Stefan Boltzmann Law

The Stefan-Boltzmann law states that the total heat radiated per second, per unit surface area, by a black body is directly proportional to the fourth power of its absolute temperature: $E\propto T^4\quad\text{or}\quad E=\sigma T^4,$ where $\sigma=5.67\times10^{-8}\ \text{W m}^{-2}\text{K}^{-4}$ is the Stefan constant. Because of this fourth-power dependence, even a modest rise in absolute temperature produces a dramatic increase in the total radiated power -- doubling an object's absolute temperature multiplies its radiated power by a factor of $2^4=16$ (exactly the scenario worked in Example 8.9, comparing two black bodies A and B). For an imperfect (non-black) emitter, the formula becomes $E=e\sigma T^4$, scaled down by the surface's emissivity $e$. This law is what makes the Sun's surface (about 5700 K) radiate …