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When I take a hot shower the mirror fogs up. I was told to run cold water in the shower first and then when I got in to turn the hot water up and the mirror wouldn't fog. This proved to be true. I do not understand - why does cold water makes the difference?
Answer 1:

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.

For air 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.


Answer 2:

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 over.

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 sprays.

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 out.

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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