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Two-phase Heat Capacity

  1. Oct 23, 2009 #1
    Hi,
    I was woindering if anyone can help me on a problem I have been stuck on for a while now.

    I have an equation to combine the heat capcity of oil and water, but I cant find an equation anywhere that combines the heat capacities for water oil and gas.

    All i have is CpL = (qo(qo+qw))Cpo+(1-(qo/(qo+qw))Cpw

    Does anyone know a formula for combing heat capacity of liquids and gases

    Thanks, Howy
     
  2. jcsd
  3. Oct 23, 2009 #2

    Mapes

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    Hi Howy, welcome to PF. This equation should work well for liquid-gas combinations too. It's simply saying the heat capacity contributions are independent and combined according to the (atomic) fraction of each material.
     
  4. Oct 23, 2009 #3
    For a two-phase solution of water and steam, say at 100 degrees C, the heat capacity should include the heat of vaporization.
    Bob S
     
  5. Oct 23, 2009 #4

    Mapes

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    Ah, good catch. I was assuming no phase change (which would apply to oil, water, and air around room temperature). Including a phase change, the heat capacity could be infinite for a solution combining a liquid with its own vapor (at constant pressure), for example. Howy, can you tell us what the gas is?
     
  6. Oct 26, 2009 #5
    Wow,

    Thanks for the hasty reply guys. Probably best to assume the following:

    Water (pure)
    Oil with a SG of 0.88 and a Cp of 1.7585 kj/kg.K
    Gas (natural) with a Sg of 0.7 and a Cp of 5.5265 kj/kg.K
     
    Last edited: Oct 26, 2009
  7. Oct 26, 2009 #6

    Mapes

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    OK, for this particular system at thermal equilibrium, I don't see a problem with calculating the mass of each component and multiplying it by the material's specific heat capacity, and summing the results to estimate the system's heat capacity.
     
  8. Oct 26, 2009 #7
    so do you think the following is acceptable?

    Cp = (qo/qt)Cpo + (qw/qt)Cpw +(qg/qt)Cpg
     
  9. Oct 26, 2009 #8

    Mapes

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    What are the definition and units of the q's?
     
  10. Oct 26, 2009 #9
    qo = quantity of oil being added
    qw = quantity of water being added
    qg = quantity of gas being added
    qt = quantity of mixture

    providing units are all the same i would have thought the units aren't important as it just a ratio
     
  11. Oct 26, 2009 #10

    Mapes

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    OK, thanks for the clarification on definitions. This equation is going to give you a specific heat capacity, which isn't really meaningful, since the system isn't homogeneous. (For example, a sample random kilogram might contain all oil, all water, a mixture also containing some gas, etc.) It would be better to multiply the mass of each component by that material's specific heat capacity, then sum the results to obtain the system heat capacity (in J/K). Does this make sense?
     
  12. Oct 27, 2009 #11
    My understanding is, first work out each phase's mass flow rate

    Wo = (densityofoil*qo)
    Ww = (densityofwate*qw)
    Wg = (densityofgas*qg)
    WTotal = Wo + Ww + Wg



    Then work out the ratio,

    CpTotal = (Wo/WTotal)*Cpo + (Ww/WTotal)*Cpw + (Wg/WTotal)*Cpg
     
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