StefanBoltzmann Law: How Bodies Radiate Energy Through Their Temperature
Formula
What do the formula symbols mean?
Radiant power
$$ \class{green}{P} $$ Unit $$ \mathrm{W} = \frac{\mathrm J}{\mathrm s} $$Surface area
$$ A $$ Unit $$ \mathrm{m}^2 $$Temperature
$$ \class{red}{T} $$ Unit $$ \mathrm{K} $$StefanBoltzmann constant
$$ \sigma $$Video
Each body, which has a temperature (thus all), radiates energy.

How much energy does our sun radiate and how much of it reaches us on earth?

How much energy does the Earth radiate into space?

What is the surface temperature of our sun?

What energy does your body radiate?
Such and similar questions can be answered by the Stefan Boltzmann law. This law describes the relation between the temperature \( \class{red}{T} \) of a body and its radiant power \( \class{green}{P} \). Also the surface \( A \) of the body influences the radiated power:
Here \( \sigma \) is the Stefan Boltzmann constant with the value \( \sigma = 5.67 \cdot 10^{8} \, \frac{\mathrm J}{\mathrm{m}^2 \, \mathrm{K}^4 \, \mathrm{s}} \). This is a constant that has an exact value that depends only on other physical constants:
~&=~ 5.67 \cdot 10^{8} \, \frac{\mathrm J}{\mathrm{m}^2 \, \mathrm{K}^4 \, \mathrm{s}} \end{align} $$
What is the radiant power \( \class{green}{P} \)? It indicates how much energy per second the surface of the body radiates. The unit of radiant power is W [watts] or J/s [joules per second].
Furthermore, the StefanBoltzmann law applies only to socalled black bodies or bodies that are almost a black body. However, the name black has nothing to do with the color of the body. For example, the sun is an approximately black body, although, as you know, it is not black. A black body absorbs all radiation that hits it. It does not reflect any radiation and does not let any radiation pass.
From the StefanBoltzmann law you can see how strongly the radiated energy depends on the temperature. Doubling the surface temperature of the sun would result in 16 times as much solar energy reaching the earth.