Chapter P.6, Problem 4P

The Greenhouse Effect and Global Warming

Electromagnetic waves are real, and we depend on them for our very existence; energy carried by electromagnetic waves from the sun provides the basis for all life on earth. Because of the sun’s high surface temperature, it emits most of its thermal radiation in the visible portion of the electromagnetic spectrum. As the figure below shows, the earth’s atmosphere is transparent to the visible and near-infrared radiation, so most of this energy travels through the atmosphere and warms the earth’s surface.

Although seasons come and go, on average the earth’s climate is very steady. To maintain this stability, the earth must radiate thermal energy—electromagnetic waves—back into space at exactly the same average rate that it receives energy from the sun. Because the earth is much cooler than the sun, its thermal radiation is long-wavelength infrared radiation that we cannot see. A straightforward calculation using Stefan's law finds that the average temperature of the earth should be –18°C, or 0°F, for the incoming and outgoing radiation to lie in balance.

This result is clearly not correct; at this temperature, the entire earth would be covered in snow and ice. The measured global average temperature is actually a balmier 15°C, or 59°F. The straightforward calculation fails because it neglects to consider the earth’s atmosphere. At visible wavelengths, as the figure shows, the atmosphere has a wide “window” of transparency, but this is not true at the infrared wavelengths of the earth’s thermal radiation. The atmosphere lets in the visible radiation from the sun, but the outgoing thermal radiation from the earth sees a much smaller “window.” Most of this radiation is absorbed in the atmosphere.

Thermal radiation curves for the sun and the earth. The shaded bands show regions for which the atmosphere is transparent (no shading) or opaque (shaded) to electromagnetic radiation.

Because it’s easier for visible radiant energy to get in than for infrared to get out, the earth is warmer than it would be without the atmosphere. The additional warming of the earth’s surface because of the atmosphere is called the greenhouse effect. The greenhouse effect is a natural part of the earth’s physics; it has nothing to do with human activities, although it’s doubtful any advanced life forms would have evolved without it.

The atmospheric gases most responsible for the greenhouse effect are carbon dioxide and water vapor, both strong absorbers of infrared radiation. These greenhouse gases are of concern today because humans, through the burning of fossil fuels (oil, coal, and natural gas), are rapidly increasing the amount of carbon dioxide in the atmosphere. Preserved air samples show that carbon dioxide made up 0.027% of the atmosphere before the industrial revolution. In the last 150 years, human activities have increased the amount of carbon dioxide by nearly 50%, to about 0.040%. By 2050, the carbon dioxide concentration will likely increase to 0.054%, double the pre-industrial value, unless the use of fossil fuels is substantially reduced.

Carbon dioxide is a powerful absorber of infrared radiation. And good absorbers are also good emitters. The carbon dioxide in the atmosphere radiates energy back to the surface of the earth, warming it. Increasing the concentration of carbon dioxide in the atmosphere means more radiation: this increases the average surface temperature of the earth. The net result is global warming.

There is strong evidence that (he earth has warmed nearly 1°C in the last 100 years because of increased greenhouse gases. What happens next? Climate scientists, using sophisticated models of the earth’s atmosphere and oceans, calculate that a doubling of the carbon dioxide concentration will likely increase the earth’s average temperature by an additional 2°C (≈ 3°F) to 6°C (≈9°F) There is some uncertainty in these calculations; the earth is a large and complex system. Perhaps the earth will get cloudier as the temperature increases, moderating the increase. Or perhaps the arctic ice cap will melt, making the earth less reflective and leading to an even more dramatic

But the basic physics that leads to the greenhouse effect, and to global warming, is quite straightforward. Carbon dioxide in the atmosphere keeps the earth warm; more carbon dioxide will make it warmer. How much warmer? That’s an important question, one that many scientists around the world are attempting to answer with ongoing research. But large or small, change is coming. Global warming is one of the most serious challenges facing scientists, engineers, and all citizens in the 21st century.

The following questions are related to the passage “The Greenhouse Effect and Global Warming” on the previous page.

The thermal radiation from the earth’s surface peaks at a wavelength of approximately 10 μm. What is the energy of a photon at this wavelength?

1. A. 2.4 eV
2. B. 1.2 eV
3. C. 0.24 eV
4. D. 0.12eV