5-3 An opaque object emits electromagnetic radiation according to its temperature

As an object is heated, it glows more brightly and its peak color shifts to shorter wavelengths

To learn about objects in the heavens, astronomers study the character of the electromagnetic radiation coming from those objects. Such studies can be very revealing because different kinds of electromagnetic radiation are typically produced in different ways. As an example, on Earth the most common way to generate radio waves is to make an electric current oscillate back and forth (as is done in the broadcast antenna of a radio station). By contrast, X-rays for medical and dental purposes are usually produced by bombarding atoms in a piece of metal with fast-moving particles extracted from other atoms. Our own Sun emits radio waves from near its glowing surface and X-rays from its corona (see the photo that opens Chapter 3). Hence, these observations indicate the presence of electric currents near the Sun’s surface and of fast-moving particles in the Sun’s outermost regions. (We will discuss the Sun at length in Chapter 18.)

Radiation from Heated Objects

The simplest and most common way to produce electromagnetic radiation, either on or off Earth, is to heat an object. The hot filament of wire inside an ordinary lightbulb emits white light, and a neon sign has a characteristic red glow because neon gas within the tube is heated by an electric current. In like fashion, almost all the visible light that we receive from space comes from hot objects like the Sun and the stars. The kind and amount of light emitted by a hot object tell us not only how hot it is but also about other properties of the object.

We can tell whether the hot object is made of relatively dense or relatively thin material. Consider the difference between a lightbulb and a neon sign. The dense, solid filament of a lightbulb makes white light, which is a mixture of all different visible wavelengths, while the thin, transparent neon gas produces light of a rather definite red color and, hence, a rather definite wavelength. For now we will concentrate our attention on the light produced by dense, opaque objects. An opaque object does not allow light to travel through it without being scattered or absorbed—opaque is the opposite of transparent. Earth’s atmosphere absorbs and scatters only some of the incoming sunlight, and we say that it is partially opaque, or partially transparent. Even though the Sun and stars are gaseous, not solid, it turns out that because they are so large, light from the inside scatters many times before emerging from the surface. Therefore, stars are opaque and emit light with many of the same properties as light emitted by a hot, glowing, solid object.

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Imagine a welder or blacksmith heating a bar of iron. As the bar becomes hot, it begins to glow deep red, as shown in Figure 5-9a. (You can see this same glow from the coils of a toaster or from an electric range turned on “high.”) While the bar emits a range of wavelengths, the dominant wavelength is red in color. As the temperature rises further, the bar begins to give off a brighter orange light (Figure 5-9b). At still higher temperatures, it shines with a brilliant yellow color (Figure 5-9c); the dominant wavelength is yellow light. If the bar could be prevented from melting and vaporizing, at extremely high temperatures it would emit a dazzling blue-white light. As shown in Figure 5-9, the temperature of a star determines its color, and the hottest stars are blue.

Figure 5-9: R I V U X G
Objects at Different Temperatures Have Different Colors and Brightnesses This sequence of photographs shows the changing appearance of a piece of iron as it is heated. As the temperature increases, the amount of energy radiated by the bar increases, and so it appears brighter. The apparent color of the bar also changes because, as the temperature increases, the dominant or peak wavelength of light emitted by the bar decreases. The stars shown have roughly the same temperatures as the bars above them.
(top row: © 1984 Richard Megna Fundamental Photographs; bottom row: NASA)

As this example shows, the amount of energy emitted by the hot, dense object and the dominant wavelength of the emitted radiation both depend on the temperature of the object. The hotter the object, the more energy it emits and the shorter the wavelength at which most of the energy is emitted. Colder objects emit relatively little energy, and this emission is primarily at long wavelengths.

These observations explain why you cannot see in the dark. The temperatures of people, animals, and furniture are much less than even that of the iron bar in Figure 5-9a. So, while these objects emit radiation even in a darkened room, most of this emission is at wavelengths greater than those of red light, in the infrared part of the spectrum (see Figure 5-7). Your eye is not sensitive to infrared, and you thus cannot see ordinary objects in a darkened room. But you can detect this radiation by using a camera that is sensitive to infrared light (Figure 5-10).

Figure 5-10: R I V U X G
An Infrared Portrait In this image made with a camera sensitive to infrared radiation, the different colors represent regions of different temperature. That this image is made from infrared radiation is indicated by the highlighted I in the wavelength tab. Red areas (like the man’s face) are the warmest and emit the most infrared light, while blue-green areas (including the man’s hands and hair) are at the lowest temperatures and emit the least radiation.
(Dr. Arthur Tucker/Photo Researchers)

Temperature and Thermal Energy

To better understand the relationship between the temperature of a dense object and the radiation it emits, it is helpful to know just what “temperature” means. The temperature of a substance is directly related to the average speed of the tiny atoms or molecules that make up the substance. As shown in Figure 5-11, the hotter the substance, the faster its atoms or molecules are moving; the colder the substance, the slower the motion of its particles. The thermal energy of an object comes from the kinetic energy of its atoms and molecules. Therefore, the hotter a substance, the greater its thermal energy.

Figure 5-11: Thermal Energy The thermal energy of an object comes from the kinetic energy of its internal particles, and the hotter the material, the faster the particles move around. For hotter solids and liquids, particles vibrate faster and collide more intensely with their neighbors; for hotter gases the particles stream around at higher average speeds.

Scientists usually prefer to use the Kelvin temperature scale, on which temperature is measured in kelvins (K) upward from absolute zero. This is the coldest possible temperature, at which atoms move as slowly as possible (they can never quite stop completely). On the more familiar Celsius and Fahrenheit temperature scales, absolute zero (0 K) is -273°C and -460°F. Ordinary room temperature is 293 K, 20°C, or 68°F. Box 5-1 discusses the relationships among the Kelvin, Celsius, and Fahrenheit temperature scales.

Figure 5-12 depicts quantitatively how the radiation from a dense object depends on its Kelvin temperature. Each curve in this figure shows the intensity of light emitted at each wavelength by a dense object at a given temperature: 3000 K (the temperature of a “cool” star, and at which molten gold boils), 6000 K (around the temperature of our Sun, and of an iron-welding arc), and 12,000 K (the temperature of a “hot” star, and also found in special industrial furnaces). In other words, the curves show the spectrum of light emitted by such an object. At any temperature, a hot, dense object emits at all wavelengths, so its spectrum is a smooth, continuous curve with no gaps in it.

Figure 5-12: Blackbody Curves Each of these curves shows the intensity of light at every wavelength that is emitted by a blackbody (an idealized case of a dense object) at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000-K curve is actually about 1000 times greater than the peak intensity for the 3000-K curve.

As we will see shortly, this is an example of blackbody radiation. Figure 5-12 shows that the higher the temperature, the greater the intensity of light at all wavelengths. One way to understand this response to temperature is that the emitted light results from the motion of the material’s atoms and molecules, which, as we saw, increases with temperature (see Figure 5-11).

The temperature not only indicates the total intensity of the light, but also the shape of its spectrum. The most important feature in the spectrum—the dominant wavelength—is called the wavelength of maximum emission, at which the curve has its peak and the intensity of emitted energy is strongest (see Figure 5-12). The location of the peak also changes with temperature: The higher the temperature, the shorter the wavelength of maximum emission.

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Figure 5-12 shows that for a dense object at a temperature of 3000 K, the wavelength of maximum emission is around 1000 nm (1 mm). Because this peak wavelength corresponds to the infrared range and is well outside the visible range, you might think that you cannot see the radiation from an object at this temperature. However, the glow from such an object is visible; the curve shows that this object emits light within the visible range, although about 90 percent of the emitted energy comes out at longer, invisible wavelengths (to the right of the visible spectrum). This invisible light is also emitted by lightbulbs. Incandescent lightbulbs create visible light by electrically heating a thin wire filament to about 3000 K, but because most of the energy is wasted at longer wavelengths, more efficient lights have become popular.

The 3000-K curve in Figure 5-12 is quite a bit higher at the red end of the visible spectrum than at the violet end, and a dense object at this temperature will appear yellowish in color. At even lower temperatures below 1000 K, the object would appear red (see Figure 5-9a). For higher temperatures, the 12,000-K curve has its wavelength of maximum emission in the ultraviolet part of the spectrum, at a wavelength shorter than visible light. But such a hot, dense object also emits copious amounts of visible light (much more than at 6000 K or 3000 K, for which the curves are lower) and thus will have a very visible glow. The curve for this temperature is higher for blue light than for red light, and so the color of a dense object at 12,000 K is a brilliant blue or blue-white. The same principles apply to stars of different temperatures, which accounts for the different colors of stars in Figure 5-9. A star that looks blue has a high surface temperature, while an orange star has a relatively cool surface.

To summarize these observations:

The higher an object’s temperature, the more intensely the object emits electromagnetic radiation and the shorter the wavelength at which it emits most strongly.

We will make frequent use of this general rule to analyze the temperatures of celestial objects such as planets and stars.

The curves in Figure 5-12 are drawn for an idealized type of dense object called a blackbody. A perfect blackbody does not reflect any light at all; instead, it absorbs all radiation falling on it. Because it reflects no electromagnetic radiation, the radiation that it does emit is entirely the result of its temperature. Ordinary objects, like tables, textbooks, and people, are not perfect blackbodies; they reflect light, which is why they are visible. A star such as the Sun, however, behaves very much like a perfect blackbody, because it absorbs almost completely any radiation falling on it from outside. The light emitted by a blackbody is called blackbody radiation, and the curves in Figure 5-12 are often called blackbody curves.

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CAUTION!

Despite its name, a blackbody does not necessarily look black. The Sun, for instance, does not look black because its temperature is high (around 5800 K), and so it glows brightly. But a room-temperature (around 300 K) blackbody would appear very black indeed. Even if a 300-K blackbody were as large as the Sun, it would emit only about 1/100,000 as much energy: Its blackbody curve is far too low to graph in Figure 5-12. Furthermore, most of the radiation from a room-temperature object is emitted at infrared wavelengths that are too long for our eyes to perceive.

Figure 5-13 shows the blackbody curve for a temperature of 5800 K. It also shows the intensity curve for light from the Sun, as measured from above Earth’s atmosphere. (This is necessary because Earth’s atmosphere absorbs certain wavelengths.) The peak of both curves is at a wavelength of about 500 nm, near the middle of the visible spectrum. Note how closely the observed intensity curve for the Sun matches the blackbody curve. This is a strong indication that the temperature of the Sun’s glowing surface is about 5800 K—a temperature that we can measure across a distance of 150 million kilometers! The close correlation between blackbody curves and the observed intensity curves for most stars is a key reason why astronomers are interested in the physics of blackbody radiation.

Figure 5-13: The Sun as a Blackbody This graph shows that the intensity of sunlight over a wide range of wavelengths (solid curve) is a remarkably close match to the intensity of radiation coming from a blackbody at a temperature of 5800 K (dashed curve). The measurements of the Sun’s intensity were made above Earth’s atmosphere (which absorbs and scatters certain wavelengths of sunlight). It is not surprising that the range of visible wavelengths includes the peak of the Sun’s spectrum; the human eye evolved to take advantage of the most plentiful light available.

Blackbody radiation depends only on the temperature of the object emitting the radiation, not on the chemical composition of the object. The light emitted by molten gold at 2000 K is very nearly the same as that emitted by molten lead at 2000 K. Therefore, it might seem that analyzing the light from the Sun or from a star can tell astronomers the object’s temperature but not what the star is made of. As Figure 5-13 shows, however, the intensity curve for the Sun (a typical star) is not precisely that of a blackbody. We will see later in this chapter that the differences between a star’s spectrum and that of a blackbody allow us to determine the chemical composition of the star.

CONCEPT CHECK 5-5

An object is at 3000 K, emitting radiation that peaks at an infrared wavelength of around 1000 nm. Now the object is heated to 12,000 K and only emits a small fraction of its total energy at infrared wavelengths. At what temperature does the object emit more infrared radiation?

CONCEPT CHECK 5-6

Does a 0°C blackbody object give off any radiation?

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TOOLS OF THE ASTRONOMER’S TRADE

Temperatures and Temperature Scales

Three temperature scales are in common use. Throughout most of the world, temperatures are expressed in degrees Celsius (°C). The Celsius temperature scale is based on the behavior of water, which freezes at 0°C and boils at 100°C at sea level on Earth. This scale is named after the Swedish astronomer Anders Celsius, who proposed it in 1742.

Astronomers usually prefer the Kelvin temperature scale. This is named after the nineteenth-century British physicist Lord Kelvin, who made many important contributions to our understanding of heat and temperature. Absolute zero, the temperature at which atomic motion is at the absolute minimum, is −273°C in the Celsius scale but 0 K in the Kelvin scale. Atomic motion cannot be any less than the minimum, so nothing can be colder than 0 K; hence, there are no negative temperatures on the Kelvin scale. Note that we do not use degree (°) with the Kelvin temperature scale.

A temperature expressed in kelvins is always equal to the temperature in degrees Celsius plus 273. On the Kelvin scale, water freezes at 273 K and boils at 373 K. Water must be heated through a change of 100 K or 100°C to go from its freezing point to its boiling point. Thus, the “size” of a kelvin is the same as the “size” of a Celsius degree. When considering temperature changes, measurements in kelvins and Celsius degrees are the same. For extremely high temperatures the Kelvin and Celsius scales are essentially the same: For example, the Sun’s core temperature is either 1.55 × 107 K or 1.55 × 107 °C.

The now-archaic Fahrenheit scale, which expresses temperature in degrees Fahrenheit (°F), is used only in the United States. When the German physicist Gabriel Fahrenheit introduced this scale in the early 1700s, he intended 100°F to represent the temperature of a healthy human body. On the Fahrenheit scale, water freezes at 32°F and boils at 212°F. There are 180 Fahrenheit degrees between the freezing and boiling points of water, so a degree Fahrenheit is only 100/180 = 5/9 as large as either a Celsius degree or a kelvin.

Two simple equations allow you to convert a temperature from the Celsius scale to the Fahrenheit scale and from Fahrenheit to Celsius:

EXAMPLE: A typical room temperature is 68°F. We can convert this to the Celsius scale using the second equation:

To convert this to the Kelvin scale, we simply add 273 to the Celsius temperature. Thus,

68° = 20°C = 293 K

The diagram displays the relationships among these three temperature scales.