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,
P = Radiated Energy,
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?
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.