All material objects emit electromagnetic radiation; the distribution of photon energies and fluxes emitted depend primarily on the object's temperature. This phenomenon is known as blackbody radiation. Because the amount of radiation, and its spectrum depends on the temperature, it is sometimes called thermal radiation, or heat radiation.

The object in question can be large (stars and planets), small (single molecules), solid, liquid, or gaseous. Blackbody radiation is a familiar phenomenon: When the temperature of an object (such as a piece of metal) is increased, it begins to glow reddish orange, and, as the temperature is further increased, its glow becomes progressively whiter. As the temperature is further increased, the glow takes on a bluish cast, however, at such high temperature, the glow is usually so intense that it is painful to look at, and even harmful to the eyes (which is why welders use dark goggles when working).

Even when an object is cool, and we do not see a glow at all, the object is constantly emitting radiation that is mostly in the infrared region. Night vision equipment detects this infrared radiation, and electronically converts the image detected in the infrared to a visible image.

Blackbody radiation is continually removing energy from an object, thereby causing it to cool. This is the reason that Earth's surface cools at night. Why doesn't an object keep cooling and cooling, eventually reaching the absolute zero of temperature? The reason is that at the same time the object is losing energy to outgoing blackbody radiation, it is bathed in the blackbody radiation emitted by everything else in its surroundings, and it absorbs some of this radiation, replacing some of the energy that is being lost. Electromagnetic radiation is continually being "exchanged" among objects. Objects that are warmer emit more energetic radiation than those that are cooler and so they cool faster. Therefore, in the absence of an external heat source, all objects in a confined space will eventually reach the same temperature. That is, they will reach thermal equilibrium. Even after thermal equilibrium is reached, the objects still exchange radiation with each other, but now the objects are absorbing and emitting energy in the form of radiation at exactly the same rate, so no net heat exchange takes place.

The blackbody radiation of the Sun, Earth, Earth's atmosphere, and clouds play an important role in Earth's climate. Most of the Sun's radiation is blackbody radiation radiated from the Sun's surface, or photosphere, whose temperature is about 5700 K. Earth's surface is warmed by absorbing this light. At the same time it is absorbing energy, Earth's surface is emitting its own blackbody radiation. At night, when the surface is no longer being illuminated by the Sun, it is still radiating its own blackbody radiation, Earth's surface to cool. Some of that radiation is absorbed by the atmosphere. The atmosphere also emits blackbody radiation, some of which is absorbed by Earth's surface. The nighttime temperature depends upon the relative rates of absorption and emission by Earth and the atmosphere. If the atmosphere is made more efficient at absorbing radiation, it will trap more of Earth's radiation, and reradiate more of it downward, making Earth's surface warmer on average. This is known as the greenhouse effect.

6.1 Examples of Blackbody Radiators

Remember that all objects are blackbody radiators, and that the spectrum of an object's blackbody radiation is determined by the object's temperature, and by its emissivity. The examples we discuss here are ones where the radiation is either visible or put to some use.

6.1.1 The Sun and other stars -- The high temperatures and pressures in the cores of stars, including our own Sun, smash atomic nuclei together to form heavier nuclei in a process called nuclear fusion. When this occurs, gamma rays (high energy photons) are produced, and these gamma rays collide with all the various particles in the star's core. When a gamma ray collides with a particle (an electron, or an atomic nucleus), it can lose energy in the collision: the gamma ray leaves the collision with somewhat less energy, the missing energy appearing as a greater kinetic energy for the particle. This process is called Compton scattering. Because the material in the star is so dense, this process happens many, many times, and before the gamma ray can reach the surface of the star its energy is comparable to the kinetic energies the particles already have. The outer region (about the outer 1/3 or so) of the star is a convective zone, which is heated below by the material heated by the gamma rays, and cooled above by the blackbody radiation from the star's surface. In the convective zone, the cooler material being formed at the surface is denser than the hotter material below, and so it tends to sink toward the star's center, displacing the hotter material and squeezing it upward to the surface.

The surface of the star (called the photosphere) is rather nonuniform in its temperature. If you were to look at small areas on the star's surface, you would find some areas with higher temperatures, where convecting hot material had just been brought to the surface, and other areas with lower temperature, where the material has had time to cool by blackbody radiation that escapes into space. How would you measure the different temperatures? By analyzing the spectra of the blackbody radiation emitted by the different regions. The average temperature of the Sun's photosphere is about 5600 K. Other stars are hotter (and so appear bluer), or cooler (and so appear redder). Generally, very young stars are very hot and have a noticeable blue color. Older stars, including red giants, are cooler, and have a noticeable color. In the Northern Hemisphere winter sky, the constellation Orion's brightest star, Betelgeuse, a red giant, appears quite red. Nearby, the brightest star in the constellation Canis Major, just at Orion's heels, is the star Sirius, which is actually a binary star. The brightest of the two stars in Sirius is a very hot, blue star, whose color is also quite noticeable.

The spectrum of a star, including the Sun, is not quite that of an ideal blackbody. The fact that the photosphere contains materials at different temperatures produces a spectrum that is not quite the shape of the ideal blackbody spectrum. Furthermore, the above the photosphere is the star's atmosphere, which contains many gases consisting of both electrically neutral and ionized chemicals. Most prominent among these are hydrogen and helium. However, the atmospheres of stars such as the Sun also contain a wide variety of heavier elements, including significant amounts of carbon, nitrogen, oxygen, silicon, potassium, sodium, iron and nickel. The temperature of the atmosphere is somewhat lower than that of the photosphere, but, because they are more tenuous than the material in the photosphere, the atmosphere's emissivity is much lower than the photosphere's emissivity. However, these materials absorb some of the radiation at certain wavelengths. These absorption lines were first noticed by Fraunhofer in 1814, who cataloged some 700 in the visible region of the electromagnetic spectrum. Using these absorption lines it is possible to learn much about the chemical composition of a star's atmosphere.

Beyond the atmosphere of most stars is a corona. Interestingly, the temperature of the corona is much greater than even that of the photosphere. It is not currently known why that is, but understanding this is one of the principal objectives of the international Solar and Heliospheric Observatory, SOHO, which has been operating since 1996. Again, the material in the corona is much more tenuous than that in the photosphere, and so its emissivity is much smaller than the photosphere's.

The Sun is a relatively strong source of x-rays and radio frequency radiation, which are both connected with storm and magnetic activity on the sun, and whose spectra deviate considerably from blackbody radiation.

6.1.2 Incandescent light bulbs, electric heaters, and stoves -- When electric current is passed through a resistive material (that is, through an imperfect conductor), it heats the material. The electrical current (I) flows in response to an applied electrical potential difference (voltage difference, V) between two points (like two ends of a segment of wire). The resistance (R) of the material is defined by the ratio of the electrical potential difference to the current:

R = V/I

This is known as Ohm's Law. The amount of energy the current deposits in the material per unit time is given by the formula is called the power dissipation (P), and is given by the expression

P = I2R

= I V

(The second equality follows by rearranging the previous expression to read V=IR.). The units of P is Watts (W), or Joules/sec (J/s), or Volt-Amperes (VA). All of these are equivalent. P is the number of Joules per second that is added to the kinetic energy of the atoms making up the material. Increased atomic kinetic energy means increased temperature. If the material were not at the same time getting rid of some of this energy, its temperature would just keep on increasing and increasing until it melted or vaporized.

A conductor (whether highly resistive or not) contains electrons that are quite free to move about. When the voltage difference is applied across a region of the material, an electric field is established at all places in the material. The electrons, being electrically charged, experience a force when they are in this field, and so they begin to accelerate toward the electrically relatively positive end of the material. While they are in motion, the electrons will inevitably start to crash into the atoms making up the material, and in these collisions some kinetic energy will be lost by the electrons and gained by whatever they are crashing into. The increased kinetic energy (eventually of the whole material) means that the material's temperature is increasing. This is a familiar phenomenon; when electrical current is run through a wire, the wire starts to become warm. If it is not too resistive, and if only a small amount of current is being drawn through it, it will not warm up very much. If this is an extension cord, you do not want it to warm up too much, of course.

It is sometimes desirable, however, to have a resistive conductor heat up. One example is the incandescent light bulb. This consists of a sealed glass container with most of the air taken out of it, in which is a coil of resistive wire. The ends of this coil are connected to the outside of the container, so that a large voltage can be applied to it from the household electric supply. When that electrical voltage is supplied (that is, when someone turns on the light), the current flowing through the wire heats the wire to a high temperature (2000-5500 K), and the wire glows. Light bulbs of inferior quality (whose wire is not as resistive, or whose glass container still has a lot of gas in it) tend to appear to have a reddish glow, since the wire filament is not as hot. When the electric supply is turned off, the filament cools. Often this happens over a long enough period of time that the glow can be observed to become both less and less intense, and redder, until its glow finally cannot be perceived. The filament cools because its blackbody radiation is carrying energy away into the space around the lightbulb.

Almost all electrical heating devices, including hair driers, clothes driers, space heaters, electric baseboard heaters, electric stove and oven heating elements, work on this same principle. When you turn a stove's burner on high, in a few moments, there is a perceptible red glow from the heating element. As this gets hotter, the color appears more and more orange. If the temperature were to be allowed to get high enough to give a yellower glow, the burner would be hot enough to melt most cookware.

When you turn a stove's burner on a low setting, you will not see the burner glow, but you can certainly feel the heat coming off of it, if you place your hand near (but at a respectful distance from) the burner. This is not because the burner is heating the air, which is heating your hand. It is because the molecules in your skin are absorbing the infrared radiation that dominates the spectrum of the burner's blackbody radiation. This is often called radiant heat. It is why you can walk by a parked car and sense whether it has been driven quite recently (so its engine compartment is still warm). It's also how radiators in older buildings heat the rooms they're in. Most of the heat transferred into the room, and to the people in it, is transferred as blackbody radiation, and not as a result of the radiator heating the air that is in contact with it, although that certainly does happen as well. You also experience radiant heating when you are next to hot coals, like the burning embers of a fire.

6.1.3 Candle flames and other flames -- The rate at which a candle burns is limited by the diffusion of oxygen into the vicinity of the flame. The combustion process is an exothermic chemical reaction in which the fuel (the paraffin), a mixture of chemical compounds comprised mostly of carbon and hydrogen atoms, is combined with oxygen from the air to form carbon dioxide (CO2) and water (H2O). The heat evolved by this process heats up and vaporizes some of the fuel, and also heats up the oxygen, nitrogen, and other atmospheric gases. An ordinary candle flame is actually quite oxygen starved, and the vaporized fuel molecules, at the elevated temperatures in the flame itself, wind up combining with other fuel molecules. Incomplete combustion of fuel molecules also results in the formation of small carbon particles. Together, the polymerized fuel and carbon particles make up soot. And when the soot is formed, it is very hot, and emits a great deal of blackbody radiation. This radiation appears reddish-orangish-yellowish. Chemical reactions in the flame plasma also emit radiation, so the emission spectrum of a complete candle flame can be quite complex. However, the characteristic continuum spectrum of the blackbody radiation from the soot is the dominant feature.

You may have used, or watched other people use gas/oxygen torches, such as are used for welding, plumbing, and glass sculpture. These torches have two supply hoses. One hose feeds fuel (natural gas, propane, or acetylene) to the torch, while the other feeds a supply of oxygen. When the torch is first lit, the oxygen feed is turned way down or even off, and you will see a bright yellow flame shooting out of the torch. This is essentially the same yellow flame as in the candle. The fuel is burning in oxygen poor conditions, relying on oxygen from the air diffusing in toward the region the previously burned fuel has depleted. When the oxygen supply is turned on, the flame is force fed with oxygen, and the flame now has a blue glow that is not nearly as bright as the yellow flame. In the oxygen rich flame there is essentially no soot production, so, even though there are gases at a very high temperature, there is nothing there like the soot particles that have sufficient emissivity to produce a great deal of blackbody radiation. The blue glow of the flame is not blackbody radiation, but rather is due to chemical reactions going on in the flame.

6.1.4 Warm blooded animals -- Humans and other warm blooded animals tend to be warmer than their surroundings. As blackbody radiators, they emit considerable amounts of energy (roughly 100 W for an average adult at rest) in the infrared region of the spectrum. Of course, at the same time, their surfaces are absorbing infrared radiation from their surroundings. But there is a net energy loss, and this energy is continually being replaced by the animal's metabolic processes.

Night vision equipment allows one to detect the presence of people and other warm animals and objects by using a kind of video camera that is sensitive to infrared radiation. The signal produced by that camera is fed into a video monitor that presents a visible image. In this image, you see a person as a glowing object, rather than, as you are accustomed to, an object that reflects the ambient light that falls on him.

The fact that people are emitters of infrared radiation is also used in a wide variety of anti-intruder devices and in automatic light switches (usually for outdoor lighting). These have infrared photosensors. When something emitting infrared radiation passes in front, the photosensor causes an electrical circuit to close, and this is in turn used to set off an alarm, turn on a light, or do something else.

6.1.5 The cooling of Earth at night -- The materials that make up Earth's surface absorb some of the Sun's radiation during the day. This results in the warming of those materials. Since all materials radiate blackbody radiation, Earth's surface is always radiating energy (in the infrared region). Of course, it is also absorbing energy from its surroundings, but as the temperature of Earth's surface increases, it ends up radiating more infrared radiation than it is absorbing.

When the night comes, the surface is no longer being heated by the Sun, but it is still radiating, and, since it is warmer than the air around it, it continues to radiate, gradually cooling it off.

If clouds are present over the surface at night, their effect is to reflect some fraction of the radiation that was emitted by the surface back down toward it. Over the course of the night, this has the effect of causing the surface to cool much more slowly. This is why clear sky nights tend to be much colder than cloudy sky nights.

6.2 The Spectrum of Blackbody Radiation

Now let's take a more quantitative look at the absorption and emission of electromagnetic radiation by any macroscopic object. An ideal blackbody is a hypothetical object that absorbs all radiation incident on its surface. (Hence the name blackbody, since something that doesn't reflect any light will appear black). Physical theory predicts the spectral irradiance emitted by an ideal blackbody at a certain temperature T. Figure 4.23 shows the theoretical spectrum of an ideal blackbody radiator at temperatures T=6000K, 5000K, 4000K, 3000K, 2000K, and 1000K. The Sun's photosphere is a little less than 6000K. The effective temperature of Earth's surface is a little less than 300K. Notice that in this figure each major tick mark represents a factor of 10 difference from the adjacent tick mark. That is, both the wavelength and irradiance scales are logarithmic.

One hallmark feature of blackbody radiation is that it has a continuous spectrum. That is, the irradiance curve is smooth. It doesn't have any wiggles in it, and it doesn't abruptly go to zero at some wavelength.

Nonideal blackbodies emit less radiation any given wavelength than an ideal blackbody would. Ideal blackbodies do not actually exist. However the radiant energy emitted by many objects, such as Earth and the Sun, can be closely matched by the emission of a blackbody at the same temperature.

The amount of emission of a blackbody at each wavelength depends only on the absolute temperature of the blackbody. Remember that heat is a form of energy so it follows that if a blackbody is heated by absorption of more energetic photons (or through other processes such as conduction) it will emit more energetic photons.

6.3 Blackbody Emissions and Temperature

We have already seen that blackbodies emit electromagnetic radiation at all wavelengths (energies) in the spectrum and that the intensity of the emitted radiation varies with wavelength, depending on the temperature of the object. Figure 4.23 shows the spectrum of electromagnetic radiation emitted by blakcbody radiators, as a function of wavelength for different temperatures.

When photons are emitted over a continuous range of the spectrum as we see from these curves, we call it continuum radiation. What happens to the peak in each curve as you go to higher temperatures? You can see that the peak in each curve shifts to shorter wavelengths (higher energies) with increasing temperature.

6.4 Absorptivity and Emissivity

Although an ideal blackbody is hypothetical, objects are often identified by how their radiative properties compare to those of a blackbody at the same temperature. Two important related properties of objects are their absorptivity and emissivity. The absorptivity, a, of an object is defined as the fraction of incident radiation that is absorbed by an object at a specific wavelength . The emissivity, e, of a material is the fraction of radiation emitted at a specific wavelength compared to that emitted by a blackbody at the same temperature. As we know from before, an ideal blackbody absorbs all incident radiation and emits the maximum amount possible at each wavelength. Therefore, the absorptivity and emissivity of an ideal blackbody at any wavelength are equal to 1. For real objects these values may vary from 0 to 1. Kirchoff's law states that for any object, a = e.

According to this, an object that is a strong absorber at a particular wavelength is also a strong emitter at that wavelength, and an object that absorbs weakly at a particular wavelength will emit weakly at that wavelength. Whether or not an object is a strong or weak emitter at a given wavelength depends on the characteristics of the material. The emissivities of various components in the atmosphere play a vital role in determining the temperature structure of the atmosphere.

6.5 Key Points About Radiant Energy and Blackbody Radiation