# Which gas model to use for dry air and N2 at 300 bar

I want to calculate the change of state for N2 and dry air at pressures above 200 bar with a max of 300 bar. Ideal gas law is not applicable at these pressures, but looking at real gas models there are several to choose from, among others:

Van der Waals
Redlich-Kwong
Virial
Bender

Can someone point me in the right direction in regards to which model should be best in predicting behavior of N2 and dry air at 200-300 bar around -10 deg to 30 deg celsius?

## Answers and Replies

Bystander
Science Advisor
Homework Helper
Gold Member
What specific properties are you after? Density, speed of sound, heat capacities, dielectric constant, E, H, A, G?

Chestermiller
Mentor
My inclination would be to use a compressibility factor/corresponding states approach at those high pressures. I don't think those other models you mentioned would be as accurate.

Chet

What specific properties are you after? Density, speed of sound, heat capacities, dielectric constant, E, H, A, G?

Sorry about not being specific enough. I want to know the pressure after a certain change of volume with no exchange of heat with the environment i.e an adiabatic process. The gas is in a cylinder doing work on a piston.

My inclination would be to use a compressibility factor/corresponding states approach at those high pressures. I don't think those other models you mentioned would be as accurate.

Chet

Good suggestion since the compressibility factor is a empirically derived factor isn't it? At least I think it is for the z factor curves I got from this site http://www.bnl.gov/magnets/staff/gupta/cryogenic-data-handbook/Section6.pdf , see the compressibility factor Z vs pressure for nitrogen below. Can you see if I am using the compressibility factor correctly in the example I describe below?

Say I have initial states P1=250 bar and arbritrary V1. I want to find P2 when V1 has decreased to V2.

First I find the compressibility factor at 250 bar, Z1, which is ~1.1 (for 300 K)

Now I think I need to take a guess at what the pressure P2 will be at after compressing the volume from V1 to V2 in order to know the comp. factor Z2 at this new pressure.

This is where I get a bit stuck.

I cannot calculate: V1*P1 / Z1 = V2 * P2 / Z2 - > P2 = V1 * P1 / Z1 / V2 * Z2

without knowing what Z2 is, and to know Z2 I already need to know the new pressure P2.

So how should one calculate P2?

Last edited:
Chestermiller
Mentor
This is not a Physics question. This is a math question.

Basically, you have two non-linear equations in 2 unknowns, P2 and Z2. One method is to plot both equations on the same graph and see where they intersect. Another method is to solve them iteratively, using successive substitution. Guess a value of Z2 (say 1), and calculate the value of P2. Look up the value of P2 on the graph, and get a new estimate of Z2. Continue this iterative procedure until the values of P2 and Z2 no longer change from one iteration to the next.

Chet

This is not a Physics question. This is a math question.

Basically, you have two non-linear equations in 2 unknowns, P2 and Z2. One method is to plot both equations on the same graph and see where they intersect. Another method is to solve them iteratively, using successive substitution. Guess a value of Z2 (say 1), and calculate the value of P2. Look up the value of P2 on the graph, and get a new estimate of Z2. Continue this iterative procedure until the values of P2 and Z2 no longer change from one iteration to the next.

Chet
Sorry for the misplaced question. I will remember to post them where they belong, which in this case would have been the mathematics section. I should probably read the guidelines for posting as I am new.

Many thanks for answering the question despite it belonging somewhere else! I'll have a go at solving it using both methods. Also, since using the compressibility factor is the most accurate, then this can be used to check the accuracy of the other models. I'll have a go at that as well.

Oh yes, one more thing. I said I wanted to find the new pressure state with an adiabatic process, but I calculated assuming an isothermic change. When considering an adiabatic process does the use of the polytropic exponent still hold when using the compressibility factor?

I.e. is this valid? :

P1 * V1 ^ n / Z1 = P2 * V2 ^n / Z2 , where the polytropic exponent n = 1.4

Chestermiller
Mentor
Sorry for the misplaced question. I will remember to post them where they belong, which in this case would have been the mathematics section. I should probably read the guidelines for posting as I am new.

Many thanks for answering the question despite it belonging somewhere else! I'll have a go at solving it using both methods. Also, since using the compressibility factor is the most accurate, then this can be used to check the accuracy of the other models. I'll have a go at that as well.

Oh yes, one more thing. I said I wanted to find the new pressure state with an adiabatic process, but I calculated assuming an isothermic change. When considering an adiabatic process does the use of the polytropic exponent still hold when using the compressibility factor?

I.e. is this valid? :

P1 * V1 ^ n / Z1 = P2 * V2 ^n / Z2 , where the polytropic exponent n = 1.4
No. You need to find out how to determine the changes in the thermodynamic functions such as enthalpy and entropy when the pressure is in the non-ideal gas region. It involves integrations involving the compressibility factor, and graphs similar to the z chart are available in most thermo books and engineering handbooks to make things easy for you.

Chet

No. You need to find out how to determine the changes in the thermodynamic functions such as enthalpy and entropy when the pressure is in the non-ideal gas region. It involves integrations involving the compressibility factor, and graphs similar to the z chart are available in most thermo books and engineering handbooks to make things easy for you.

Chet
I really appreciate the pointers you've given. Thanks for your time. I've got some studying to do on this.