Applications of Stefan-Boltzmann Law

In the real world, there are many applications of Stefan-Boltzmann Law. Some of those applications are as follows:

  • Stefan-Boltzmann Law helps scientists in the calculation of the luminosity of celestial bodies such as stars, planets, and galaxies
  • As we know, the amount of heat absorbed by the atmosphere due to the presence of greenhouse gases, causes the temperature of our earth to rise. By using Stefan-Boltzmann Law, to calculate the amount of energy absorbed by the atmosphere scientists can predict the effect of this rise in temperature.
  • By comparing the surface temperatures for various materials, engineers can make more power-efficient designs that do not need active cooling to work.

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Stefan-Boltzmann Law

Stefan-Boltzmann Law relates the power radiated by the black body to its temperature and surface area. In the study of thermodynamics and astrophysics, the Stefan-Boltzmann Law is widely used to better our understanding of the subject. Other than this, Stefan-Boltzmann Law helps scientists understand the behavior of objects that emit radiation, such as stars and planets. Stefan-Boltzmann Law also has some applications in the real world as well such as, in designing solar panels and other energy conversion instruments.

Table of Content

  • What is Stefan-Boltzmann Law?
  • Formula for Stefan-Boltzmann Law
  • Stefan-Boltzmann Constant
  • Value of Stefan-Boltzmann Constant
  • Formula for Stefan-Boltzmann Constant
  • Black Body Radiation
  • Planck’s Law for Black Body Radiation
  • Derivation of Stefan-Boltzmann Constant
  • Calculation of Stefan-Boltzmann Constant
  • Applications of Stefan-Boltzmann Law
  • Sample Problems on Stefan-Boltzmann Law

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What is Stefan-Boltzmann Law?

The Stefan Boltzmann law states that the total energy emitted per unit surface area of a black body across all wavelengths per unit of time is directly proportional to the fourth power of the black body’s thermodynamic temperature and emissivity. It expresses the power emitted by a black substance as a function of temperature and emissivity....

Formula for Stefan-Boltzmann Law

Mathematically, Stefan Boltzmann’s law for the black body is given by...

Stefan-Boltzmann Constant

Stefan-Boltzmann Constant is the physical constant that is named after Josef Stefan and Ludwig Boltzmann, an Austrian and Dutch physicist respectively. The Stefan-Boltzmann Constant is denoted by the Greek alphabet σ. Stefan-Boltzmann Constant is the proportionality constant in Stefan-Boltzmann law....

Value of Stefan-Boltzmann Constant

The value of Stefan-Boltzmann contact in SI units is approximately 5.67 ×10-8 Watt per square meter per Kelvin to the fourth power and other units and the values in other systems of the unit are given as follows:...

Formula for Stefan-Boltzmann Constant

Other than the Stefan-Boltzmann law, there are some more formulas involving the Stefan-Boltzmann Constant. One such formula can be derived from Planck’s law of radiation i.e., integrating Planck’s Radiation formula, and is given as follows:...

Black Body Radiation

Black Body Radiation is the electromagnetic radiation by the Black Body which is an opaque ideal body that absorbs all the radiation and is also a perfect emitter of radiation i.e., an object that can emit radiation of all the wavelengths depending on the temperature of the surface of the body....

Planck’s Law for Black Body Radiation

Planck’s Law or Planck’s Radiation Law states the relationship between temperature and radiation emitted by the black body and is given as follows:...

Derivation of Stefan-Boltzmann Constant

The formula for the Stefan-Boltzmann constant can be derived from the integral of Plank’s Radiation Law, as integrating Planck’s Radiation Formula gives a similar relation as the Stefan-Boltzmann law. From where we can compare the Stefan-Boltzmann constant in both formulas and formulate the formula for Stefan-Boltzmann Constant. The complete derivation for the same is given as follows:...

Calculation of Stefan-Boltzmann Constant

Using the formula we derived we can calculate the value of the Stefan-Boltzmann constant i.e.,...

Applications of Stefan-Boltzmann Law

In the real world, there are many applications of Stefan-Boltzmann Law. Some of those applications are as follows:...

Sample Problems on Stefan-Boltzmann Law

Problem 1. Calculate the radiation power for a black body of 100 sq. m at a temperature of 200 K....

Stefan-Boltzmann Law – FAQs

What is the Stefan-Boltzmann Law?...