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Help needed on calculating system pressure during rapid phase transition of CO2

  1. Aug 13, 2011 #1
    Dear Members,
    I am strugling with calculations on rapid phase transition (RPT) of co2 in a high pressure
    vessel. I looked everywhere, from isochoric data to ...you name it but can't get there...

    The question:
    What will the resultant pressure be when solid or liquid co2 in area A contacts with a
    high temperature or vacuum in Area B, while passing supercritical phases?

    Discription of the first problem :

    A closed system with two chambers
    Chamber A: containing liquid CO2 at 25 bar (for example 1 liter volume)
    let's say at metastable temperature

    Chamber B:Volume 50 liter

    What will the resultant pressure be in chamber B when a large valve
    opens and reliefs the content of Chamber A rapidly (0,1 sec1)

    If: temperature in chamber B is 305 K
    350 K
    400 K

    At: Atmospheric pressure
    or: @ -1 bar (not sure how much Tor that is)
    @ -10 bar

    Problem 2:
    How would the data look like when solid CO2 (dry ide) was used instead of liquid CO2?

    Problem 3:
    I am trying to calculate the gas dynamics such as the velocity of the pressurewave.

    Is there anyone who can help me out? I am working with metric value's here, but any
    calc would be wonderful.
    thx so much
    Last edited by a moderator: Sep 26, 2011
  2. jcsd
  3. Aug 14, 2011 #2


    User Avatar

    Energy conservation principle says that the final pressure/temperature cannot depend on how rapidly you perform the process (if the vessel may be considered as thermally insulated). So you may forget about process dynamics.

    The easiest approach is to use energy conservation: at the start you have some liquid/solid CO2 at some temperature, you know its heat capacity and vapourisation/sublimation heat. At the end you have a large vessel containing gas.
    If you need to be precise you should use equation for real gases, as after expansion to the volume only 3 times bigger than solid/liquid fraction, ideal gas is rather coarse approximation.

    I don't understand what you mean by temperature of vessel B: isn't it empty at the start? If it contains air at some pressure and temperature - you must take its energy at the account solving your gas equations.

    Prob.2 - there is no difference between solid and liquid CO2, except, of course, different values of specific heats.
    Last edited: Aug 14, 2011
  4. Aug 14, 2011 #3
    thank you for your reply.
    I agree with you that process dynamics are not connected to eq.of state.
    I didnt understand your "only 3 times bigger than solid liquid fraction", going to look it up now.
    With temp. in vessel B I meant that the walls of the vessel could be heated by
    values high enough to reach and end-temp. as stated. The vessel itself doesnt
    contain air (is evacuated)
    prob.2: Also here I am trying to figure out how the density of dry ice (for example
    the size of particles plays it's part in sublimation rates.

    I'm not far from the right direction but i am beter in mech. engineer than phys. ):
    Trying to understand how to put thermodyn. state functions and learn how to see
    this in relation to process dynamics.

    I am strugling with the answer for weeks now, wld appreciate yr reply
    Last edited by a moderator: Sep 26, 2011
  5. Aug 14, 2011 #4


    User Avatar

    Thats good - you shouldn't understand it, as it was me who misunderstood your original post :frown: I mistakenaly took that your liquid CO2 vessel is 25 litres, while the empty one is 50 litres.

    So the problem gets even simpler now - if your final temperature is known and forced by external source of heating, then you know amount of CO2 (mass => no. of molecules) then you may use ideal gas law to determine pressure.

    They definitely play such role, but I am not brave enough to propose any theoretical model...
  6. Aug 14, 2011 #5
    Thanks again...your right on that, I can follow ideal gas calc's initially.

    I have some of the information complete to make approp. calc's and I realized earlier
    that some of the missing info will have to be validated on a test bench sooner or earlier.

    I have a press available with 1000t closing force and now completing the chambers.
    Did'nt hope to catch the perfect calculator online (: but perhaps there are members
    who read this message and have experience in the field of rapid phase transition.

    I have to work out a model of some sort before I can start testing...don't want to
    see my press passing my bedroom window lol
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