Returning to Wood’s Experiment to Test Pouillet’s Backradiation Hypothesis & Arrhenius’ Greenhouse Effect’

We may well ask if it is at all possible for backradiation to coexist as a significant process alongside contact transfer. It would certainly seem possible within the limitations of thermal gradients. However, if we revisit the experiment conducted by Robert Wood in 1909, an entirely different picture emerges. Wood constructed two miniature greenhouses identical in all but one respect. One used a plate of halite to transmit light into the interior, while the other used a plate of glass to transmit light into the interior (Wood, 1909). While glass absorbs more than 80% of infrared radiation above 2900nm, halite does not and is regarded as quite transparent to infrared. The point of the experiment was to test whether the halite’s lack of absorption and re-emission of infrared radiation relative to that of glass would have any effect on the temperature of the greenhouse.

Taking Pouillet (1838) and Arrhenius (1906a) into account, we may extend the backradiation hypothesis to this particular situation. In this case, the glass lets through the light of the sun but absorbs 85% of the terrestrial infrared radiation radiation returning to space – at least that emitted above 2900nm. We may suppose that this 85% is of the half of the radiation that is absorbed above 2900nm and is augmented by about 15% of the other half of the outgoing infrared radiation based on the numbers from Nicalau and Maluf (2001). That is a total absorption of 50% of the outgoing radiation. This radiation is subsequently emitted from the glass itself; half radiated outside and half radiated back inside the miniature greenhouse. The amount of radiation reaching the bottom of the greenhouse is equal to that directly received from the sun plus the 25% radiated back by the glass. Although halite is more transmissive than glass in the visible spectrum, this is offset by the fact that halite is much more reflective than glass in the visible spectrum (Lane & Christensen, 1998). The difference in light transmission is less than 5%. Thus in the case of this experiment, the glass greenhouse bottom can be said to have received at least 120% (100-5+25) of the radiation received by the halite greenhouse bottom according to the Arrhenius’ revision of Pouillet’s hypothesis. Thus we expect the temperatures of the respective greenhouses to reflect this significant difference in hypothetical radiation reaching the respective bases.

In Wood’s experiment, the halite greenhouse interior temperature rose to 65ºC or 338ºK (Wood, 1909). Applying the Stefan-Boltzmann equation as shown above, to the relationship between incident radiation and body temperature we may determine from:
Wm = σT4

Wm = 0.000000056704 x 3384
Wm = 740 Wm-2

Now, according to the backradiation hypothesis and the measurable optical properties of glass and halite, this 740 Wm-2 should be supplemented, in the glass greenhouse, by 20% in backradiation from the glass. Thus we may surmise, via Arrhenius’ variation on Pouillet’s backradiation idea, that the radiation at the bottom of the glass greenhouse in the first stage of Wood’s experiment was 888 Wm-2. This predicts the temperature of the glass greenhouse as follows:
T = {Wm/σ}0.25

Given Wm = 888 Wm-2:
T = {888/0.000000056704}0.25 = 353.8ºK = 80.6ºC

As you can see, Arrhenius’ hypothetical backradiation should raise the glass greenhouse temperature 15ºC above the halite greenhouse temperature, in Wood’s experiment. In fact, the first stage of the Wood experiment resulted in the glass greenhouse being slightly cooler than the halite greenhouse. Considering the possibility that this could be due to the fact that the glass filters some of the sun’s radiation that is not filtered by the halite, Wood proceeded to conduct a second stage in his historic experiment. This time, he filtered the radiation entering both greenhouses with a sheet of glass. This had the effect of reducing the internal temperature of the halite greenhouse to 55ºC or 328ºK. Thus the radiation incident on the bottom of the halite greenhouse is as follows:
Wm = σT4

Wm = 0.000000056704 x 3284
Wm = 656 Wm-2

Allowing for additional 20% of backradiation gives us Wm = 788 Wm-2 in the glass greenhouse, predicting:
T = {Wm/σ}0.25

Given Wm = 788 Wm-2:
T = {788/0.000000056704}0.25 = 343.3ºK = 70.2ºC

Once again, the backradiation hypothesis predicts a temperature difference of 15ºC but in this second stage of the Wood experiment no significant difference in temperature was recorded between the glass greenhouse and the halite greenhouse. From the recorded results of the Wood experiment, we can only conclude that the backradiation hypothesis of Arrhenius creates heat ex nihilo, but only in theory.

Article credits to

Leave a Reply