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Mass of solid water and gaseous water?

  1. Jan 31, 2007 #1
    1. The problem statement, all variables and given/known data
    a 1kg of Water at 25 degrees celsius is in a container. A solid block of 1kg Carbon Dioxide at its sublimation temp of -80 degrees celcious is placed into the container, with the lid then closed.
    Final temperature of entire system = 0 degrees celcius
    Final phase of the Carbon Dioxide is gas

    *What is the final mass of the liquid H20, solid H20, and gaseous H20?

    2. Relevant equations
    Heat of Vap of Water = 2000 kj/kg
    Heat of Melt of Water = 300 kj/kg
    Csp of Water = 4 kj/kg
    Csp of CO2 gas = 1 kj/kg
    Heat of Sub of CO2 = 200 kj/kg

    [delta]Ethermal = mc[delta]T
    [delta]Ebond = ([delta]m)([delta]Heat of...)

    3. The attempt at a solution
    From what I understand, the H20's conditions change as follows:
    Temp Initial = 25 degrees celcius
    Temp Final = 0 degrees celcious
    Phase Initial = Liquid
    Phase Final = Solid

    Thus, the H20 will have its thermal energy increasing and its bond energy increasing as well.

    As for the CO2's conditions:
    Temp Initial = -80 degrees celcius
    Temp Final = 0 degrees celcius
    Phase Intial = Solid
    Phase Final = Gas

    Since it is at it's sublimation temperature, it will skip over its intermediate state as a liquid and its thermal energy is increasing and its bond energy decreasing.

    So, to find the final mass of the liquid water, do I just use:
    [delta]Ethermal = Q
    mc[delta]t = Q
    (1kg)(4kj/kg K)(0celcius-25celcius) = Q
    -100 kj = Q

    [delta]m = Q/[delta]Heat of...
    [delta]m = -100/300 kg/kg <-- do I use Heat of melting for the liquid phase?

    What should be the next step I take in finding the mass of solid water and gaseous water?
  2. jcsd
  3. Jan 31, 2007 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Assume that a portion of the H2O is in the form of liquid. Work out an algebraic formula for the heat flow in terms of the quantity of liquid and solid H2O. You know that they sum to 1 kg. Use the specific heat of liquid water for the entire mass of H2O but use the specific heat of fusion only for the portion that ends up as ice.

    Last edited: Jan 31, 2007
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