Monday, November 22, 2010

I Tackle Feynman

In my previous blog post I took on Steven Holtzner, the author of Physics Workbook for Dummies. I've found four mistakes now, the earliest being on page 10. When I told my 18 year old son about them, he gave me a bunch of other, better physics books to read, one being Six Easy Pieces by Richard Feynman. This is a series of lectures he did for first and second year college kids at Caltech in 1961-62. These lectures were written down, then carefully edited for publication.

In his obituary, Richard Feynman was described by the New York times as “arguably the most brilliant, iconoclastic and influential of the postwar generation of theoretical physicists.” He won a Nobel prize for his work on quantum electrodynamic theory. Referring to this book, Feynman said “ I tried very hard to make all the statements as accurate as possible.”

So surely there wouldn't be any errors in HIS book.

Yet I found one. On page 7! There he says:

“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 [water] molecules in a whole room ....”

To me that's blatantly wrong. You can SEE steam. In order to see it, there must be a huge number of water molecules in it, thus the statement must be false. So I decided to find out how many molecules of steam there really are in a room.

First of all, what IS steam? Wikipedia says it is water molecules in the air, commonly known as water vapour.

To make things simple, I figured I'd first work out how many grams of water there'd be in a cubic meter of air and work from there. For those who don't know metric, a meter is about a yard, and a gram is about .04 ounces.

Wikipedia says:

If all the water in one cubic meter of air were condensed into a container, the mass of the water in the container could be measured with a scale to determine absolute humidity.... Absolute humidity on a volume basis is the quantity of water in a particular volume of air.

That's exactly what I'm trying to work out.

So, how to you find out what this number is?

Well, it depends on the temperature and the relative humidity of the air, as you can see from this chart.

At the moment, my room is at 21 degrees C and the relative humidity is 68%. Caltech is in Pasadena California, so this would have been normal for them in the first weeks of October 1961 when Feynman would have given this lecture. So, using this chart, making the temperature to be 20 degrees and the humidity to be 70%, you get that the absolute humidity is about 12 g/m3. So in every cubic meter of air in my room there are 12 grams of water.

So how many water molecules are there in a gram of water? Yahoo Answers says:

If you have 1 g of water, you therefore have 1/18 of a mole, or 3.34E22 molecules.

E just means “times ten to the power of” . To make things simple, let's call 10 to the power of 22 a muvillion (a word I made up).

So, you have 3.34 muvillion molecules in a gram of water. But I have 12 grams in a cubic meter of air, so that makes 12 x 3.34 which equals 40.08 muvillion molecules in a cubic meter of air.

Now Feynman said on a previous page that the average [lecture?] room was 40 feet by 40 feet. He didn't say how high the ceiling was, so I'll say it's the height of our ceiling, which is 2.4 meters. 1 Foot = 0.3048 Meters, so 40 feet is 12.192 meters, so the calculations can begin.

12.192 m (length of room) x 12.192 m (width of the room) x 2.4 m (height of the room)= 356.75 cubic meters in a room that size. Now multiply that by the 40.08 muvillion molecules in a cubic meter of air and you have the number of water molecules in a room that size.

The answer comes to 14298.5 muvillion. Written out and rounded off that comes to 143,000,000,000,000,000,000,000,000 steam molecules in that room. That's a heck of a lot more than three!

So what was Feynman thinking? That's my next post.


Physics Workbook for Dummies, by Steven Holtzner, Wiley Publishing Inc 2007

Six Easy Pieces by Richard P Feynman, Penguin Group, Copyright California Institute of Technology 1963,1989,1995 The quote is on Page xxiv.