Maxwell's Construction

Ah, this would be cleaner if I continued from the previous post, but I worry it’d get needlessly long,

so in this post I’ll briefly cover only Maxwell’s construction and move on.

I’ll explain with this figure again.

(source: UT Austin lecture notes on thermal physics)

The fact that V/V_c differs at points 2 and 6 was interpreted as ’the phases are different'.

But, the Gibbs’ free energy at those two points is the same!!!!

We’ll use the above.

This integral, can I

write it like this??? No problem at all, right

The left-hand side of this equation

this, by the definition of the Gibbs function, is the volume V.

And if you look at the G-function part of the graph above,

you can see this!!! Why??? Because the function values are the same!!! lol lol lol

exactly exactly, byebye~~~~

That is,

This means

the p and T that make the integral zero

are where “phase transition or phase coexistence” occurs!!!

If you get the ordered pairs of p and T that make such phase coexistence happen and plot them, the graph apparently comes out looking like this.

(source: ResearchGate: van der Waals phase diagram)

For now I’ll say just this much.

And a more detailed discussion will come in maybe the next-next post??, where I’ll cover just “phase transitions” in full detail.

Well then, see ya~~~~