# Stefan Boltzmann Law

## What is Stefan Boltzmann Law?

According to Stefan Boltzmann Law, the total radiant heat energy that is emitted by a surface is proportional to fourth power of its absolute temperature. The same law was derived by Austrian physicist Ludwig Boltzmann in 1884 based on thermodynamic considerations which state: if E denotes radiant heat energy to be emitted by a unit area in one second and T denotes absolute temperature (in Kelvin), then E=σT4 . The Stefan’s law is applicable only to black bodies and theoretical surfaces that absorb the incident heat radiation.

For hot objects apart from ideal radiators, the law is described in the following manner.

 PA=eσT4

Here,

E indicates the object’s emissivity which is 1 for an ideal radiator

If the hot body radiates energy to cooler objects at temperature Tc, the rate of net radiation loss is of the form,

 P=eσA(T4−T4c)

Where,

The constant of proportionality σ is called the Stefan Boltzmann constant and has a value of σ=5.6704×10−8 watt per metre 2.K4

E is emissivity shows radiating area

Tc is surrounding temperature

The actual law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time is directly proportional to the fourth power of the black body’s temperature. The expression for this is;

j=σT4 : For a Black Body

j=ϵσT4 : For Real bodies with emissivity < 1

Thermal radiation is the transfer of energy by emitting electromagnetic waves that carry energy away from the emitting body. The radiation lies in the infrared region of the electromagnetic spectrum. The relevance that governs net radiation from hot bodies is known as Stefan-Boltzmann law.

If the surrounding is at higher i.e, Tc > T, you obtain a negative value which implies net radiative transfer to the object.

Stefan Boltzmann Law has been used to accurately find the temperature of several celestial bodies like the Sun, the Earth and the Stars.

• Sun: Stefan used a thin metal plate to approximate the energy received and radiated by the Earth. Assuming that the sun is a black body, Stefan was successfully able to incorporate Earth’s received radiation into his calculation. Stefan calculated the temperature to be 5700 K which is very close to the modern value of 5778K. In contrast, the values then were ranging from 1800∘C to as high as 13000000∘C.
• Stars: By using the Luminosity of a star, its surface temperature could be found. The stars in this case are treated as Black Bodies. Using this not only can the temperature be found, but also the radii of very distant stars.
• Earth: Stefan calculated the temperature of the Earth by using the energy received from the sun and energy radiated by the Earth. He unfortunately failed to account for the reflection of a part of the received radiation, greenhouse effect and thereby was not able to calculate the temperature of the Earth with considerable accuracy. He calculated the average temperature of the Earth as 6∘C On including such effects we come upon the correct answer of 15∘C.