Thermal radiation

From Free net encyclopedia

Thermal radiation is electromagnetic radiation from the surface of an object which is due to the object's temperature. Heat from a common household radiator is an example of thermal radiation, as is the light emitted by a glowing incandescent light bulb. The thermal radiation is generated when heat from the movement of charged particles within atoms is converted to electromagnetic radiation.

The emitted wave frequency of the thermal radiation is a probability distribution depending only on temperature, and for a genuine black body is given by Planck’s law of radiation. Wein's law gives the most likely frequency of the emitted radiation, and the Stefan-Boltzmann law gives the heat intensity.

1 Properties
2 Formulae
3 Constants
4 External links

[edit]

Properties

Thermal radiation is an important concept in thermodynamics as it is responsible for heat exchange between objects, as warmer bodies radiate more heat than colder ones. The play of energy exchange is characterized by the following equation:

<math>\alpha+\rho+\tau=1 \,</math>

Here, <math>\alpha \,</math> represents spectral absorption factor, <math>\rho \,</math> spectral reflection factor and <math>\tau \,</math> spectral transmission factor. All these elements depend also on the frequency <math>\upsilon \,</math>. The spectral absorption factor is sometimes called emissivity, and is denoted <math>\epsilon \,</math>.

In a practical situation and room-temperature setting, objects lose a lot of energy due to thermal radiation. However, the energy lost by emitting infrared heat is regained by absorbing the heat of surrounding objects.

[edit]

Formulae

Thermal radiation energy per unit of volume is thus given by <math>u(\upsilon,T)d\upsilon \,</math>, where:

<math>u(\upsilon,T)=\frac{8\pi h\upsilon^3}{c^3}\cdot\frac1{e^\frac{h\upsilon}{k_BT}-1}</math>

For a radiating body, integrating the above equation obtains the output in watts given by the Stefan-Boltzmann law, as:

<math>W = \epsilon(\upsilon)\cdot\sigma AT^4</math>

Here, <math>\epsilon \,</math> is an emissivity correction factor between 0 and 1. It is a practically useful term to account for the fact that the radiating body is not a perfect black body. Furthermore, the emissivity can be found to depend on the frequency <math>\upsilon\,</math>. Objects that appear white (reflective in the visual spectrum) are found to be near perfect black bodies in the infrared spectrum, which is why most household radiators are painted white.

Further, the wavelength <math>\lambda \,</math>, for which the emission intensity is highest, is given by Wien's Law as:

<math>\lambda_{max} = \frac{b}{T} </math>

[edit]

Constants

Definitions of constants used in the above equations:

<math>h \,</math>	Planck's constant
<math>b \,</math>	Wien's displacement constant
<math>k_B \,</math>	Boltzmann constant
<math>\sigma \,</math>	Stefan-Boltzmann constant
<math>c \,</math>	Speed of light
<math>T \,</math>	Temperature
<math>A \,</math>	Surface area