__What is a Black Body?__

The radiation emitted by a black body is called *black body radiation.*

*A black body is one which neither reflects nor transmits but absorbs whole of the heat radiation incident on it.*

A black body has following characteristics –

*Absorptive power*of a black body is one. It means a black body absorbs all of the radiation energy incident on its surface.*Reflective power*and*transmittive power*of a perfect black body are zero.- When a black body is heated to high temperature, it emits
*radiations*of all possible*wavelengths*within a certain wavelength range.

__Emissive Power__

*The emissive power of a radiant body at a given temperature and wavelength is defined as the amount of radiant energy of given wavelength emitted per unit time per unit surface area of that body.*

Let, a radiant energy ( Q ) of a given wavelength is radiating from a body of surface area ( A ) in time ( t ) .

Then, emissive power of that body will be \quad e = \left ( \frac {Q}{A t} \right )

The SI unit of emissive power is ( J \ s^{- 1} m^{- 2} ) or ( W \ m^{- 2} )

__Emissivity__

*Emissivity of a radiant body is defined as the ratio of the amount of heat energy radiated per unit time per unit surface area of the body in a certain time to the total amount of heat energy emitted by a perfect black body at the same temperature.*

Therefore, emissivity ( \epsilon ) of a radiant body is the ratio of emissive power ( e ) of a body to the emissive power ( E ) of a black body at the same temperature.

Thus, \quad \epsilon = \left ( \frac {e}{E} \right )

- Emissivity being a ratio of two similar quantities, it is dimensionless.
- The emissivity of a perfect black body is 1 .

__Ferry’s Black Body Radiation__

The concept of black body is hypothetical. A perfectly black body can’t be realized in practice. Ferry’s black body is the nearest to a perfect black body.

- A surface coated with lamp black or platinum black can absorbs maximum of ( 95 \ \text {to} \ 97 \% ) of the incident radiation. But on heating it doesn’t emit full radiation spectrum.
- Hence, the concept of ferry’s black body is in existence.
- The nearest example of an ideal black body is
**Ferry’s black body.**

A Ferry’s black body is shown in figure. It has following features –

- It consists of a hollow double walled metal sphere coated inside with lamp black and nickel polished from outside as shown in figure.
- There is a fine hole in it. All radiations entering through this hole is completely absorbed due to multiple reflections as shown in figure.
- The conical projection opposite to the opening prevents direct reflection.
- If this black body is heated to high temperature then it emits radiations of all
*wavelengths*. - The wavelength range of emitted radiation is independent of the material of the body and depends only on the
*temperature*of the black body.

__Kirchoff’s law of Radiation__

In radiation mode of heat transfer, Kirchhoff’s thermal radiation law tells about the radiation of certain wavelength emitted or absorbed by a body in thermodynamic equilibrium.

- Kirchoff’s law of radiation consists of two statements.

**FIRST STATEMENT –**

It states that –

*At any given temperature, the ratio of emissive power ( e ) and the absorptive power ( a ) corresponding to a certain wavelength is constant for all surfaces.*

Therefore, \left ( \frac {e}{a} \right ) = \text {Constant}

**SECOND STATEMENT –**

It states that –

*At any given temperature, the ratio of emissive power ( e ) and the absorptive power ( a ) corresponding to a certain wavelength is equal to the emissive power ( E ) of a perfectly black body at that temperature to the same wavelength.*

Therefore, \quad \left ( \frac {e}{a} \right ) = E

Or, \quad e = E \ a ……… (1)

Also, emissivity ( \epsilon ) of a surface is given by the ratio of emissive power ( e ) of that surface to the emissive power ( E ) of a perfect black body.

\epsilon = \left ( \frac {e}{E} \right ) …….. (2)

Putting the value of ( e = E \ a ) from equation (1) in equation (2), we get –

\epsilon = \left ( \frac {E \ a}{E} \right ) = a

Or, \quad \epsilon = a

*Thus, the absorptive power of a body is equal to its emissivity. *

- This is another form of Kirchoff’s law.
- Hence, a good absorber is a good emitter and so a poor reflector.

__Stefan Boltzmann Law of Radiation__

Stefan-Boltzmann law of energy radiation states that –

*The total heat energy emitted by a perfect black body per second per unit area is directly proportional to the fourth power of the absolute temperature.*

Thus, \quad E \propto T^4 .

Or, \quad E = \sigma T^4 .

If ( H ) is the rate of radiation emitted by a black body of surface area ( A ) , then –

H = EA = \sigma T^4 A

- In ( SI ) units \quad \sigma = 5.67 \times 10^{-8} W m^{-2} K^{-4}

__Wien’s Displacement Law__

Wien’s displacement law of wavelength of emitted energy states that –

*When a black body emits maximum energy, the wavelength of the radiation are inversely proportional to its absolute temperature.*

Therefore, \quad \lambda_{max} \propto \left ( \frac {1}{T} \right )

Or, \quad \lambda_{max} T = b

- Here ( b ) is a constant called
**Wien’s constant.** - Value of Wien’s constant is \quad b = 2.9 \times 10^{-3} m K

__EXAMPLE –__

- When an iron piece is heated in a hot flame, its colour first becomes dull red, then reddish yellow and finally white.
- This observation is in accordance with the Wien’s law. With increase in temperature the emission of energy is maximum at smaller wave lengths. Because \quad \lambda_{white} < \lambda_{yellow} < \lambda_{red}

See numerical problems based on this article.