
State Kirchhoff’s law of radiation and prove it theoretically.
Answer
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Hint: Kirchhoff’s law of thermal radiation states that the emissive power to the coefficient of absorption is constant for all the substances at a given temperature. We can say that at a given temperature, the emissivity of a substance is equal to the coefficient of absorption.
Formula used:
Complete step by step answer:
In heat transfer, Kirchhoff’s thermal radiation law refers to the wavelength-specific radiative emission and absorption by a body in thermodynamic equilibrium. Kirchhoff’s law states that: For a body made up of any arbitrary material, the emitting and the absorbing thermal electromagnetic radiation, the ratio of its emissive power to its coefficient of absorption is equal to a universal function. That universal function describes the emissive power of a perfect black body.
Explanation of Kirchhoff’s thermal radiation law:
If is the emissive power of a substance and is the coefficient of absorption, then by Kirchhoff’s law of radiation,
Or we can say,
Theoretical proof of Kirchhoff’s law of thermal radiation:
We will consider two bodies A and B being suspended in a constant temperature enclosure. A is a normal material body and B is a perfectly black body. After some interval of time both A and B will attain the same temperature as that of the enclosure. Prevost heat exchange theory states that every body will emit and absorb thermal radiations.
Let be the emissive power of A and be its coefficient of absorption. Let be the emissive power of B. Let be the radiant heat incident per unit time area of each body.
Heat absorbed by body A per unit time per unit area =
Heat emitted by body A per unit time per unit area =
As the temperature remains constant, heat absorbed will be equal to the heat emitted
Perfectly black body will absorb the entire heat incident on it
Heat absorbed by body B per unit time per unit area =
Heat emitted by body B per unit time per unit area =
As the temperature remains constant, heat absorbed will be equal to the heat emitted
From above equations, we get
But,
Therefore,
Thus, the coefficient of emission is equal to the coefficient of absorption. This proves Kirchhoff’s thermal radiation law theoretically.
Note: Students should keep in mind that Emissivity is a measure of how strongly a body interacts with thermal radiation. Always remember, a high emissivity of material comes together with a high absorptance. Emissivity of a black body is 1.
Formula used:
Complete step by step answer:
In heat transfer, Kirchhoff’s thermal radiation law refers to the wavelength-specific radiative emission and absorption by a body in thermodynamic equilibrium. Kirchhoff’s law states that: For a body made up of any arbitrary material, the emitting and the absorbing thermal electromagnetic radiation, the ratio of its emissive power to its coefficient of absorption is equal to a universal function. That universal function describes the emissive power of a perfect black body.
Explanation of Kirchhoff’s thermal radiation law:
If
Or we can say,
Theoretical proof of Kirchhoff’s law of thermal radiation:
We will consider two bodies A and B being suspended in a constant temperature enclosure. A is a normal material body and B is a perfectly black body. After some interval of time both A and B will attain the same temperature as that of the enclosure. Prevost heat exchange theory states that every body will emit and absorb thermal radiations.

Let
Heat absorbed by body A per unit time per unit area =
Heat emitted by body A per unit time per unit area =
As the temperature remains constant, heat absorbed will be equal to the heat emitted
Perfectly black body will absorb the entire heat incident on it
Heat absorbed by body B per unit time per unit area =
Heat emitted by body B per unit time per unit area =
As the temperature remains constant, heat absorbed will be equal to the heat emitted
From above equations, we get
But,
Therefore,
Thus, the coefficient of emission is equal to the coefficient of absorption. This proves Kirchhoff’s thermal radiation law theoretically.
Note: Students should keep in mind that Emissivity is a measure of how strongly a body interacts with thermal radiation. Always remember, a high emissivity of material comes together with a high absorptance. Emissivity of a black body is 1.
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