2
A blackbody is an ideal body which absorbs the whole incident radiation at any wavelength and angle of incidence of a particular substance. At thermal equilibrium, a blackbody will be an ideal absorber as well as an ideal emitter. Therefore, the amount of radiation it absorbs will be equal to the amount of radiation it emits. In addition to that, the radiation emitted or absorbed by a blackbody will not be affected by its position or orientation, thus, it is isotropic in nature. However, it can only absorb or emit radiation within narrow wavelength. This means that a blackbody is an ideal absorber at any wavelength but this does not imply that same intensity will be absorbed at varying wavelength. It was also proven that any substance will continuously emit radiation energy at any temperature greater than absolute zero as stated in the Prevost’s theory of heat exchange. Different experimental data regarding blackbody radiation was gathered until the middle of nineteenth century but it was Kirchhoff who first interpreted the data theoretically. First, he suggested that the set of wavelengths emitted or absorbed by a substance is unique for that substance. This theory proposed by Kirchhoff now served as a basis for spectral analysis of a substance. Aside from that, he also suggested that radiation spectrum does not depend on chemical composition but on the temperature of a substance. Years later, it was W. Wien who verified Kirchhoff’s theory experimentally. Wien used a hollow sphere with holes in the wall in which the diameter of the holes is very small compared to the diameter of the sphere. By observing the radiation passing through the hole, he concluded that light beam undergoes multiple radiations but does not exit the hole. Other than that, he also observed that the hole brightly shines under very high temperature. From that experiment, he formulated the Wien radiation law with the following formula I λ ( T,λ ) T 5 = C 1 π ( λT ) 5 exp( C ¿¿ 2 / λT ) ¿ where I is the intensity, T is the temperature, and λ is the wavelength. Another law regarding blackbody radiation which considers the general thermodynamics is the Stefan-Boltzmann law which computes

Introduction Blackbody Radiation

Embed Size (px)

DESCRIPTION

Physics

Citation preview

Page 1: Introduction Blackbody Radiation

A blackbody is an ideal body which absorbs the whole incident radiation at any wavelength and angle of incidence of a particular substance. At thermal equilibrium, a blackbody will be an ideal absorber as well as an ideal emitter. Therefore, the amount of radiation it absorbs will be equal to the amount of radiation it emits. In addition to that, the radiation emitted or absorbed by a blackbody will not be affected by its position or orientation, thus, it is isotropic in nature. However, it can only absorb or emit radiation within narrow wavelength. This means that a blackbody is an ideal absorber at any wavelength but this does not imply that same intensity will be absorbed at varying wavelength. It was also proven that any substance will continuously emit radiation energy at any temperature greater than absolute zero as stated in the Prevost’s theory of heat exchange.

Different experimental data regarding blackbody radiation was gathered until the middle of nineteenth century but it was Kirchhoff who first interpreted the data theoretically. First, he suggested that the set of wavelengths emitted or absorbed by a substance is unique for that substance. This theory proposed by Kirchhoff now served as a basis for spectral analysis of a substance. Aside from that, he also suggested that radiation spectrum does not depend on chemical composition but on the temperature of a substance. Years later, it was W. Wien who verified Kirchhoff’s theory experimentally. Wien used a hollow sphere with holes in the wall in which the diameter of the holes is very small compared to the diameter of the sphere. By observing the radiation passing through the hole, he concluded that light beam undergoes multiple radiations but does not exit the hole. Other than that, he also observed that the hole brightly shines under very high temperature. From that experiment, he formulated the Wien radiation law with the following formula

I λ(T , λ)T 5 =

C1

π ( λT )5exp (C¿¿2 / λT )¿

where I is the intensity, T is the temperature, and λ is the wavelength. Another law regarding blackbody radiation which considers the general thermodynamics is the Stefan-Boltzmann law which computes the surface density of total blackbody radiation using the following formula:

q (t )=n2σ T 4

Where q(t) is the total blackbody radiation, σ is the surface density, and T is the temperature. However, it was Wien who took into consideration how energy was distributed in a particular blackbody and then found out that the maximum radiation moves to shorter wavelength at increasing temperature. This results in the formulation of Wien’s displacement law which states that

I λ (T , λm )=T5 C1

πC 53[exp (C2−C3 )−1]

However, the expression of the radiation law was then proven to be valid only at low temperature and at short wavelengths. These limitations forced Max Planck to consider harmonic oscillator which has been the source and absorber of energy of radiation. He then formulated the Planck’s law for energy distribution which gives the maximum value of the intensity that can be emitted by a blackbody at any given temperature and wavelength and is computed as follows

Page 2: Introduction Blackbody Radiation

πI v (T , λ)T5 =

C1

(λT )5

1[exp (C¿¿2 / λT )−1]¿

The result of these experiments was so significant that it is widely used up until now and is used to explain astronomical phenomena which have characteristics that are very close to that of the blackbody radiation. One example is the sun in which the presence of thermal blackbody radiation with brightness temperature of 5800 K was observed. Other than that, the Earth itself possesses radiation somehow similar to blackbody radiation.