tisdag 19 februari 2013

Radiation of Solid vs Gas

A solid like a glowing lump of iron shows a continuous radiation emission spectrum in accordance with Planck's radiation law, while a gas shows an emission/absorption line spectrum with resonances at specific wave lengths, as illustrated above. What is then the difference between a solid and a gas, which generates different spectra?

The analysis presented on Computational Blackbody Radiation suggests the following answer:  A solid can be modeled as continuous web or string of atoms which by collective vibration can generate a full sequence of harmonics with frequencies  n ranging over the natural numbers n =1,2,3..., with higher frequencies like 10000, 10001, 10002, ... practically generating a continuum.

The acoustic analog is a vibrating guitar string capable of generating all harmonics corresponding to  n =1, 2, 3, ..., because it can macroscopically be viewed as a continuum governed by a wave equation over a continuum of real numbers.

In this perspective a gas would be modeled instead as a finite collection of oscillators, each oscillator with a specific resonance frequency, thus with a discrete line spectrum. The coupling between molecules in solid allowing collective coordinated vibration generating a continuous spectrum, would thus be missing in a gas with the effect that the gas spectrum would be restricted to a discrete set of molecular resonances.

In short: The strong coupling of atoms in a solid allows collective coordinated vibration over a continuum of resonances, while the free flying atoms of a gas can only sustain discrete atomic or molecular resonances. In general the total emissivity of a solid is big and of a gas small.

For perspective, recall in particular the previous post on radiation and radiative heat transfer as a resonance phenomenon rather than an an exchange of energy carrying photons.

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