# Stefan Boltzmann Law

## Stefan Boltzmann Law

What is Stefan Boltzmann Law?

The Stefan – Boltzmann Law deals with the black body radiation. It states that the total energy radiated per unit surface area of a black body in unit time is directly proportional to the fourth power of the black body’s thermodynamics temperature.

Formula to find the Stefan Boltzmann Law:

The Stefan Boltzmann Law describes the power radiated a body that absorbs all radiation that falls on its surface in terms on its temperature. The radiation energy per unit time from a black body is proportional to the fourth power of the absolute temperature and can be expresses with Stefan Boltzmann Law as the Stefan Boltzmann Constant.

P = ϵ σ T⁴A; Where,

ϵ = Emissivity of the material,

σ = Stefan – Boltzmann Constant,

T = Absolute Temperature,

A = Area of the emitting body.

Problems on Stefan Boltzmann Law:

A black body has an emissivity of 0.1 and its area is 100m², at 200K. At what rate does it radiate energy?

Solution: Given,

Emissivity (ϵ) = 0.1

Area (A) = 100 m²

Temperature (T) = 200 K

Stefan Boltzmann Constant (σ) = 5.67 x 10⁻⁸ W/ m²K⁴

We know that:

Radiated Energy (P) = ϵ σ T⁴A = 0.1 x 5.67 x 10⁻⁸ W/ m²K⁴ x (200 K)⁴ x 100 m² = 907.2W

∴ Radiated Energy (P) = 907.2W.