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What is an Equation of State ?

Equation of State

(EOS) is an equation that relates the pressure, temperature, and the molar volume of a substance.

You already know a few things about one EOS.
You probably call it the Ideal Gas Law.
We call it the

Ideal Gas Equation of State

, because it is definitely NOT a law because it does not always accurately describe the relationship between P, V and T.

In this lesson, we will discuss the Ideal Gas EOS and a graphical EOS called the

Generalized Compressibilty Factor

EOS.

Lesson 2E: page 1 of 13

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Ch2, Lesson E, Page 1 - What is an Equation of State ?

An equation of state is an equation in terms of three variables, P, molar volume and T.
I like to abbreviate equation of state by just EOS.
Some EOS’s have theoretical bases, but some do not.
An equation of state can be considered to be the result of a curve fit of a set of experimental data.
The set of data consisting of P, molar volume and T measurements.
Lets try a “thought experiment.”
Imagine that we keep a cylinder full of gas at a constant temperature.
We add a small weight to the piston. The pressure increases and the volume decreases, right ?
It’s fairly straightforward to predict the increase in pressure if we know how much weight we added to the piston.
But, what’s the new volume ? That isn’t quite as simple, is it ?
Hopefully, you are thinking that this problem doesn’t seem too difficult. Just apply the Ideal Gas EOS, right ? Well, maybe and maybe not.
Under certain circumstances the Ideal Gas EOS is reasonably accurate, but all to often it is not.
When the Ideal Gas EOS is NOT accurate, we need to use a more sophisticated EOS.
In any case, the function of an EOS remains the same.
Given any 2 out of the three variables, P, molar volume and T, an EOS lets you calculate the value of the unknown variable.
In this lesson, we will review what you learned about the Ideal Gas EOS in Freshman chemistry.
We will also discuss why the Ideal Gas EOS often fails.
Finally, we will discuss one of the many more sophisticated EOS’s. This is a graphical EOS and it is effective even when the Ideal Gas EOS fails.
This EOS is called the Generalized Compressibility Factor EOS.
We will discuss other sophisticated EOS’s in the final lesson of this chapter.

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