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Heat, Steam, and Ambiguity


I wish I could talk with Ötzi; I wish I could ask him what he knew about air. I wonder if he realized that it's a substance. What about steam? Did he sense that, when water turns to vapor, a powerful beast is unleashed?

Ötzi suggests a way in which we can gain a fresh look at the prehistory of steam. You and I live with the motive power of gases and vapor every moment. They propel our automobiles, illuminate our lamps, air-condition our sometimes-feverish world. And yet, try to look at air; is anything really there?

Still, air had already been harnessed in Ötzi's time. He'd probably seen, even ridden in, a boat driven by sails. And we're pretty sure he did his own smelting, since tell-tale traces of arsenic in his hair are a byproduct of smelting.

And to smelt, he needed mechanical means for driving air into a charcoal fire. It may have been a bellows, it may've been nozzles blown by human lungs, or some natural-convection draft arrangement. His fire would not've been hot enough to melt copper without it. Ötzi must've spilled water on the heated stones that formed his smelting furnace. He had to've had some visceral sense of the power in the explosive hissing and white billows that formed as water first boiled, and then condensed.

Did he equate those billows with the clouds, or the fog of early morning? He was less likely to've realized that the billows above boiled water are water droplets, stripped of the gaseous energy they once held. And I'll bet that, at least once, he put his hand into the clear vapor above a boiling pot (not yet condensed into benign droplets) and scalded himself.

For you and me, steam speaks of power, force, energy -- it speaks of both danger and of useful potential. We think we see steam here, yet even we misread the signs. For this is only a cloud of water droplets that condensed, almost immediately, out of the vital but invisible steam leaving a locomotive cylinder. (photo by author)

Let me tell a very old story about a traveler lost in a vast forest on a winter night. He stumbles into the hut of a mysterious woman -- a woman of the forest -- and begs for warmth and sustenance. The woman says, "Yes, of course." She invites him to sit by the fire, and sets about to serve him a steaming bowl of soup. He blows on his hands while she ladles it from the pot. "What are you doing?" she snaps. "Why, my hands are cold. I'm warming them with my breath."

She eyes him suspiciously as she hands him the soup. He blows across the spoon before he puts it in his mouth. "Now what're you doing," she cries, increasingly agitated. He glances up, surprised, and says, politely, "The soup is so wonderfully hot. I simply meant to cool it before I try to swallow it." At that point the woman seizes a stick of firewood and shouts, "Get out! Get out of my house! I'll have no sorcerer who can blow both hot and cold under my roof!"

Perhaps the purpose of the story was to tell children to be consistent. Yet we learn something about consistency when we literally blow hot and cold: Air leaves our body at a little over 98°F. When we come in out of the cold, we open our mouth wide and exhale that warm air upon our hands. We clear our own air passage so the warm air leaves almost unimpeded.

Cooling soup is another matter. Now we purse our lips to block the outflow of air and to increase the pressure of air in our lungs and mouth. That causes what is called an isentropic expansion of the air in our lungs, which we cause by creating this pressure-drop across our lips.

On either side of the expansion nozzle, formed by our mouth, the ratio of the absolute temperature of exiting air to that in our body varies roughly as the one-quarter power of the ratio of atmospheric pressure to that in our lungs. So the air emerges a good deal cooler, depending upon how hard we can blow. More than that, a relatively small pressure drop creates quite a fast-moving jet. However, the jet that crosses the soup spoon is largely room air, drawn in by the jet. While our breath truly is now much cooler, the soup is largely cooled by room air.

Pause and try it. Hold your hands up and blow upon them in both ways. There's no sorcery; we all really do blow hot and cold, and we do it instinctively. Ötzi did so 5300 years ago and even someone who knows all about air entrainment and isentropic expansions, cools his soup without giving conscious thought to the science of it.

Yet we have that story -- it and one like it, about a king who grew frustrated with advisors who kept telling him, "On the other hand..." The king finally shouted to his chamberlain, "Go out and find me a one-armed advisor." I suppose we all carry an "anti-ambiguity gene." An intolerance for ambiguity is stronger in some than in others, but it is always there. And we all like the comfort of a matter that's been settled.

Well, sorting out the substance of gases has been a long and tortuous matter of resolving ambiguities. And that brings us, once more, back to Ötzi.

I am grateful to Stein Kuiper, a Lead Scientist at the Phillips Research Labs in Eindhoven, the Netherlands, for pointing out the dominant role of air entrainment in yielding a cool jet. The dependence of the jet velocity on pressure drop, and the entrainment process, are both too complex to describe here. For the lesser effect – the isentropic cooling – we can write p1/p2 = (T1/T2)(cp/cv - 1)/cp/cv. The pressures p1 and p2 are those in the supply reservoir (1) and the region to which the gas expands (2). T1 and T2 are the related absolute temperatures expressed in degrees Kelvin or Rankine. The terms cp and cv are the specific heats for constant pressure and constant volume in the gas. For air their ratio is 1.405. Such a process is called isentropic because the entropy of the gas remains constant throughout the expansion.