The fog in the mirror is the condensation of water
vapor as it touches a colder surface. By running
cold water you just cool down the bath tub and
everything around it. Now the vapor coming from
the hot shower will mostly condense right there
and will not reach the mirror.
At the same
time, the mirror is heated by hot dry air, and
then the condensation of water vapor becomes less
likely on the warmer surface.
containing a certain amount of water vapor
(moisture), there is a maximum temperature at
which the water will condense. This is called the
dew point. For example, our breath condenses in a
fog when the external temperature is below the dew
point corresponding to the concentration of water
in the gas we exhale. If the temperature is above
that dew point, no fog will form.
Fogging means that steam condensed on the
mirror.Steam can condense on any cold" surface,
but on a mirror we can see the result. Clearly,
for fogging to occur, the steam, originating at
the shower spray, must reach the mirror. Also it
should be quite clear that steam (a gas) has to
"travel" through the air to reach the mirror
location. When you turn the cold water on first,
and leave it for some time, you cool the air in
the bathroom, some. The process of steam
generation, its transport away from the water
spray, and possible recondensation in tiny
(aerosol) droplets while it is being transported
by, and through, the surrounding air is very
complex, but crudely put, steam cannot go too far
when the surrounding air is relatively cool.
Thus, no fogging if we pre-cool the air by turning
the cold water on first.
However, even in
cool air, the water will vaporize and will tend to
heat up the surrounding air as it condenses in it.
Since the air is easy to heat, we would expect
that the effect of pre-cooling is short lived, and
only a matter of time before the mirror fogs
So, we can now see that the statement
"the mirror wouldn't fog" is incorrect. Fogging
will occur sooner or later, and the delay will
depend on the size of the room, whether it is
vented or not; the location of the mirror; the
temperature of cold and hot water; and, yes, even
the intensity and configuration of the
I will suggest that you repeat the
experiment with a closed-off bathroom, keeping
everything the same, including the hot and cold
water temperatures, and the water flow turned in
the fully "on" position. First, measure the time
for the first fog to appear with hot water
running. Then, let the room cool, the mirror to
clear (do not wipe off), and run the experiment
with cold water first on for some specified length
of time, followed by hot water. Again, measure
the time it took from the moment you turned on the
hot water, till you saw the first fog on the
mirror. This should be a little longer than the
in hot-water-only experiment. Further, this delay
should grow bigger as the time of the cold water
period is increased, or as the hot water
temperature is decreased.
As always in
experimentation, we should have repeat tests to
make sure the effects we measure are significant
and not the result of errors.
I would be
interested to know how all this worked
Actually, it is a very interesting
question and provides opportunity to discuss many
important things, including proper use and control
of experiments towards reaching conclusions.
Also, one can discuss the concepts of steady state
(mirror doesn't fog) vs. transient response
(mirror does not fog for some length of time).
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