Real Gas Laws: Exploring Alternatives to PV=nRT

In summary, the ideal gas law PV=nRT can only be used for ideal gases. To consider real gases, the Van der Waals equation is commonly used, which takes into account the volume occupied by each molecule and the internal energy density due to intermolecular interactions. There are also other equations, such as the Beattie-Bridgeman and Benedict-Webb-Rubin equations, which provide more accuracy but can be complex to use. In some cases, the ideal gas law is sufficient, especially at high temperatures and low pressures. However, for more accurate modeling, various levels of thermodynamics and statistical mechanics can be applied. Ultimately, the equations of state for real fluids are often determined computationally and numerically, with
  • #1
newton1
152
0
the ideal gas law PV=nRT only can used on the ideal gas, right?
if the we want consider the real gas...
what equation should we used??
 
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  • #2
The most famous 'real' gas equation of state is the so-called Van der Waals equation

(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
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=RuT/v2*(1-c/(vT3))*(v=B)-A/v2

Benedict-Webb-Rubin

P=RuT/v + (B0RuT - A0 - C0/T2)*1/v2 + (bRuT - a)/v3 + a* α / v6 + c/(v3T2)*( 1 + γ / v2)* e- γ / v^2

(Don't ask me how to apply those... I don't even claim to know...)
 
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  • #4
in fact, the ideal gas law is usually sufficient too - especially at high temps and low pressures (if you can arrange both) - just allow for extra degrees of freedom in the specific heat if its polyatomic.

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
Yep, in general most situations where the pressure < 150 bar and the temperature > 200K are very accurately modeled by the ideal gas law.

- Warren
 
  • #6
More a historical curiosity than anything else:

van der Waals never really wanted a and b to be taken as constants, in fact, if you look at his later work in the area, he sought to see how they varied with changing parameters. However, it tends to be something that is not overly productive and has long since fallen by the wayside.

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. :wink: 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.
 

1. What is the purpose of exploring alternatives to the ideal gas law?

The ideal gas law, PV=nRT, assumes that gases behave ideally and do not interact with each other. However, real gases deviate from this behavior under certain conditions, making it necessary to explore alternative equations that take into account these deviations.

2. What are some common real gas laws used in scientific research?

Examples of real gas laws include the van der Waals equation, the Redlich-Kwong equation, and the Soave-Redlich-Kwong equation. These equations incorporate factors such as intermolecular forces and molecular size to better describe the behavior of real gases.

3. How do real gas laws differ from the ideal gas law?

The ideal gas law assumes that gases have no volume and do not interact with each other, while real gas laws take into account the volume of gas molecules and the attractive and repulsive forces between them. Real gas laws also include correction factors to account for non-ideal behavior.

4. What are some applications of real gas laws in industry?

Real gas laws are commonly used in the design and operation of industrial processes, such as in the production of liquefied natural gas. They are also important in the development of new technologies, such as fuel cells and gas storage systems.

5. How do temperature and pressure affect the behavior of real gases?

Temperature and pressure have a significant impact on the behavior of real gases. As temperature decreases and pressure increases, real gases tend to behave more like ideal gases. However, at high pressures and low temperatures, real gases can deviate significantly from ideal behavior.

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