# 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 T^{4} 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 m^{2}, at 500K. At what rate does it radiate energy?

Answer: The energy radiated is given by the formula:

P = є σ T^{4} A

P = 0.1*5.67*10^{(-8)} W/(m^{2} K^{4})* (500 K)^{4} * 200 m^{2}

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 r^{2} = 4 π (0.03m)^{2} = 0.011 m^{2}.

The energy radiated is given by the formula:

P = є σ T^{4} A

P = 0.5*5.67*10^{(-8)} W/(m^{2} K^{4})* (5273 K)^{4} * 0.011 m^{2}

P = 2.4*10^{(5)} W

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