The Freezing Point And The Dew Point

http://math.nyu.edu/~gladish/teaching/eao/water-phase-diagram.jpg

Fresh water freezes at 0ºC on the surface of the earth (mp on the diagram.) It doesn’t matter if you are in Arizona or Ireland.  It doesn’t matter what the partial pressure of water is in the air (i.e humidity.) The freezing point is unchanged.

Yet we know that there is still vapour in the air at minus 10ºC. How can this be? The phase diagram shows no vapour at mp, and certainly not to the left of mp.

The reason we have vapour in the air is because some of the molecules of frozen water are constantly being raised to higher energy states through collisions with photons, and collisions with other molecules.

The temperature can be well below 0ºC, and yet there is no frost on the car. That is because there are just as many molecules being sublimated as there are being frozen. Thus there is no net buildup of ice.

Now suppose the humidity increases, or the temperature decreases to a point where more water molecules are freezing out of the air than are being sublimated. Then we start to see accumulation of frost. That is called the dew point.

If you are clever, I think you will see where I am taking this discussion.

About stevengoddard

Just having fun
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9 Responses to The Freezing Point And The Dew Point

  1. Ric Werme says:

    Now suppose the humidity increases, or the temperature decreases to a point where more water molecules are freezing out of the air than are being sublimated. Then we start to see accumulation of frost. That is called the dew point.

    More precisely, it’s called the frost point. The frost point doesn’t exist above freezing, both exist for a ways below freezing. The dew point is used in meteorlogy because clouds often have supercooled droplets of water. The frost point for some temperature is a bit warmer – this fall look on your windshield for a clear line between frost and dew – the dew is probably supercooled but the frost has reduced the relative humidity (as far as the dew is concerned) and is evaporating.

    I’m going to write up an article for the Davis weather newsletter, maybe this weekend, I’ll let you know.

    I plot dewpoint and frostpoint at http://home.comcast.net/~ewerme/wx/current.htm currently the dewpoint is 50°F, so no frostpoint today.

    If you want to play with some of the math, there are far too many choices at http://cires.colorado.edu/~voemel/vp.pro . In my Python code, I settled on the following, excuse the ugly inline fahrenheit conversion:

    # Convert temperature (F) and relative humidity (%) into dewpoint (F).
    # It’s easier to just use the Celcius equation and convert between scales
    # than deriving Fahrenheit equations.
    # To do: experiment with dewpoint over ice equation.
    # Sources the original buck equation from
    # http://cires.colorado.edu/~voemel/vp.pro (program of many equations)
    def dew_point(temp, humidity):
    tc = (temp – 32) * 5.0 / 9.0
    e = humidity / 100.0 * 0.61121 * exp(17.502 * tc / (tc + 240.97))
    le = log(e / 0.61121)
    return 1.8 * ((240.97 * le) / (17.502 – le)) + 32.0

    def frost_point(temp, humidity):
    tc = (temp – 32) * 5.0 / 9.0
    e = humidity / 100.0 * 0.61121 * exp(17.502 * tc / (tc + 240.97))
    # e = humidity / 100.0 * 0.6115 * exp(22.452 * tc / (tc + 272.55))
    le = log(e / 0.6115)
    return 1.8 * ((272.55 * le) / (22.452 – le)) + 32.0

  2. Matt says:

    Steve:
    You really need to take a review thermodynamics course. Or at least understand that phase diagrams refer to an equilibrium state (and understand what ‘equilibrium state’ means).

    Maybe this will help: you have a pot filled with room temperature water on a hotpad which being heated to 120ºC. If you leave the pot on the hotpad for 1 hour (i.e. until the system reaches thermodynamic equilibrium), what phase has all the water become?

    • Matt,

      LOL. Last week I was pointing out on WUWT that phase diagrams refer to an equilibrium state in a closed system, and it started an uproar.

      But you don’t give enough information. In a closed system (essential for a phase diagram to work properly) you will have a mixture of liquid and gas, because the water vapour will saturate and condense.

      It would be easier to talk to you if you left the accusations out of your comments.

      • Matt says:

        Steve:
        Sorry about the accusations and fair enough.

        And yes, regarding my example, you are correct… I didn’t give any information about the temperature of the room, so assuming the room is at room temperature, there may be condensed water vapor around.

        But I think we’re saying the same thing. The information on the phase diagram refers to a system in thermodynamic equilibrium (i.e. a closed system). Therefore, a precisely defined concept such as the triple point is relatively meaningless in the real-world. So saying water at the arctic is at the triple point because all three phases exist is not correct. The arctic is not at thermodynamic equilibrium so it is entirely possible for all three phases to exist without having to apply a special term.

      • Matt,

        I am half scientist and half engineer. Engineers are practical people. so the presence of all three phases is close enough for me. ;^)

  3. Matt says:

    Yeah, I’m the same way with cars, anything with 4 wheels, a couple doors and an engine is a Porsche 😉 Makes car shopping so much easier 😛

    • The joke goes :

      A boy is ten feet away from a girl. He walks half way towards her. And again. He keeps repeating that. Does he ever reach her?

      Scientist says : No
      Engineer says : Yes, he gets close enough ;^)

  4. Matt says:

    Nice, reminds me of this (one of many variations):

    From http://obeythemew.livejournal.com/6659.html:
    A physicist, an engineer, and a psychologist are called in as consultants to a dairy farm whose production has been below par. Each is given time to inspect the details of the operation before making a report.

    The first to be called is the engineer, who states: “The size of the stalls for the cattle should be decreased. Efficiency could be improved if the cows were more closely packed, with a net allotment of 275 cubic feet per cow. Also, the diameter of the milking tubes should be increased by 4 percent to allow for a greater average flow rate during the milking periods”.

    The next to report is the psychologist, who proposes: “The inside of the barn should be painted green. This is a more mellow color [sp] than brown and should help induce greater milk flow. Also, more trees should be planted in the fields to add diversity to the scenery for the cattle during grazing, to reduce boredom”.

    Finally, the physicist is called upon. He asks for a blackboard and then draws a circle. He begins: “Assume the cow is a sphere in a perfect vacuum….”.

    On a side note, I’m selling a brand new Porsche if anyone wants it – only $35,000 😉

  5. Pingback: The Freezing Point And The Dew Point Part 2 | Real Science

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