Wednesday, May 1, 2013

The Surface Area - Volume Paradox

Even simple surfaces can display surprisingly counterintuitive properties.
Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, (1st edition), p. 1763

It was while conducting research on the job of the "thinking about thinking" project that carried the Oracle of Ottawa to You Tube to observe a large number of videos on HHO production. As mentioned in earlier posts the Oracle marveled at the utter imagination and craft of the various home experimenters and builders, in their search of the most efficient machine to produce hydrogen and oxygen gas.

Gabriel's Horn - Finite volume - Infinite surface area...

Of all the time the Oracle spent in schools various, the one chemistry demonstration that I clearly remember is the one in grade 7 or 8 when the science teacher actually took the trouble to demonstrate the electrical decomposition of water. Using two test tubes and a dry cell lantern battery the teacher soon had a nice pile of hydrogen and oxygen gas in their respective tubes. After demonstrating to us visually that the chemistry text was indeed correct, in that, there was indeed twice as much hydrogen as oxygen we were asked to possibly put forward an explanation. The Oracle of Ottawa proposed simply that the oxygen atoms had much better union representation than the hydrogen atoms! Which earned a hearty laugh from the class.

The teacher than explained to use the correct answer; for every unit of water there must be two hydrogen atoms bonded to one oxygen atom, because our Maker had engineered it that way. (of course this was a Catholic school....) Then he asked what would happen if the two gases were combined in the presence of a spark or open flame? Of course the Oracle of Ottawa at that time had no idea. So the teacher got two volunteers from the class. One had the hydrogen and another the oxygen test tube. A smoldering wick was lit. The tubes were turned slowly over and the hydrogen and oxygen escaped perfectly in unison to the open spark. KA - BOOM !! There was a white flame with a cherry pink edge and the cloud of mist was perfectly white! I can remember it all like yesterday. There is a shit load of energy, in hiding, in water.

 Now ponder this Dear Reader; You have a plate that measures 10 units by 10 units with a thickness of say 2 units. Calculate the volume, now calculate the exposed surface area in square units. Now cut the plate in half. Calculate the volume and the exposed surface area. Continue. In the words of William Shatner; how weird is that? The total surface area continues to increase, yet the total volume remains the same!

Now ponder this. You take a 1 cm.stainless steel rod, 10 cm. long to use as an electrode in your HHO machine or water decomposition experiment. Weigh the electrode, and then calculate the surface area. Now run you device and time how long it takes to generate say 10 ml. of hydrogen gas. Now substitute a stainless steel scouring pad for your honking stainless steel rod. Which electrode will generate more gas? What is the surface area of the scouring pad? What is the weight of the scouring pad compared to the honking rod?

Could it be Dear Reader that it is not about honking massy plates or about the amount of current, but rather the whole thing depends on exposed surface area? Feel free to let the Oracle of Ottawa know how that all works out for you.... Then ponder porous iron granules... 

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