Re: [Phys-l] Water vapor condensation

[John Denker <jsd@av8n.com>]

On 07/02/2010 01:58 AM, Savinainen Antti wrote:

> a student of mine is doing a HS project in which she is seeking for a
> correlation between relative humidity and temperature difference of a
> surface and air. 

That doesn't seem like a very good experimental design.

> Her idea is to use a plate that is taken from a
> freezer and measure the mass of water condensed onto the plate within
> a certain time frame. Obviously, among other things, the mass depends
> on the area of the plate.

Superficial analysis:
  
 *) In the proposed scenario, the result will also depend 
on the total heat capacity of the plate, in a weird nonlinear
way:
 -- If you take a very thin plate out of the freezer,
  it will immediately warm up and there will be no
  condensation at all.  The air will dominate the plate.
 -- If you take a very thick plate out of the freezer,
  it will cool off the local air, causing condensation.
  The plate will dominate the air.

 *) Similarly the result will depend (in a weird
nonlinear way) on how much you stir the air.

Deeper analysis:

The twin notions of relative humidity and dew point 
are defined in terms of equilibrium thermodynamics.
At equilibrium, everything is at the same temperature.

In the proposed scenario, you cannot even define
"the" temperature of "the" air or "the" solid,
because the temperature will be varying as a
function of time, and of position throughout the
materials.

If you tried to make this a controlled experiment,
you would need to control for two heat capacities,
two thermal conductivities, convection, other flow,
and who-knows-what else.  I don't recommend it.

> I was wondering whether of not any other properties of the *surface*
> besides the area, temperature difference might affect the condensing.

A hydrophilic surface is thermodynamically different
from a hydrophobic surface.  This directly affects the
energy as you can see by relating the height of the
meniscus to the surface tension.

This affects the first layers of water as they condense,
but has less and less effect after the surface becomes
thickly coated.

This is at least reproducible physics, understandable
in terms of equilibrium thermodynamics, but it is 
still a red herring.  Dew point and relative humidity
are defined in terms water vapor in equilibrium with
the bulk liquid (or solid), not in equilibrium with a 
chemically active solid surface.

  To say the same thing the other way, there is a 
  lot you can learn about a surface by measuring the 
  "adsorption isotherms" but such an experiment is
  probably more advanced and more tricky than what
  the student was looking for.

If you want to understand the basic physics of the
situation, a straightforward measurement of the SVP
(saturated vapor pressure) seems like a more sensible
place to start.