# Temperature of a compressed gas

• men5j2s
In summary, the user is trying to calculate temperature changes of a pressurized gas in a cylinder and its temperature when flowing into another vessel. They used the ideal gas law with initial values of 300 bar, 112 L, 0.082 atm.L/mol.k, and 377.1 mol, which gave a temperature of 1072.4 K. However, they are unsure if this result is correct and are seeking clarification on their process and data. They also mention the possibility of a mistake in the volume of the cylinder and the effect of heat transfer on the accuracy of their calculations. They are ultimately trying to understand the temperature changes in the second vessel during the filling process and how to accurately model it.

#### men5j2s

TL;DR Summary
What is the temperature of the compressed helium in a cylinder
How can I calculate the temperature changes of a pressurized gas as it is in a cylinder, then as it is when flowing into another vessel?

my best guess was using the ideal gas law (with help from this forum), but I feel like I'm using it wrong.

P = 300bar or 296.08 atm
V = 112 L (is this supposed to be the volume of the vessel?)
R = 0.082 atm.L/mol.k
n = 377.1 mol (based on the manufacturers spec of the cylinder stating the contents are 8.56m3)

This gives me a Temp of 1072.4 K, which surely cannot be right, what have I done wrong/misunderstood?

men5j2s said:
my best guess was using the ideal gas law (with help from this forum), but I feel like I'm using it wrong.

P = 300bar or 296.08 atm
V = 112 L (is this supposed to be the volume of the vessel?)
R = 0.082 atm.L/mol.k
n = 377.1 mol (based on the manufacturers spec of the cylinder stating the contents are 8.56m3)

This gives me a Temp of 1072.4 K, which surely cannot be right, what have I done wrong/misunderstood?
How did you get that answer from that data?

To start with here, you need to clearly define the states and processes. How much gas is in the cylinder to start? At what temperature and pressure? How much is left at the end? And do you just want to calculate something about the end state or model a continuous process?

Also, what happens in the original cylinder and what happens in a different cylinder are different, but possibly related problem. Both have to be clearly defined.

We've had some similar threads recently, I'll see if I can find one that goes through an example.

I did PV/nR

(296.08*112)/(377.1*0.082)

What I would ideally like to do, is understand what's happening in the second vessel (the first one is just a pressurized helium cylinder acting as a reservoir), the second is going to be filled to around 8 bar, from empty.

So if I can model the temperature at given time points, I will be able to derive mass flow rate by using a pressure transducer.

Will there be a point at which the initial cylinder becomes so empty that there will be a noticeable difference in the temp that I calculate assuming it is full?

Thanks for the help, I will eventually get my head around this.

Your calculation is correct, but where did you get your numbers from? Standard cylinders I use, about 40L, at 230 bar, contain about 400 moles of gas. 112 L looks high, if the other numbers are right.

mjc123 said:
Your calculation is correct, but where did you get your numbers from? Standard cylinders I use, about 40L, at 230 bar, contain about 400 moles of gas. 112 L looks high, if the other numbers are right.

Quite possible that there's a mistake there...

BOC stated 8.56m^3 as the volume (of He)
at stp we have 1 mole in 22.7L
8560/22.7 = 377 moles.

I used the physical height of the cylinder to estimate the volume, but looking at BOC website now, they give the "water capacity" of the cylinder as 50L, using that volume would give 3.22K, which sounds more like it.

A significant factor in accurately predicting the reduction in the supply gas during the transfer and can prevent an accurate modeling of the temperature drop in the supply tank is the heat transfer into the tank from the surrounding ambient temperature during the filling process and the differential in the calculated result and the actual result will be significant.

This is not a theoretical statement, it is the result of my experience while developing a program related to the filling of scuba bottles from a supply vessel. In that project, the heat transfer issue's significance was verified by the recording the T vs P of the air in the vessel during a step wise controlled venting test where the measurements were taken in 5 minute increments because that represented the time normally used for each bottle filling and the transfer time is a significant factor for the heat transfer rate. It should also be noted that the results of that test were only accurate for the surrounding ambient air temperature at the time of the test and it results will not be accurate for other surrounding ambient temperature changes. In fact, it was the heat transfer issue for both the supply tank and receiving bottle during filling that ultimately prevented the program from delivering the level of accuracy desired.

men5j2s said:
Quite possible that there's a mistake there...
I think you should already know everything except maybe the moles in the starting state; Isn't the cylinder just sitting there at room temperature?

russ_watters said:
I think you should already know everything except maybe the moles in the starting state; Isn't the cylinder just sitting there at room temperature?

The cylinder is, but what I'm ultimately trying to do is use a supply cylinder to fill a smaller cylinder and I'm trying to get a feel for the temperature changes I can expect to see during this process.

That sounds like a very complex problem to me (but I'm not the sharpest knife in the drawer either). Seems to me it depends a lot on how fast the tanks transfer thermal energy to the surrounding environment. That's a function of the thermal conductivity of the tank material, and to ambient air. And that can be affected greatly by air flow. And the temperature rise is gradual, over the time you transfer the gas. There will also be the thermal 'soaking' of the tank material.

Bottom line, I'm thinking you would be better to try some empirical measurements. Is there some reason you can't do this? I would think if you got a few data points, you could build a formula to predict various scenarios. Though I also appreciate wanting to understand it from the basic principles and formulas, but often real life conditions create some very significant and complex variations that are not considered in the basic formulas.

I'd also consider putting the cylinders in a water bath for better heat transfer, if better heat transfer is helpful to the process.

men5j2s said:
Summary: What is the temperature of the compressed helium in a cylinder

How can I calculate the temperature changes of a pressurized gas as it is in a cylinder, then as it is when flowing into another vessel?

my best guess was using the ideal gas law (with help from this forum), but I feel like I'm using it wrong.

P = 300bar or 296.08 atm
V = 112 L (is this supposed to be the volume of the vessel?)
R = 0.082 atm.L/mol.k
n = 377.1 mol (based on the manufacturers spec of the cylinder stating the contents are 8.56m3)

This gives me a Temp of 1072.4 K, which surely cannot be right, what have I done wrong/misunderstood?
At that pressure, there are way less than 377 moles in the cylinder. Use room temperature of 293K, and calculate the number of moles. Also, at that pressure, the gas may not be behaving ideally. You may need to use a z-factor chart. What is the reduced pressure and reduced temperature of the gas at 300 bars and room temperature?

Chestermiller said:
At that pressure, there are way less than 377 moles in the cylinder. Use room temperature of 293K, and calculate the number of moles. Also, at that pressure, the gas may not be behaving ideally. You may need to use a z-factor chart. What is the reduced pressure and reduced temperature of the gas at 300 bars and room temperature?
I'm not sure I'm with you here.. I calculated the number of moles by using 8.56m^3 (amount of helium in the cylinder, as per BOC) and 0.1785 g/l (as the density of helium).

At STP I get 22.7 moles/L => 22.7*8.56 => 8560/22.7 = 377.1 moles in 8.56m^3

Also if i do Volume / density, then mass over molar mass, I get 382 moles in 8.56m^3

Not sure if I'm way of the mark here.

Let me understand correctly. The manufacturer specifies that there are 8.56 m^3 of helium in the cylinder for STP conditions, correct?

Chestermiller said:
Let me understand correctly. The manufacturer specifies that there are 8.56 m^3 of helium in the cylinder for STP conditions, correct?
Yes, that's correct

Data in the literature indicate that the compressibility factor for helium at 300 bar and 300K is about 1.2. So that would reduce your estimated temperature a little, but not much. Maybe the manufacturer's estimate of the amount of Helium in the cylinder (1.5 kg) is low.

If you're supplying it from another compressed cylinder, it's not the same as compressing it from room temperature, so you can't analyze it that way. Instead, you'll initially get basically free expansion from the supply cylinder into the cylinder being filled, and then you'll get slower (and less-lossy) flow as the pressure gets closer to equilibrium.

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