Colour Temperature of Black Body Radiation

What is black Body?

Black body is any inanimate body that always absorbs all radiation completely falling on it and radiates same amount of energy it receives at a constant temperature. There is no real existence of black body. But approximation leads the idea to a perfect black body in practice. As per this approximation, the black body is a hollow insulated enclosure containing a small hole in one wall.
The incident energy goes inside the black body and gets reflected again and again against the inner wall of that black body. The black body acts as a perfect absorber. Whether this cavity is heated, all energy will be emitted through this hole. Black body radiation curved is shown below.

Theoretically, the total energy radiated from a black body at a particular temperature is fixed but during radiation of the black body, this total energy is not of a single wavelength. Rather, the total energy radiated from this black body is of various wavelengths zero to infinity. From wavelength 780 nm to 380 nm the radiated energy is within visual sensation. Here it is to be noted that amount of radiation energy per wavelength is not same for all wavelength rather it varies with wavelength. For every temperature, there is a particular wavelength for which the radiated energy per wavelength becomes maximum.


That means at a particular temperature, peak spectral radiant exitance is at a particular wavelength. This wavelength (wavelength for peak energy radiation) depends on the temperature of this black body. Decreasing of temperature the peak of the curve shifts rightward as per the figure is given above. That implies in the graph, the peak of the each curve appears at a shorter wavelength as the temperature increases. As the energy radiation occurs at all wavelengths the curve comes very closer to the horizontal axis but never touches the axis even when the wavelength is infinitely long. The area enclosed by the curve of any temperature indicates the total energy radiated by the black body at this particular temperature. If the temperature varies, the total amount of energy radiated also varies. If we connect peak of all curves we will get a parabola as shown in the figure above. Above graph shows the spectral exitance versus wavelength. Spectral Exitance means power per unit area per unit wavelength. As per radiation physics, Stefan-Boltzmann law is applicable here. This law states that the total power radiated per unit surface area of a black body across all wavelengths is directly proportional to the fourth power of the black body temperature.

 

Here, M_e is the radiated power per unit area and T is the temperature in Kelvin and also σ is the Stefan-Boltzmann constant. This power emits from this hole of the black body. As per Plank’s Law

Where, P_e is the radiated power per unit area in the normal direction per unit solid angle per unit frequency by this black body at temperature T. h is the Planck constant; k is the Boltzmann constant; c is the speed of light in a vacuum; T is the absolute temperature of the body. υ is the frequency of the electromagnetic radiation; Following the classical theory, Wien proved that at this peak of the wavelength the absolute temperature gives a constant value, viz.,



This above expression is called Wien’s displacement Law. This Law describes the hyperbola passing through the peak points of the curves shown in the above graph.

Practical Blackbody

But the blackbodies are covering the range of temperature from about -20 to 3000 degree Celsius (253 K to 3273 K) in the practical cases. And accordingly the peak wavelengths are from 885 nm to 11500 nm. 885 nm is in the visible range whereas 11500 nm is infrared ray (IR). The temperatures of the black bodies can be determined in a freezing point black body calibration source. Generally, a black-body appears black at room temperature. Again most of the energy it radiates is in the form of an infra-red ray. A black body’s infrared ray radiation cannot be perceived by the human eyes as the human eyes never perceive color at very low light intensities. So a black body that is viewed in the dark at the lowest visible temperature i.e. just faintly, practically it appears grey. When we make the black body a little hotter, it appears dull red accordingly. Again black body’s temperature is increased further it eventually becomes bright blue-white. The chromaticity diagram shows the color temperature of a blackbody.

This color bar given below, shows the color temperature of a black body.