Stephan-Boltzmann Law Formula

The Stephan-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 expressed with Stefan-Boltzmann Law as: The Stefan-Boltzmann Constant.

Radiate energy = (Emissivity) * (Stefan-Boltzmann constant) * (Temperature)⁴ * (Area)

The equation is:

P = є σ T⁴ A

P: Radiate energy

σ: The Stefan-Boltzmann Constant

T: absolute temperature in Kelvin

є: Emissivity of the material.

A: Area of the emitting body

Stephan-Boltzmann Formula Questions:

1) A black body has an emissivity of 0.1 and its area is 200 m², at 500K. At what rate does it radiate energy?

Answer: The energy radiated is given by the formula:

P = є σ T⁴ A

P = 0.1*5.67*10^(-8) W/(m² K⁴)* (500 K)⁴ * 200 m²

P = 7.08*10⁽⁴⁾ W

2) A metal ball of 3 cm in radius is heated in to 5000°C, if its emissivity is 0.5, at what rate does it radiate energy?

Answer: The temperature in kelvin is (5000°C + 273°C) K/°C = 5273 K.

The surface of the sphere is 4 π r² = 4 π (0.03m)² = 0.011 m².

The energy radiated is given by the formula:

P = є σ T⁴ A

P = 0.5*5.67*10^(-8) W/(m² K⁴)* (5273 K)⁴ * 0.011 m²

P = 2.4*10⁽⁵⁾ W