# Ideal gas vs. real gas calulations

#### Karma

Dear Physicists,
I would ask about the confirmation of my concept, because at work I don't have any thermodynamic specialist to consult it with.
I am not a physicist and probably this problem will be trivial for you, but I will appreciate any comments.
My project is to recover greenhouse gases from pneumatic installation (CF4, SF6, C3F8 (know as well as R218) and C2H2F4 (R134a)).
The process is foreseen to look as following: open the valves between installation and recovery unit, suck the gas using a compressor to the tank, up to the moment of reaching 0 bar absolute (vacuum) in the installation and close the valves. The most important factor for the compressor is the flow rate and unfortunately they seems to be pretty small and that makes it difficult to find a proper compressor.
So I would like to be absolutely sure that I have calculated it correctly.

Let's go to specifics.
My data is as following, I have 2 parts of the pipe (all int. dimeter 8mm):
part 1 length=0.5m under 50 bar
part 2 length=1m under 10 bar
So I am able to calculate the total volume of the gas (under different pressures and sum it up) from Boyle's law. When I have that I need to know how much volume it will take in the tank which we would like to keep under 10 bars.
So i use Boyl's Law again to know how much volume the gas will take in the tank (V2) under 10bars (p2) by using data from part 1 i.e. So (i will give different data cause the volumes for those pipes are really small and it will mess up the view):
V1 = 50m3 p1 = 50bars
V2 = ? p2 = 10 bars
V2 = (V1*p1)/p2

The other solution that came to my mind is not calculate this total volume to mass (which independently on pressure will not change) and than make calculations for the tank. After i will know how much mass I need to transfer I will do reverse calculation to know the volume of the tank. To mass calculation I used ideal gas Clapeyron's Law.

In the end it is all for ideal gas, so will be nice to repeat all the process for real gas according to real gas equation with van der Waals constants. (that will be also another reason to use mass calculations)

Could you please give me some advice if this could be the optimal way to have my tank volume (also I need to than know he flow rate for the compressor) and if there is any mistake in my way of thinking?

#### Woody

The most obvious problem is zero bar Absolute!
You will never get zero,
Even the very best scientific equipment can't achieve that.
So how close is close enough for your application?

The effectiveness of any compressor will depend at least as much on the differential pressure across it as on the absolute pressure it is working on.

Indeed I think you could probably relate the effectiveness of the compressor to
the difference in pressure and the density of the gas.

#### Karma

Yes, of course not 0 bars, we will be fine with low/medium vacuum which means 0.13 - 0.09 bars (100-70 Torr). Pressure differance will be than maximum 10-12 bars.

The biggest concern I have now is how much different will be the real volume of the gas / mass of the gas comapring to my calulations?
Will it make troubles if it will be jsut an estimation instead of detailed calulations for real gas...