Did somebody say this is an obvious but yet unmentioned connection: the Planck box of radiation and the Schrodinger box with a cat in it? Well nobody has mentioned it to me yet. I thought of it yesterday after editing my previous post. A cat in a closed box is a source of thermal radiation, the average body temperature of cats being about 101.5 Fahrenheit. The box would have to be insulated so the walls don't radiate away the heat and it just bounces around as thermal radiation inside the box. That's the necessary condition of the Planck box of radiation anyway.
This idea might lead somewhere if the cat is idealized to be a hot body composed of electromagnetic harmonic oscillators: an ideal, thermal, macroscopic solid. Planck's analysis was for a box containing nothing but thermal radiation. Einstein's analysis in 1916-17 put atoms inside the box, so it was not just the walls of the box producing the radiation but also an enclosed gas of particles with two energy levels that emitted and absorbed radiation. Einstein derived in a simpler way the expression that Planck found in 1900, plus he predicted the existence of stimulated emission of light from an atom, which became the basis for the laser many years later.
So, first "nothing" in the box (Planck), then a gas of atoms (Einstein), and now a cat! The cat consists of atoms in an amorphous solid state. Well, now that I think about it, it's not all that exciting, sorry. The effect is just to change the shape of the box which itself is a hollowed-out solid. The Planck thermal spectrum and its derivation are independent of the shape of the box.
The question of entropy is something to keep thinking about though. Actually, it was the entropy of the box of radiation that Planck calculated, while Lord Rayleigh and others were trying to calculate the energy spectrum directly. Planck calculated the energy spectrum by calculating entropy then using the thermodynamic relation between energy and entropy to find the average energy, then in the last step he derived the energy spectrum of box of thermal radiation.
And I'll just mention one source of black-body or thermal radiation that seems pretty nearly ideal and also unpleasant and menacing under the midday August sun: the new asphalt paving I've driven on in several places around Pine Bluff recently. Some hellacious heat absorption and emission going on there!
But! the iron manhole covers are even better heat absorbers and radiators than black asphalt. In fact, the emissivity of asphalt is only 0.88. This is a number between zero and one that is the ratio of the thermal radiation the material is emitting at a particular temperature to the thermal radiation an ideal black-body would emit. See the table of emissivities and the infrared photo of the cube with sides made of different materials at the Wikipedia entry on emissivity. Iron isn't listed but some other substances with surprising values of emissivity higher than asphalt are listed.
Finally, different materials at the same temperature will feel hotter or colder when you touch them--even though they are at the same temp!--because of their different thermal conduction properties. The iron manhole cover under direct sun in the summer will feel hotter and thus burn you quicker than the asphalt next to it. The thermal conductivity of iron is about 100 times that of asphalt.
The question of entropy is something to keep thinking about though. Actually, it was the entropy of the box of radiation that Planck calculated, while Lord Rayleigh and others were trying to calculate the energy spectrum directly. Planck calculated the energy spectrum by calculating entropy then using the thermodynamic relation between energy and entropy to find the average energy, then in the last step he derived the energy spectrum of box of thermal radiation.
And I'll just mention one source of black-body or thermal radiation that seems pretty nearly ideal and also unpleasant and menacing under the midday August sun: the new asphalt paving I've driven on in several places around Pine Bluff recently. Some hellacious heat absorption and emission going on there!
But! the iron manhole covers are even better heat absorbers and radiators than black asphalt. In fact, the emissivity of asphalt is only 0.88. This is a number between zero and one that is the ratio of the thermal radiation the material is emitting at a particular temperature to the thermal radiation an ideal black-body would emit. See the table of emissivities and the infrared photo of the cube with sides made of different materials at the Wikipedia entry on emissivity. Iron isn't listed but some other substances with surprising values of emissivity higher than asphalt are listed.
Finally, different materials at the same temperature will feel hotter or colder when you touch them--even though they are at the same temp!--because of their different thermal conduction properties. The iron manhole cover under direct sun in the summer will feel hotter and thus burn you quicker than the asphalt next to it. The thermal conductivity of iron is about 100 times that of asphalt.
