- #1

newton1

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if the we want consider the real gas...

what equation should we used??

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- Thread starter newton1
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- #1

newton1

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if the we want consider the real gas...

what equation should we used??

- #2

(P+a*(n/V)^2)(V-nb)=nRT

that can be derived by ideal gas equation substituting

V->V-nb

P->P+a*(n/V)^2

The first substitution compensate for the volume occupied by each molecule (we can think of b as the volume occupied by a mole of gas at 0 Kelvin)

The second substitution compensate for the internal energy density due to intermolecular interaction

a and b are considered constants dependent on the gas only.

You can note that the equation depends on P, T and V/n only, once a and b are fixed.

Try and search on the web for Van der Waals equation...

- #3

enigma

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There are other equations also which are more precise than Van der Waals.

The problem is, they are get more and more complex as the precision gets higher. For many applications, Van der Waals is sufficient.

Examples:

Beattie-Bridgeman

P=R_{u}T/v^{2}*(1-c/(vT^{3}))*(v=B)-A/v^{2}

Benedict-Webb-Rubin

P=R_{u}T/v + (B_{0}R_{u}T - A_{0} - C_{0}/T^{2})*1/v^{2} + (bR_{u}T - a)/v^{3} + a* α / v^{6} + c/(v^{3}T^{2})*( 1 + γ / v^{2})* e^{- γ / v^2}

(Don't ask me how to apply those... I don't even claim to know...)

The problem is, they are get more and more complex as the precision gets higher. For many applications, Van der Waals is sufficient.

Examples:

Beattie-Bridgeman

P=R

Benedict-Webb-Rubin

P=R

(Don't ask me how to apply those... I don't even claim to know...)

Last edited:

- #4

Andersen

- 13

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to add more detail, there are various levels of thermodynamics through to statistical mechanics that you can apply, if needed - you can model for the "exact" interaction your gas has (in prinicple - these things are hard to solve sometimes, and you'll probably have to use perturbation theory)

for "maximum realness", you'll need Quantum Stat-Mech, but that is probably serious overkill.

Joe

- #5

chroot

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- Warren

- #6

Mike H

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van der Waals never really wanted

Back on topic...

A good bit of determining equations of state for real fluids is done computationally/numerically, with the algebraic expression extracted after fitting the data. While you not unexpectedly see this in chemical engineering, you also see this quite a bit in condensed matter/chemical physics where we still can't seem to model water accurately all the time. A good bit of the interest in formulating better quality models of fluids is due to the interest in biological systems, where figuring out solvation can be a non-trivial exercise.

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