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Outgassing Units

What are Those Weird Units?

Before reading this, make sure you've read and understand What is Outgassing Rate?

From the arguments in What is Outgassing Rate? you know is that can be expressed in any units that follow the format:

PRESSURE x VOLUME per unit AREA per unit TIME

However, to exercise your inquiring mind, find your copy of John O'Hanlon's “A User's Guide to Vacuum Technology” second edition, look at page 445, and see that outgassing rates are quoted in W/m2. Huh? Say what? Or more correctly, say WATT? Yes, that's right. O'Hanlon quotes outgassing rates in WATTS per SQUARE METER!

How, in the name of James, did watts get into this act? Where's the time needed to claim it's a rate? Where's the quantity of gas? Has Elvis really left the building? No doubt such questions are valid, but wait. With some scientific skill maybe we can make sense of it. Let's start back with an outgassing rate unit mentioned in What is Outgassing Rate? (the one labeled: Pascal x Cubic Meter per Square Meter per Second).

If you remember only one vacuum factoid, it should be that Pascal (the SI pressure measurement unit) is defined as one Newton per Square Meter. Which (remembering “per” means “divided by”) makes the outgassing rate units in (1) above look like this:

        Newton x Cubic Meter
       ——————————                      per Square Meter per Second
              Square Meter

I've separated the expression so we can concentrate on the first bit, where we see Cubic Meters divided by Square Meter. Hmm, doesn't that just equal Meter? Sure does. So we rewrite:

Newton x Meter       per Second per Square Meter

Notice how cunningly “per Square Meter” and “per Second” changed places in the right hand bit? More of that later. For now watch the Newton × Meter part while we do some wizardry. If you apply a force of one Newton for one Meter you are doing one Joule's worth of work. You want proof? See Handbook of Chemistry and Physics under definition of a Joule (page F88 in 67th edition). Now expression (3) above becomes:

Joule per Second       per Square Meter

If you are still paying attention, you noticed that the “per Second” chunk was dragged from the right group to the left, leaving the “per Square Meter”' on the right (since we know O'Hanlon's expression has “per Square Meter” too). From here, it really is only a hop, step, and jump to home base. Under the definition of a Joule, the Handbook of Chemistry and Physic states:

Joule = Watt x Second

That is, if you apply one joule of work to a task, it is the same as applying one watt of power for one second to the same task. From this, fifth grade arithmetic dealing with dividing both side by the same thing, tells us:

Joule per Second = Watt

Going back to expression (4) we find “Joule per Second” there large as life and twice as ugly. Doing what we mathematicians call a substitution, we see that Outgassing is given in SI units as

WATTS per SQUARE METER

Impressed? Truth is I'm much more impressed by O'Hanlon giving me the conversion units that let's me get from his, or anybody else's, quoted outgassing values in Watts/Square Meter to the much more amenable Torr-L/(cm2-sec) by dividing the former value by 1333.2.

So, what does this “watts per square meter” nonsense mean to us vacuumists? Is it something to do with the work that's needed to get the gas off the surface? No! While the watt is a unit of power or rate of doing work, in this case, it's the power available in the gas as it leaves the surface. I'll try to explain.

Imagine a surface with an outgassing rate of 10-3 W/m2. According to results quoted by O'Hanlon, slightly rusted steel that has just been put into a vacuum outgases at this rate. If you (magically) suspended a plastic sheet, one square meter weighing one gram (1/1000 kg), a short distance from the surface and evacuated the far side of the sheet to zero pressure (no atoms or molecules at all!), then after one second the sheet will have moved 100 cm (1 m) away from the surface and be moving at velocity of 100 cm/sec (1 m/sec) and accelerating. The gas atoms and molecules leaving the surface would push the sheet (since there is no corresponding gas pressure on the other side). The work done on the sheet in one second under those conditions is one milliwatt (10-3 watts -- as given in the first line of this paragraph).

Take a more common vacuum material, electropolished stainless steel, that has been in under vacuum for 10 hours. O'Hanlon quotes its outgassing rate as almost 3 × 10-7 W/m2. To move the sheet 100 cm away and with a velocity 100 cm/sec (at that instant) in one second means the sheet cannot weigh more than 0.3 milligrams - the merest gossamer.

Oh, come on! Who am I kidding? We'll accept that a set of European burgers, wrapping themselves in SI's cloak of dignity has dictated that we will use weird units which, by some fluke, equate to watts per square meter. But does this work-on-a-gossamer stuff really mean anything to we vacuistic cognoscenti? Isn't it more the province of the vacuous literati? Truth is, I don't know. I presume it means something to, say, NASA's scientists. I expect they have calculate the effects of the “solar wind“ from sun's “outgassing“ on their large solar panels (if photon radiation pressure doesn't swamp all other effects). Hey Werner, help me out here.

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