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# Thermal radiation

Radiation emitted by such a body due to its temperature is called thermal radiation.All bodies not only emit such radiation but also absorb it from their surroundings.If the rate of absorption and emission from a body become equal ,the body is said to be in thermal equilibrium with its surroundings.

The spectrum of thermal radiation from a hot solid body is continuous with the following characteristics.

1:The higher the temperature,greater the thermal radiation is emitted.At first the body appears dim and then it glows brightly.

2:The higher the temperature,the shorter is the wavelength of that part of spectrum radiating most intensity.This is supported by the fact that the colour of hot body shifts from dull red through high yellow among to bluish white heat.From the colour of the hot body which the sees we can estimate its temperature.

Thermal radiation emitted by a hot body depends not only on its temperature but also on the material of the body,its shape and the nature of its surface.For example,a hot body with a polished surface emits less radiation than does hot body with rough surface.Just as properties of real gases can be understood by introducing the concept of an “ideal gas” the properties of thermal radiation can be understood by introducing an ideal radiator”.This is because the spectrum of emitted thermal radiation depends only on the temperature of the radiator and not only on the material,shape or nature of the surface of the ideal radiator.

An ideal radiator can be determined by forming a cavity with in a black of a material with its walls being held at a uniform temperature.A small hole is drilled through the wall to allow the radiation.Inside the cavity to escape into the laboratory for experimentation. Such thermal radiation is called cavity radiation or black body radiation or temperature radiation as it depends only on the temperature of the walls of the cavity and not on its material and other factors out lined above cavity radiation helps us to understand the nature of thermal radiation just as the ideal gas helps us to understand matter in its gaseous form.Radiation emerging from the hole of the cavity is much more intense than that from the walls of the cavity.

There are three interrelated properties of cavity radiation,all well verified in laboratory,that any theory of cavity radiation most explain.

## 1:The Stephen Boltzmann law

The total radiated power per unit area of the cavity aperture summed over all wavelength is called its radiant intensity I(T) and is related to the temperature by the radiation:

[latex]I(T)=\sigma { T }^{ 4 }\quad \quad ……………(1)\\ [/latex]Where σ=5.67 × 10-8 watt/m² -k4 is a universal constant,called Stephen Boltzmann constant.Ordinary hot objects radiate less efficiently than does cavity radiator ,this fact can be incorporated into the Stephen Boltzmann law by generalizing it to the form:

[latex]I(T)=\epsilon \sigma { T }^{ 4 }\quad \quad ……………(2)\\ [/latex]Where ∈ is a dimensionless quantity ,called the emissivity of the surface material.

## 2:Spectral Radiancy

The spectral radiancy R(λ) tells us how the intensity of cavity radiation varies with wavelength for a given temperature.It is defined so that the product R(λ) dλ gives radiated power per unit area with wavelength range extending from λ to λ+dλ.R(λ) is statistically distribution function of the form.

[latex]R(\lambda )=A{ e }^{ -e\lambda }\quad \quad ……………(3)\\ [/latex]The radiant intensity I(T) for any temperature can be obtained by integrating the spectral radian over the complete wavelength range i.e:

[latex]I(T)=\int _{ 0 }^{ \infty }{ R(\lambda )d(\lambda ) } ,T=constant\quad \quad ……………(4)\\ [/latex]Spectral radian is expressed in watt/m² per unit wavelength (watt-m² m-¹).

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