Thursday, November 25, 2010

Feynman: What Was He Thinking?

In his book “Six Easy Pieces" Richard P Feynman said this:

“In figure 1-2 we have a picture of steam. This picture of steam fails in one respect: at ordinary atmospheric pressure there might be only a few molecules in a whole room ....”

Last post I showed how actually, there'd be about 143,000,000,000,000,000,000,000,000 of them in that 40 foot square lecture room.

Feynman was too great a physicist to make an error of that magnitude- so I'm guessing there is some kind of a misunderstanding.

Earlier in the book he said you'd have to increase the size of a drop of water a billion times before you could see the water molecules in it. According to Wiki Answers a water molecule is about .0000000003 m big, so each molecule would be 30 cm. big (about a foot).

So think of a magnifying glass looking at a thousands of dots on a page. With each magnification, the dots are bigger, but you see less of them. Eventually you magnify it so much you can only see a couple of the dots at a time. So maybe that's what he meant.

So what if you shrunk that room so it got smaller and smaller. At half the volume, it would only hold half the molecules, at a quarter it would only hold one quarter of the molecules, so at a billionth volume it would only hold one billionth of the molecules. What you are doing is the same as with the magnifying glass, only in 3 dimensions, not just 2.

So let's divide the number of steam molecules in the room by 1 American billion. To do this you'd take the 143,000,000,000,000,000,000,000,000 and knock off 9 zeroes from the end. But that's just shrinking it down a billion times lengthwise. You also want to shrink it down 1 billionth of its height and 1 billionth of its width. So move the decimal point another 18 places to the left. Doing that you get .143 molecules in that room. Put another way, you'd only have a molecule in there about 1/6 of the time.

So it still doesn't agree with Feynman. Of course I might have got the height of the ceiling in the lecture room wrong, so let's double it. That's .286 molecules.

Maybe he meant that when the air is fully saturated. Wikipedia says that the most you can get is 30 grams of water in a square meter of air. I was calculating it with 12. Two and a half times 12 is 30 so let's multiply the number of molecules in the shrunken room by two and a half.

You get .715 molecules. Meaning you'd get a molecule in there about 70% of the time. It's still not what Feynman said. So I think he got it wrong. My husband who understands physics very well (and has an Honours degree in Mathematics) agrees with me.
Six Easy Pieces by Richard P Feynman, Penguin Goup, Copyright California Istitute of Technology 1963,1989,1995 Quote is on page 7.