# Heat Radiation

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## Heat radiation

The energy radiated by solids, liquids, and gases as a result of their temperature. Such radiant energy is in the form of electromagnetic waves and covers the entire electromagnetic spectrum, extending from the radio-wave portion of the spectrum through the infrared, visible, ultraviolet, x-ray, and gamma-ray portions. From most hot bodies on Earth this radiant energy lies largely in the infrared region. *See* Electromagnetic radiation, Infrared radiation

Radiation is one of the three basic methods of heat transfer, the other two methods being conduction and convection. *See* Conduction (heat), Convection (heat), Heat transfer

A hot plate at 260°F (400 K) may show no visible glow; but a hand which is held over it senses the warming rays emitted by the plate. A temperature of more than 1300°F (1000 K) is required to produce a perceptible amount of visible light. At this temperature a hot plate glows red and the sensation of warmth increases considerably, demonstrating that the higher the temperature of the hot plate the greater the amount of radiated energy. Part of this energy is visible radiation, and the amount of this visible radiation increases with increasing temperature. A steel furnace at 2800°F (1800 K) shows a strong yellow glow. If a tungsten wire (used as the filament in incandescent lamps) is raised by resistance heating to a temperature of 4600°F (2800 K), it emits a bright white light. As the temperature of a substance increases, additional colors of the visible portion of the spectrum appear, the sequence being first red, then yellow, green, blue, and finally violet. The violet radiation is of shorter wavelength than the red radiation, and it is also of higher quantum energy. In order to produce strong violet radiation, a temperature of almost 5000°F (3000 K) is required. Ultraviolet radiation necessitates even higher temperatures. The Sun emits considerable ultraviolet radiation; its temperature is about 10,000°F (6000 K). Such temperatures have been produced on Earth in gases ionized by electrical discharges. The mercury-vapor lamp and the fluorescent lamp emit large amounts of ultraviolet radiation. Temperatures up to 36,000°F (20,000 K), however, are still much too low to produce x-rays or gamma radiation. A gas maintained at temperatures above 2 × 10^{6°}F (1 × 10^{6} K), encountered in nuclear fusion experiments, emits x-rays and gamma rays. *See* Nuclear fusion, Ultraviolet radiation

A blackbody is defined as a body which emits the maximum amount of heat radiation. Although there exists no perfect blackbody radiator in nature, it is possible to construct one on the principle of cavity radiation. *See* Blackbody

A cavity radiator is usually understood to be a heated enclosure with a small opening which allows some radiation to escape or enter. The escaping radiation from such a cavity has the same characteristics as blackbody radiation.

Kirchhoff's law correlates mathematically the heat radiation properties of materials at thermal equilibrium. It is often called the second law of thermodynamics for radiating systems. Kirchhoff's law can be expressed as follows: The ratio of the emissivity of a heat radiator to the absorptivity of the same radiator is a function of frequency and temperature alone. This function is the same for all bodies, and it is equal to the emissivity of a blackbody. A consequence of Kirchhoff's law is the postulate that a blackbody has an emissivity which is greater than that of any other body. *See* Kirchhoff's laws of electric circuits

Planck's radiation law represents mathematically the energy distribution of the heat radiation from 1 cm^{2} of surface area of a blackbody at any temperature. Formulated by Max Planck early in the twentieth century, it laid the foundation for the advance of modern physics and the advent of quantum theory.

*R*

_{λ}is the total energy radiated from the body measured in watts per square centimeter per unit wavelength, at the wavelength λ. The wavelength in this formula is measured in micrometers. The quantity

*T*is the temperature in kelvins, and

*e*is the base of the natural logarithms. The illustration presents graphs of Planck's law for various temperatures and shows substances which attain these temperatures. It should be noted that these substances will not radiate as predicted by Planck's law since they are not blackbodies themselves.

The Stefan-Boltzmann law states that the total energy radiated from a hot body increases with the fourth power of the temperature of the body. This law can be derived from Planck's law by the process of integration and is expressed mathematically as Eq. (2), where *R*_{T} is the total amount of energy radiat

*R*

_{T}is multiplied by the total emissivity, the total energy radiated from a real heat radiator is obtained.

## Heat Radiation

a form of electromagnetic radiation emitted by a substance as a result of its internal energy. Heat radiation is contrasted, for example, to luminescence, which results from external energy sources. Heat radiation has a continuous spectrum whose maximum is a function of the temperature of the substance. As the temperature increases, the total energy of the emitted heat radiation grows, and the maximum shifts toward shorter wavelengths. Examples of emitters of heat radiation are the surface of an incandescent metal and the earth’s atmosphere.

Heat radiation is characteristic of all nonradiative processes exhibiting detailed balancing—that is, various types of particle collisions in gases and plasma and the exchange of energy between the electronic and vibrational motions in solids. (*See*DETAILED BALANCING, PRINCIPLE OF.) The equilibrium state of a substance at each point in space, called the state of local thermodynamic equilibrium, is expressed as a temperature; moreover, the heat radiation of the substance at any given point is a function of this temperature.

In the general case of a system of bodies in which only local thermodynamic equilibrium exists and different points have different temperatures, the heat radiation is not in thermodynamic equilibrium with the substance. Hot bodies radiate more than they absorb, and the reverse is true for colder bodies. Radiative transfer from the hotter bodies to the colder bodies takes place. Maintenance of a steady state, in which the temperature distribution in the system is preserved, requires that heat be supplied to the hotter bodies and be drawn off from the colder bodies. This may occur either under natural conditions, as in the earth’s atmosphere, or artificially, as in incandescent lamps.

In complete thermodynamic equilibrium, all parts of a system of bodies have the same temperature, and the energy of the heat radiation emitted by each body is balanced by the energy of the heat radiation absorbed from other bodies. In this case the heat radiation is in thermodynamic equilibrium with the substance and is called equilibrium radiation; an example is the thermal radiation of a blackbody. The spectrum of equilibrium radiation is independent of the nature of the substance and is determined by Planck’s radiation law.

In the general case, the thermal radiation of heated bodies satisfies Kirchhoff s radiation law, which relates the bodies’ emissivity and absorptance to the emissivity of a blackbody.

Radiative transfer processes can be studied by applying Kirchhoff’s and Planck’s radiation laws to the emission and absorption of heat radiation in gases and plasma, assuming local thermodynamic equilibrium. This approach is widely used in astrophysics, particularly in the theory of stellar atmospheres.

### REFERENCES

Planck, M.*Teoriia teplovogo izlucheniia*. Leningrad-Moscow, 1935. (Translated from German.)

Sobolev, V. V.

*Perenos luchistoi energii v atmosferakh zvezd i planet*. Moscow, 1956.

Bosworth, R. C. L.

*Protsessy teplovogo perenosa*. Moscow, 1957. (Translated from English.)

El’iashevich, M. A.

*Atomnaia i molekuliarnaia spektroskopiia*. Moscow, 1962.

M. A. EL’IASHEVICH