vertical centimeter of air at any given point. Of course, this is just a crude estimate, and there are other factors to consider such as the likelihood of actual absorption. The air itself will be emitting far infrared radiation too, and about half of that will be upward. As this process repeats during ascent to higher atmospheric levels, the heat being lost to space will become attenuated. Eventually, at around 5 kilometers, the concentration of CO2 and other such gases is too low to block radiation, and whatever gets there is lost to space.

Some say that we already have saturated the heat absorbing capabilities of CO2 in the air. That idea does not fit with this analysis or with the data. The data show definitively that 17% of incoming thermal radiation radiates back from the surface and that 12% makes it to space, while 5% is blocked by CO2, methane, and other gases that absorb in the far IR. This 5% warms the air more than it would be if those gases were missing. That warmth is radiated back to the Earth’s surface and, in turn, warms it. The net effect of all greenhouse gases raises the temperature of the Earth an estimated 30°C. Some fraction of that amount is due to CO2. The concentration of CO2 has recently blasted through 350 ppm in 1990 and now nears 400 ppm. That’s more than a 10% increase in the interval between these events. If you can say that CO2 accounts for just half of the greenhouse effect, then that increase could cause an increase of the Earth’s temperature of 1.5°C. The actual increase is about half of that, meaning that these estimates aren’t all that bad.

There’s a bit more arithmetic to get the exact numbers, but it should be clear that we still have 12% of solar radiation to absorb with more CO2, and that we have only used up about 0.5% of that in the last 25 years with the increase from 350 to 400 ppm.

All of the above data are available on the Internet. This sort of analysis can provide motivation for students to do mathematics, to research information, and to try out simple experiments. The Civil War era paper by John Tyndall, also from the Internet, can be the starting point for many such investigations. Someday, Tyndall’s experiments may be available on the Internet for students to try out. Anyone could readily make simulations of them, although I’ve not seen any. However, a reenactment of the actual experiments along with the ability of students to take data themselves from them would add much to the excitement involved in exploring this very topical area. Technology makes all of this possible even if not yet realized.

These sorts of online experiences can form the future of education through appropriate use of technology.

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