Physics Question #1291

Andy (Dionne) Setlow, a 70 year old male from Madison, Alabama, USA asks on February 26, 2003,

I have long struggled to understand why the temperature of various wavelengths track so closely with magnitude shifts in Kelvin units. For example, 1mm wavelength corresponds to 3K; 100µ = 30K; 10µ = 300K, and so forth. My problem in comprehension appears to be that the Kelvin unit is based on the Centigrade interval, which is based on the rise in temperature of water upon absorption of a specific level of heat. (1 calorie absorbed by 1 gram of water raises its temperature 1ºC .) I suspect it's related to the arbitrary definition of a calorie -- had a calorie been defined at a different level of energy, the association would occur at different (but still repetitive) spectal lines. Can you help?

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The answer

Doug Hube answered on March 14, 2003

Andy Setlow has answered his own question.

The thermal energy of a particle is linearly proportional to the temperature. The energy of a photon is inversely proportional to its wavelength.

In conditions of local thermodynamic equilibrium (LTE) between radiation and matter, the average particle and photon energies are equal. Hence, under the stated LTE condition which is implied by the question, temperature is inversely proportional to wavelength.

More exactly, and except for a small numerical factor, T = (hc/k)/L ... where L represents wavelength, i.e. T = constant/L (h, c and k are universal physical constants)

In the examples given, there is a common factor of 3 in the ratios. That particular value is simply a consequence of the choice of units for temperature and distance. The fundamental inverse relationship between T and L is independent of the units.

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