## What is a Blackbody?

Gustav Kirchhoff introduced the term blackbody in 1860. A blackbody is a body that can neither reflect nor transmit the radiation falling on its surface. It can absorb most of the heat radiations incident on it. It emits radiations based on Planck's quantum theory. For a perfect blackbody, the absorptive power is unity.

### Blackbody Radiation

The property of a blackbody is to emit most of the radiations striking its surface when heated to a very high temperature. The radiation lies within a certain range of wavelength. This process of emission of radiation from a blackbody is called blackbody radiation. It is also called thermal radiation.

The electromagnetic wave theory explains blackbody radiation. When a blackbody is heated to a particular temperature, the intensity of radiation increases with a decrease in wavelength.

Lamp black and platinum black can absorb more than 97% of the incident radiation. When their surfaces are heated, they do not emit 100% radiation. Therefore, they act as blackbodies only for the absorption of heat radiation.

### Phenomenon of Blackbody radiation

When a metal body with a high melting point is heated, its atoms emit radiations of frequency *f*. When the body is heated further, it emits radiations of a different color.

Initially, the radiation is of red color. On heating, it first changes to yellow and then, to blue.

### Cavity radiation

When a hollow cavity is heated to a very high temperature, it emits spectrum radiation from its inner surface. This type of radiation is called cavity radiation. Therefore, a heated cavity acts as a perfect blackbody for both emission and absorption of heat radiation.

## What is Frey's blackbody?

Frey's blackbody is a metal sphere with a hollow double layer coated with lamp black from the inside and nickel from the outside. It works on the principle of multiple reflections of radiation. The temperature of the entire enclosure is kept constant. The wavelength of the emitted radiation is independent of the material of the object. It depends only on the temperature of the blackbody.

### Sketch of a blackbody absorber

### Sketch of a blackbody emitter

## How is energy distributed in blackbody spectrum?

A blackbody emits radiations of different wavelengths. The arrangement of these wavelengths in the increasing order is called blackbody radiation. The radiation corresponding to each wavelength has a fixed energy at a specific temperature.

### Sketch showing the distribution of energy in blackbody spectrum

## Conclusions for Blackbody spectrum

The conclusions regarding the blackbody spectrum are:

- A blackbody emits continuous heat radiation at a particular temperature.
- When there is an increase in temperature, the energy associated with the radiation also increases.
- The area under the curve shows the total energy emitted by a perfect blackbody per second per unit area, at the particular temperature.
- The curves of blackbody radiation depend only on the surface temperature of the object.
- The energy of the blackbody is distributed non-uniformly among all wavelengths.

## What are the properties of Blackbody radiation?

The following laws explain the properties of blackbody radiation:

- Planck's law of quantum theory
- Wein's displacement law
- Stefan-Boltzmann law

## Wein's displacement law

According to Wein's displacement law, the maximum wavelength of radiation emitted by a blackbody is inversely proportional to its absolute temperature.

The formula for Wein's displacement law is:

${\lambda}_{max}=\frac{b}{T}$ ...(1)

Here, b is Wein's constant with the value $2.3\times {10}^{-3}\mathrm{mK}$ and ${\lambda}_{max}$ is the wavelength.

## Stefan-Boltzmann law

According to the Stefan-Boltzmann law, the energy that a perfect blackbody emits per second per unit area is directly proportional to the fourth power of the absolute temperature of its surface.

The formula for the Stefan-Boltzmann law is:

$E=\sigma {T}^{4}$ ...(2)

Here, σ is the Stefan-Boltzmann constant with the value $5.67\times {10}^{-8}{\mathrm{Wm}}^{-2}{\mathrm{K}}^{-4}$ and *T* is the absolute temperature.

The rate of energy loss by a blackbody per unit area per unit time is:

$E=\sigma ({T}^{4}-{{T}_{0}}^{4})$ ...(3)

Here, ${T}_{0}$ is the enclosure temperature.

If an object is not a perfect blackbody, we define the emissivity term for it.

Emissivity is the ratio of the energy radiated per unit area per unit time by a non-perfect blackbody and a perfect blackbody, at the same temperature. It is denoted by ε. The value of emissivity lies between 0 and 1. For a perfect blackbody, its value is 1.

In terms of emissivity, the rate of heat loss per unit area per unit time is:

$H=\epsilon \sigma A({T}^{4}-{{T}_{0}}^{4})$ ...(4)

Here, *H* is the rate of energy emitted by the body.

## How is Newton's law of cooling derived for blackbody radiation?

Consider a blackbody of surface area *A* and surface temperature *T*. The body is kept in an enclosure at temperature *T0. *

By the Stefan-Boltzmann law, the net rate of loss of heat from the body is:

$H=\epsilon \sigma A({T}^{4}-{{T}_{0}}^{4})=\epsilon \sigma A(T-{T}_{0}T+{T}_{0}{T}^{2}+{{T}_{0}}^{2})$

As $T-{T}_{0}$ is very small, *T* is approximately equal to T0.

The rate of heat loss from the body is:

$H=4\epsilon \sigma A({{T}_{0}}^{3}T-{T}_{0})$ ...(5)

Let the specific heat capacity of the body be *s *and its mass be *m*.

The expression for the rate of fall in temperature is:

$-\frac{dT}{dt}=Hms-\frac{dT}{dt}=4\epsilon \sigma A({{T}_{0}}^{3}ms-{T}_{0})$

Solving the above equation, the formula for Newton's law of cooling is:

$\frac{-dT}{dt}=kA(T-{T}_{0})$ ...(6)

## Quantum theory of radiation

In 1901, Max Planck explained blackbody radiation using the concepts of quantum theory of radiation.

The main postulates of the quantum theory are:

- The energy emitted by a blackbody is in the form of small packets called quanta.
- The energy of each quantum number is directly proportional to its frequency of radiation.
- The formula for Planck's quantum theory is E=hf . Here, h is Planck's constant and
*f*is frequency. - The energy of each quantum is quantized.

Max Planck suggested that light consists of particles called photons. The energy of each photon is quantized, and it depends on the frequency of the incident radiation.

## Common Mistakes

Students often get confused between blackbody radiation and photoelectric effect. As the electromagnetic wave theory fails to explain both these phenomena, students sometimes consider them to be the same, which is incorrect.

Photoelectric effect is the phenomenon in which electrons eject from a metal surface when radiation strikes it. On the other hand, blackbody radiation is the radiation emitted by a blackbody, which absorbs most of the incident radiation.

## Context and Applications

This topic is significant for the professional exams of both graduate and undergraduate courses, especially:

- Bachelor in Engineering in Chemical Engineering
- Bachelor in Science in Physics
- Masters in Science in Chemistry
- Masters in Science in Applied Chemistry

## Related Concepts

- Wein's displacement law
- Stefan-Boltzmann law
- Blackbody spectrum
- Newton's law of cooling
- Emissivity
- Planck's quantum theory

## Practice Problems

Q.1 Which of the following options represents a blackbody?

(a) Tungsten filament of a bulb

(b) A black painted steel ball

(c) Black sandpaper

(d) An igneous rock

Correct option: (a)

Q.2 Which of the following options gives the correct definition of the blackbody?

(a) A blackbody is a body that absorbs only a few wavelengths from the incident radiation.

(b) A blackbody is simply a black-painted body.

(c) A blackbody is a body that absorbs most of the heat radiations incident on it.

(d) A blackbody is a body that reflects all the radiations incident on it.

Correct option: (c)

Q.3 Which of the following options gives the scientist who introduced blackbody?

(a) Georg Ohm

(b) Gustav Kirchhoff

(c) Alessandro Volta

(d) Joseph Henry

Correct option: (b)

Q.4 Identify the use of a blackbody.

(a) A blackbody is used for lighting and heating purposes.

(b) A blackbody is used as the reflecting surface in solar heaters.

(c) A blackbody is used as an emitter in spectroscopic experiments.

(d) There is no such use of a blackbody in real life.

Correct option: (a)

Q.5 A blackbody radiates how much energy when the temperature of the body is elevated?

(a) Maximum

(b) Minimum

(c) No energy is radiated

(d) 50% of the energy is radiated

Correct option: (c)

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