On Mon, May 27, 2013 at 4:00 PM, Jed Rothwell <jedrothw...@gmail.com> wrote:
> Joshua Cude <joshua.c...@gmail.com> wrote: > > >> It is positive in that case, but it's not obvious that it's always >> positive, because the way they choose the effective exponent is not given >> quantitatively. The paper does not report trying the same thing at lower >> emissivity like 0.2. >> > > This is an *equation* for crying out loud. Not an experiment. You do not > have to "try" anything. You just plug the number into the equation. The > temperature is inversely proportional to the emissivity number. The close > to zero, the higher the calculated temperature. They have it set to 1 which > gives you the lowest possible calculated temperature. > I think you're mistaken. The emissivity comes in twice. Once when you calculate the temperature from the power, and then again when you calculate the power from the temperature. And it's not inversely proportional; the temperature is proportional to the emissivity to the (-1/4) power, for a given emissive power. So, yes, 1 gives the lowest temperature, but the highest power when you calculate the power from the temperature. You see, that equation gets used twice; once the lower emissivity gives a higher temperature, and once the lower emissivity gives a lower output power. If the power were measured by the camera over the entire spectrum, the result of this would be a complete wash. There would be no effect of emissivity on the resulting power, because of course the camera measures *power*. The reason it's not a wash is because the power is measured in a restricted wavelength range, and to correct for that the camera's software uses an effective value of the exponent on the temperature. This effective value depends on the temperature itself, and since the company literature does not disclose how that exponent is determined, we can't know what power would have resulted if an emissivity of 0.2 had been used. Furthermore, if the emissivity is dependent on wavelength, then the effective exponent is just wrong, because it assumes a grey body. > > > >> And none of this says anything about objects that don't behave like grey >> bodies. >> > > Nothing can produce a lower temperature per unit of emissivity than a > black body. Grey would be better than black, not worse. > > It's not just temperature though. The calculation of the final power also involves emissivity and here a lower emissivity gives a *lower* power. The two compensate, but not exactly because the correction is not known. Yes, grey gives a higher temperature than black, but not necessarily higher power. And furthermore, I'm talking about non-grey bodies, where the emissivity depends on wavelength. In that case, the effective exponent used is just wrong, and it can go either way. They say as much in their literature. > So, in the December experiment, the actual power is very uncertain, and >> not necessarily conservative. It's sloppy work, plain and simple. >> > > It cannot be more conservative than e=1. You do not understand arithmetic. > > > Unfortunately, it's more than arithmetic, and you don't understand why.
