# Pressure vessel ideal gas calculation

1. Jun 22, 2014

### paulos

Hello all,

As part of a research project, I am trying to calculate the amount of water/dry ice I would need to put in a cylindrical pressure vessel to obtain an internal pressure of ~100 psi at 200C (from room temperature, ~23C).

I haven't had to do a calculation like this in awhile, but here are my thoughts so far:
I will know the volume of water, dry ice, and air at room temperature (and consequently the amount of moles). I can then use the PV/T=constant relation to calculate the final pressure. I would use the internal volume of the pressure vessel minus the volume of the water/dry ice cube as the initial volume and the internal volume of the pressure vessel as the final volume. Also, T1=23C, T2=200C, P1~1 atm.
I would then check that the partial pressure of water (from P2 and moles of water) is below the saturation pressure of water, but at 200C this is likely the case.
Do you see anything wrong with this calculation? Is ideal gas law still reasonably applicable at ~100 psi? 5-10% accuracy is reasonable for my application.

I feel like there should be a way to do this calculation more accurately using steam and CO2 properties tables.

2. Jun 23, 2014

### Staff: Mentor

Your methodology looks sound, although the answer is not going to be unique, depending on the proportions of water and CO2.

Chet

3. Jun 23, 2014

### Staff: Mentor

As long as there is liquid water present some of the CO2 will be dissolved. I don't think it will matter if 5-10% accuracy is OK, but it won't hurt to check.

4. Jun 23, 2014

### Staff: Mentor

The equilibrium vapor pressure of water at 200 C is about 200 psia. So, as Borek indicates, you really do have to consider the possibility that liquid water may be present.

Chet

5. Jun 25, 2014

### paulos

Maybe I have this backwards, but if the final pressure inside the pressure vessel is 100 psia, then the partial pressure of water will be less than 100 psi which is much lower than the water saturation pressure of 225 psi at 200C so no liquid water can be present.
The saturation pressure of CO2 is much higher so all of the CO2 should be gaseous at both temperatures.

6. Jun 26, 2014

### Staff: Mentor

Yes. Sorry, this is all correct. Somehow I got confused, and got it in my head that the final pressure was going to be 200 psi rather than 100 psi.

Chet