Temperature in Vacuum Insulation

if there is double walled chamber where the gap between inner and outer chamber is vacuum and inside box temperature is 77k and outer temperature is 300k then what will be the temperature in the vacuum area?
- c p bhagyanath (age 23)
punjab,india

That's a nice question. Let me answer on the assumption that the walls are perfect absorbers-emitters, just for simplicity. In a real thermos bottle or dewar they would actually be silvered to make them very poor absorber-emitters.

 It turns out that the intermediate space doesn't have a definite temperature. Any definite temperature implies a particular spectrum of how much radiation energy there is in each frequency range. In this case the radiation spectrum is a mix of 77K and 300K spectra. If you were to pick a temperature based on the radiation at one frequency you'd get a different temperature than what you'd calculate based on the radiation at another frequency. The average energy density, however, does correspond to that of an intermediate temperature, ((77⁴+300⁴)/2)^1/4 K or about 253 K. The mix of different frequencies will not match a true 253 K spectrum, however.

Mike W.

(published on 03/30/2015)