Volume of CO2 from a Tank at 30psi

In summary: I'll go back and fix it.In summary, the conversation discusses building a solar shower using PVC and the use of a portable air pump or compressed gas tank with a regulator. The goal is to determine how many gallons a 20oz CO2 tank, filled with 20oz of gas, would expand to fill at 30psi and 70°F, as well as how many times a 5 gallon tank could be filled at 30psi from the 20oz tank. The conversation also includes a question about using the ideal gas law to relate atmospheric pressure to gage pressure and a calculation error correction.
  • #1
sean882
10
0
First off, this is not a homework question nor assignment. I'm working on building a solar shower to mount on my car out of PVC, and don't feel like pumping large volumes of air with a bike pump. I'm looking at a portable air pump, or compressed gas in a tank with a regulator (and blow off valve).

I'm posting here rather than the projects section as my question is a direct use of the ideal gas law; I'm not looking for critiques on the design itself.

Goal: How many gallons, at 30psi and 70°F, would a 20oz CO2 tank (assume properly filled with 20oz of gas) expand to fill? How many times could a 5 gallon tank be filled at 30psi from the 20oz tank?

Question: I believe I figured out the volume at STP correctly (1ATM of pressure, 0°C). When I relate that to my desired conditions, I used PV/T = P2V2/T2. When relating atmospheric pressure to gage pressure (30psi, 2.04 ATM), can I simply add 1 ATM to the desired gage pressure, making my P2 value 3.04 ATM? See starred (in margin) line in my work.

Work and attempt is attached. Thanks for your help and review! It's been about 10 years since I did this in school, and haven't really had to apply it between then and now.

-Sean
 

Attachments

  • CO2 vs Compressor.pdf
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  • #2
As the CO2 leaves the tank, what happens to the pressure in the tank?
 
  • #3
Chestermiller said:
As the CO2 leaves the tank, what happens to the pressure in the tank?
I'd expect that, up until most of the CO2 has left the tank, the pressure in the tank would remain constant at roughly 860 psi (with minor fluctuations with temperature). The CO2 should primarily be in the liquid form in the tank if filled properly, converting to gas phase as gas escapes (slightly lower pressure, some liquid turns to gas, 'rinse & repeat').

After all the liquid had turned to gas, the pressure would drop, and this pressure should equalize to the pressure of the vessel being filled.
 
  • #4
The universal gas constant in convenient units is 10.731 (psi-ft^3)/(degR-lb_mole). You have ##20 oz =1.25 lb=0.159 lb-mole## So, $$V=\frac{nRT}{P}=\frac{(0.159)(10.731)(562)}{(44.7)}=21.4\ ft^3$$
 
Last edited:
  • #5
Chestermiller said:
The universal gas constant in convenient units is 10.731 (psi-ft^3)/(degR-lb_mole). You have ##20 oz =1.25 lb=0.159 lb-mole## So, $$V=\frac{nRT}{P}=\frac{(0.159)(10.731)(562)}{(44.7)}=21.44\ ft^3$$

My gut feeling says that is a bit much - how did you get to 562 for temperature?

Also, for my knowledge - it is acceptable and proper to simply add standard pressure of 14.7psi to the desired gage pressure of 30psi?

Thanks for your help,
-Sean
 
  • #6
Oops. My mistake. R = F + 460. So it should only be 530 R, and V = 20.3 ft^3.

As far as the pressure part is concerned, that is done correctly. Psia = Psig + 14.7
 
  • #7
sean882 said:
First off, this is not a homework question nor assignment. I'm working on building a solar shower to mount on my car out of PVC, and don't feel like pumping large volumes of air with a bike pump. I'm looking at a portable air pump, or compressed gas in a tank with a regulator (and blow off valve).

I'm posting here rather than the projects section as my question is a direct use of the ideal gas law; I'm not looking for critiques on the design itself.

Goal: How many gallons, at 30psi and 70°F, would a 20oz CO2 tank (assume properly filled with 20oz of gas) expand to fill? How many times could a 5 gallon tank be filled at 30psi from the 20oz tank?

Question: I believe I figured out the volume at STP correctly (1ATM of pressure, 0°C). When I relate that to my desired conditions, I used PV/T = P2V2/T2. When relating atmospheric pressure to gage pressure (30psi, 2.04 ATM), can I simply add 1 ATM to the desired gage pressure, making my P2 value 3.04 ATM? See starred (in margin) line in my work.

Work and attempt is attached. Thanks for your help and review! It's been about 10 years since I did this in school, and haven't really had to apply it between then and now.

-Sean
I think you should go with the air pump. Something like this (about $100 @ Walmart) is a good thing to have in your car or truck anyway. This one can deliver 100 psi (I don't know the cfm), and will automatically limit to a preset pressure:

s-l1600.jpg
 

Attachments

  • s-l1600.jpg
    s-l1600.jpg
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  • #8
Chestermiller said:
20oz=1.25lb=0.159lb−mole

@Chestermiller - shouldn't that be $$1.25~lb~*~ \frac {lb-mole} {44~lb}~=~0.028~lb-mole$$

That would give 3.6 ft^3 or 27 gallons, just exactly what the OP calculated in his attached pdf.
 
  • #9
gmax137 said:
@Chestermiller - shouldn't that be $$1.25~lb~*~ \frac {lb-mole} {44~lb}~=~0.028~lb-mole$$

That would give 3.6 ft^3 or 27 gallons, just exactly what the OP calculated in his attached pdf.
Yes. I have no idea how I ended up with that 0.159 lb-moles. Should have double checked.
 

1. How do you calculate the volume of CO2 from a tank at 30psi?

To calculate the volume of CO2 from a tank at 30psi, you can use the ideal gas law equation: V = (nRT)/P, where V is volume, n is the number of moles of CO2, R is the gas constant, T is temperature in Kelvin, and P is pressure. Rearrange the equation to solve for V and plug in the known values to get the volume of CO2 in liters.

2. Does the volume of CO2 change when the pressure is increased to 30psi?

Yes, the volume of CO2 will decrease when the pressure is increased to 30psi. This is because the ideal gas law states that when pressure increases, volume decreases, and vice versa.

3. Can the volume of CO2 from a tank at 30psi be converted to other units?

Yes, the volume of CO2 can be converted to other units such as cubic meters or cubic feet. You can use conversion factors to convert from liters to the desired unit.

4. How does temperature affect the volume of CO2 at 30psi?

According to the ideal gas law, temperature and volume are directly proportional. This means that as temperature increases, the volume of CO2 at 30psi will also increase.

5. What is the significance of knowing the volume of CO2 from a tank at 30psi?

Knowing the volume of CO2 from a tank at 30psi is important for various reasons. It can help determine the amount of CO2 available for use, as well as the amount needed for certain experiments or processes. Additionally, it can aid in safety measures when dealing with pressurized tanks of CO2.

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