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

• ironic
In summary, the pressure in the vessel will be higher when the solid CO2 is used instead of liquid CO2.
ironic
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:
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:
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
thanks

Last edited by a moderator:
ironic said:
I didnt understand your "only 3 times bigger than solid liquid fraction",
Thats good - you shouldn't understand it, as it was me who misunderstood your original post I mistakenaly took that your liquid CO2 vessel is 25 litres, while the empty one is 50 litres.

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.
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.

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.
They definitely play such role, but I am not brave enough to propose any theoretical model...

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

## 1. What is CO2 and why is it important to calculate system pressure during rapid phase transition?

CO2, or carbon dioxide, is a colorless and odorless gas that is a naturally occurring component of Earth's atmosphere. It is also a greenhouse gas that contributes to climate change. The rapid phase transition of CO2 refers to the process of converting from a gas to a liquid state under certain conditions, such as high pressure and low temperature. It is important to calculate system pressure during this transition because it can affect the efficiency and safety of various systems that use CO2.

## 2. How is the system pressure during rapid phase transition of CO2 calculated?

The system pressure during rapid phase transition of CO2 can be calculated using the Clausius-Clapeyron equation, which relates the pressure and temperature of a substance during a phase transition. This equation takes into account the specific heat capacity, latent heat of vaporization, and change in temperature and pressure of the system.

## 3. What factors can affect the accuracy of calculating system pressure during rapid phase transition of CO2?

There are several factors that can affect the accuracy of calculating system pressure during rapid phase transition of CO2. These include the assumptions made in the equation, the complexity of the system, and the accuracy of the input data used. It is important to carefully consider these factors and use reliable data to ensure accurate results.

## 4. What are some common applications where calculating system pressure during rapid phase transition of CO2 is necessary?

Calculating system pressure during rapid phase transition of CO2 is necessary in various industrial and scientific applications. Some common examples include the design and operation of refrigeration and air conditioning systems, carbon capture and storage processes, and chemical production processes that use CO2 as a reactant.

## 5. Are there any safety concerns when dealing with rapid phase transition of CO2 and calculating system pressure?

Yes, there can be safety concerns when dealing with rapid phase transition of CO2 and calculating system pressure. CO2 is a high-pressure gas and can be hazardous if not handled properly. It is important to follow proper safety protocols and use accurate calculations to avoid any potential risks or accidents.

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