The Rabett writes:

Universitaets Prof. i.R. Dr. Jürgen U. Keller (another one gone emeritus)
Universität Siegen
FB11-Maschinenbau
Institut für Fluid- und Thermodynamik
Paul-Bonatz-Str. 9-11
57072 Siegen (Spent a year there one night)

Dear Prof. Keller,

Recently some (resident fireflies) have brought to our attention (tried to shove down our throats is more like it) a paper by Essex (clueless about climate), McKitrick (an economist who can't tell the difference between degrees and radians and gets off on odd interpolations) and Andresen (who happens to be on your editorial board, something we recommend you change right quick) that appeared in the February issue of the Journal of Non-Equilibrium Thermodynamics (the manga edition. Please include more nude scientists for the ladies), entitled "Does a Global Temperature Exist?" (floated a real air biscuit there Jürgen)

After a careful reading (two days later we were able to stop laughing long enough to take pen in hand) it is our considered opinion (even the damn mice cracked up) that arguments advanced (couldn't float a chickenwire canoe on a dry lake) are either irrelevant or incorrect (be kind, be kind...). While others will be writing (to the IgNobel Prize Committee, although the competition in category is strong) about technical matters (did ANYONE stay awake through the seminar?) we restrict ourselves here to basic issues (which establish that you should be convicted of criminal electron waste, there being no paper edition of your fishwrap).

The paper tries (and fails miserably) on all points. You are referred first (clearly if you had read the thing you would have circular filed it) to 3.1.2 where EMA attempt (and do a cannonball splatter) to show the results of averaging the temperature when a glass of ice water@ 2 oC and a cup of coffee at 33 oC cool separately in a 20 oC room. (proportional to T^4 following the Stefan-Boltzmann law). They claim to plot the predictions of the arithmetic average, the harmonic, the RMS and what they call radiation (proportional to T^4 following the Stefan-Boltzmann law). I have also shown the temperatures of the coffee and the ice waterThe only one they get right is the arithmetic average (see below).

Essex and McKitrick then riff about how the radiation curve is higher than the RMS, and the arithmetic average, and the harmonic is lower



Unfortunately, (a shooting foul in thermo) the authors (silly bunnies) fail to use the appropriate temperature scale. Thermodynamics demands the use of the Kelvin temperature scale (students fail for not doing this). To make their point, the authors (very silly bunnies) use Celsius. To assert that radiative emission is proportional to the fourth power of the temperature in Celsius, (is a clusterfuck of the order of invading Iraq to deal with 9/11 and) is a spectacular error (world class in a Journal claiming to be about thermodynamics), but the authors make it (shows what happens when a math and an eco guy get together at the faculty bar and write a paper). In a few cases, one can use Celsius to calculate thermodynamic quantities, an average temperature being one, this is only the case when the function varies linearly with temperature, and even there, not always. For example, the average energy of an ideal gas is 3/2 nRT where T must be in Kelvin.

The dotted brown line next to the arithmetic average shows the result for the "radiation" average if Kelvin is used (makes you kind of want to zot the paper Juergen?). As a matter of fact, if one uses Kelvin for all the other averages


the differences by which the authors set great store vanish.

Is there anything that sets the arithmetic average apart? (Why yes, happy that you asked.) If you had first equilibrated the ice water and the coffee, and then let them warm up to room temperature you would get the blue dots which overlay the arithmetic average. That is a fine physical reason for preferring the arithmetic average. Then, the energy of the liquids pretty much depends on mCT, where m is the mass, C the specific heat and T the absolute temperature (true C(T) has a weak dependence on T, but the difference is small).

More tomorrow, Eli must resnark.....