Re: Density of gas mixture

[John Denker <jsd@MONMOUTH.COM>]

Hi Folks --

John C. has clearly stated the right answer.

Let me take a moment to analyze the *wrong* answer a little bit also.

I haven't made a scientific study of the abnormal psychology of moist air,
but my experiences tend to confirm Alvin's report : the wrong opinion is
widely and often strongly held.

1) Most people have no way of measuring the quantity physicists call
density, so for them the word is an abstract, almost metaphorical concept.
Density may be a metaphor for "resistance" --- in the sense that the
"sticky" summer air "resists" my efforts to run a marathon.

This leads to the question:  who cares about the physical (as opposed to
metaphorical) density?  Answer:  pilots, among others.
  a) If you are flying a balloon, you care quite directly about the
physical density.
  b) For an airplane, you care about the dynamic pressure (1/2 rho V
squared), so when rho goes down, you need a higher V to support the weight
of the airplane.  The higher speed means more runway for takeoff and landing.
  c) For any typical fuel-burning engine, increased humidity leads to
decreased performance.  The effect is even worse than you would predict on
the basis of density alone, because at any given pressure the H2O is
*displacing* the O2.  Consider "air" when the dewpoint gets to 99C;  it is
almost pure water vapor.

2) Consider the psychological rule of thumb: "Learning proceeds from the
known to the unknown".  People support the wrong answer by arguing by
analogy:  when I take a dry sponge and add water to it, the sponge gets
heavier and more dense.  They think that the atmosphere is analogous to a
sponge.  They use this wrong analogy in many ways.  In particular, they use
it to form a wrong model of "relative humidity", by saying that the air can
only "hold" so much moisture.  Fooey!  At any given temperature, a box with
no air in it can "hold" just as much moisture as a box with air in it.

In my experience, until you get people to grok this picture (a box with no
air, just water vapor in equilibrium with a small pool of water at the
bottom) then there is little chance of getting them to accept Dalton's law
of partial pressure.

Read my lips:  it's not a sponge!

Cheers --- jsd



At 06:10 AM 7/20/99 -0400, John Cooper wrote:
> > dry air is actually denser than moist air, contrary to what majority of
> > our clients thought. in one particular session, i encountered a teacher
> > who was quite hard to convince. kindly provide me with a thorough
> > explanation.
>   For a 'perfect' gas mixture, P = (Sum n) RT/V.
>   But Density = (Sum n*FW)/V
>   Since the formula weights of water, N2 and O2 are .018, .028 and .032,
> replacing the latter two with water results in a lower density at
> constant temperature and total pressure.