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Tuesday, March 26, 2024

Does the state equation matter for Boyle's law?

 First, you need to know that the works on which Boyle's law are based are very old.

Boyle's law is due to the investigations of Robert Boyle by the years 1660! Follow this link if you want read the originial text.

On the other hand, the first equation of state, which is that for the ideal gas law,

$PV=n\text{R}T$

was assembled in 1834 by Emil Clapeyron. Notice, that I said assembled because, as in many fields of science, the ideal gas law is based on the findings of researchers before  1834, Robert Boyle included!

On  the other hand, the second most known equation of state is that of van der Waals,

$\left(P+\dfrac{an^2}{V^2}\right)\left(V-nb\right)=n\text{R}T$

in 1873! Then, what is clear at this point, in answer to the question, is that Boyle's law does not care about the state equation you are using.

Why is it that Boyle's law does not care about the state equation?

The answer is simple. Boyle's law describe the behavior of a system and although it was empirically determined it has been demonstrated its validity in many different systems. However, the state equations are based on Boyle's law (or the findings of Robert Boyle) and worst, the state equations (as the two mentioned early), not always work for every condition.

Any question? Write in the comments and I shall try to help.

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