Atmosphere 1: Shiny Hot Objects

We have to start, for this, looking at shiny hot objects (which is how I’ll refer to, hm, thermodynamics).

Most people who were born before The Matrix Reloaded probably remembers incandescence lamps. For anyone else, I’ll try to describe: they were like normal lamps but 98% less sophisticated, they were filled with a vacuum (well, emptied with a vacuum) and contained a solitary tungsten filament (a bit of metal) that would become enormously hot.

As a consequence of being hot, they would emit visible light. As it turns out, this isn’t a property of lamps: every single object has a temperature and, as a consequence, shines. It doesn’t need to be super hot: you, gorge, have a body temperature of roughly 310 K and shine infrared light (unless your temperature is roughly 462 K, in which case I rejoice that one of our Venus-based overlords is reading my blog).

In case you want to see a formula, here it is:

$P = A \cdot \sigma \cdot T^4$

We call this the Stefan-Boltzmann Law and looks a bit complex. Let’s demystify it.

• $P$: how much energy it emits per second.
• $T$: how warm it is.
• $\sigma$: a constant. Consider it just a number that we have to put in to make the maths work.
• $A$: the surface area of our shiny hot object.

Do you want to know how much energy is being emitted? It’s a function of the temperature. The hotter, the more energy.

I would be remiss if I didn’t mention the thingie that is the cause for almost all heat on our planet: it’s the Sun. It’s really hot, it’s really shiny, and it keeps emitting energy (under the form of light) that we, though so far away, can use for our own purpose.

As a matter of fact, once you put in all the correct numbers and some scaling, the Earth receives a power of 341.3 W/m$^2$. That is, each square meter receives 341.3 joule per second of energy. It’s roughly the energy needed to warm up a kilogram of copper by one degree per second.

I’ll call this number $\Phi_\text{Sun}$ = 340 W/m$^2$.

So far, so simple. So, what’s the catch?