# What is an Equation of State ?

An

## Equation of State

(EOS) is an equation that relates the pressure, temperature, and the molar volume of a substance.
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.
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### Ch 2, 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.