Stefan Boltzmann Law

Heat is one of the most important concepts in Physics. It is the basis of many theorems and laws in science. It is the energy that gets transferred because of the temperature difference. While ironing your clothes, the heat from the iron box gets transferred to your clothes. Heat flows from the hotter body to comparatively cooler bodies. Or while making a buttered omelette, you bring out the butter box from the refrigerator. You take some quantity of butter and put it in the hot pan, and the butter melts. The heat of the pan gets transferred to the butter, and butter changes its physical state. Another important fact that we must keep in mind is the difference between Temperature and Heat. Heat is the form of energy; while, the temperature is the measure of identifying that energy.

This form of energy gets transferred to another body in three ways. These ways include- Transfer through Conduction, Transfer through Convection, and Transfer through Radiation. Over the years, many scientists and physicists came up with several laws. For example- Law of Radiations, Quantum Concepts, Stefan-Boltzmann Law, etc. Stefan Boltzmann Law is also known as Stefan’s Law, in the world of Physics. These laws helped in providing various theories and assumptions in the field of Science and Physics.

Let us understand the Stefan Boltzmann Law.

Stefan’s Law

As per Stefan Boltzmann Law, the quantity of heat radiated from an area (of say, a black body) is directly proportional to the fourth power of the temperature. This law was formulated by Josef Stefan in the 1870s and it was derived by Ludwig Boltzmann in the 1880s. We must always keep in mind that Stefan Boltzmann Law is applied surfaces that can absorb all the radiated heat. These surfaces or bodies can be Blackbodies, theoretical surfaces, etc. The law makes equivalences to the power radiated by a black body through temperature. This law can be written as-

Ua = σ. t⁴

Here,

• Here, “U” is heat radiated in the area “a”
• t is the non-variable temperature of the body, and
• σ is the constant of this proportionality

This constant of proportionality is also known as the Stefan Boltzmann Constant. This constant has a fixed value, which is- 5.6703 * 10^-8 watt/m2K4. The above Stefan Boltzmann law formula shows the maximum amount of radiation that is possible at a temperature for any surface. This kind of emitter is popularly known as the Black body.

Let us briefly discuss what Blackbodies are.

Blackbodies

Blackbodies are an essential part of Stefan Boltzmann Law or for any other radiation transference. It is considered an ideal and perfect emitter. That means that heat emitted by a black body at the same temperature is comparatively more than any other emitter. In addition to being a perfect emitter, the black bodies are also diffusing emitters.

Let us look into the meaning of blackbodies. These emitters are known as blackbodies only because they can absorb all heat or light that falls into their surface. It does not reflect any heat or light. It is practically dependent on the wavelength of the angle of incidence.

For example, you have bought a very dark and black material to make some sort of craft product at home. This material can absorb the maximum amount of heat around, say 99.9 percent. In addition to this physical factor, the chemical factor of this material is such that the nickel-phosphorus alloys are vertical to the carbon nanotube arrays. Now, this material can be classified under Blackbodies.

The formula for black bodies is similar to that of Stefan Boltzmann’s law formula. It is-

U = σ t⁴

Here,

• U is the amount of heat radiated
• t is the temperature, and
• σ is the constant having the value 5.6703 * 10^-8watt/m2K4.

In addition to this, we must also consider the non-blackbodies. These bodies or surfaces have less radiation power compared to blackbodies. The Stefan Boltzmann law formula for non-blackbodies is-

U = m a σ t⁴

Here,

• U is the amount of heat radiated
• t is the temperature, and
• σ is the constant having the value 5.6703 * 10^-8 watt/m2K4.
• m is the emission power
• a is the area

Note: The emission power of the non-blackbodies lies between zero and one. It cannot be greater than 1.

Conclusion

The energy that gets transferred because of the temperature difference is known as Heat. It is the basis of many theorems and laws in Science. This form of energy gets transferred to another body in three ways. It includes- Transfer through Conduction, Transfer through Convection, and Transfer through Radiation. The Stefan Boltzmann Law states that the transferring rate of radiated heat from one body to its surrounding is proportional to the absolute temperatures of the fourth power. This law was formulated by Josef Stefan in the 1870s and it was derived by Ludwig Boltzmann in the 1880s. Blackbodies are an essential part of Stefan Boltzmann Law or for any other radiation transference. It is considered an ideal and perfect emitter. These bodies have the capacity to absorb the maximum amount of heat around, say 99.9 percent. The non-blackbodies or other surfaces have less radiation power compared to blackbodies.