Day 130 - Temperature of nothing

Sorry if this post is too meteorological or technical, but there's another philosophical question that I can't get out of my mind: If the energy budget of a surface is balanced (i.e., the energy going into the surface is equal to the energy leaving the surface), how can any net heating or cooling of the surface occur?

It's easy to understand why if the "surface" is defined as a layer with a finite volume and mass. In this case, if the energy input and outgoing fluxes balance each other, no change in temperature change occurs. But in a finite non-zero volume, the energy input and surface fluxes don't have to balance each other. The energy budget is closed by net heating or cooling of the volume. No problem so far.

But it's also possible (and is commonly done, for example in model I've been modifying) to define the surface as an infinitesimally thin (i.e., zero mass and volume) interface. In that case, the net energy input to the surface must always equal the fluxes of energy leaving the surface. But if that is true, no heating or cooling can occur.

This contradicts what we know from observations -- that a surface temperature can change regardless of whether it's defined as a volume or an interface.

If we calculate (by integration) the average rate of temperature change over the depth of the volumeless layer, the equation reduces to 0 divided by 0. Just try doing that on a calculator, hehe. It's not necessarily 0, 1, or infinity. But in this case, could it be a finite non-zero number that's equal to the rate of change in the surface temperature?

I think the key might be in the fact that something with no mass or dimension can't have a temperature, much less a temperature change. It is in fact, by definition, nothing.

posted by Matt @ 11:41 PM