Spinodal and Isotherms graph on P-V diagram

[ReuvenD10]

Homework Statement

During my work I have to show on a P-V diagram certain points on the spinodal for water

Relevant Equations

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Hey guys,

During my work I have to show on a P-V diagram certain points on the spinodal for water.

How do I draw the spinodel and isothermal lines on a diagram (for example in Excel)? Is it something that I need to calculate? I'm lost on this, I did not find anything relevant on the internet.

Thanks for the help.

 

[dRic2]

*If I remember correctly* (big emphasis on that) a spinodal line is defined by the property $\frac {\partial^2 F}{\partial V^2} = 0$. Since the free energy $F$ is a function of temperature this defines a function of temperature ($T$). Moreover pressure is $P = -\frac {\partial F} {\partial V}$ so a spinodal line could be seen in PV graph as a line that satisfies $\frac {\partial P}{\partial V} = 0$. In order to plot this line you need an equation of state $P = f(T, V)$ (for example Van der Waals if you are dealing with a fluid) then you:
-fix a value of $T$
-evaluate $\frac {\partial P(T, V)}{\partial V} = 0$
-store that point
-repeat steps 1, 2, 3 for a different values of $T$
-plot the line.
This could be done easily with a software like MATLAB or phyton or whatever you like.

 

[ReuvenD10]

Thank for the answer.
Besides Van Der Waals, do you have a suggestion for another equation of state that is suitable for fluid?

 

[dRic2]

Redlich–Kwong or Redlich–Kwong-Soave come to mind. RKS I think is most used for organic compounds, but it's just a guess. Maybe @Chestermiller could help

 

[ReuvenD10]

Thank, I want to find a development for a state equation to get points on the spinodal for fluid (except a VDW state equation).

 

[MathematicalPhysicist]

There's a nice explanation on spinodal diagram and also binodal in Principles of Condensed Matter Physics of Chaikin and Lubensky.

 

[ReuvenD10]

Redlich–Kwong or Redlich–Kwong-Soave come to mind. RKS I think is most used for organic compounds, but it's just a guess. Maybe @Chestermiller could help

I try to find the reduce form of Redlich Kwong equation.
you have the reduce form for this EOS? or some good book/ article that show how to develop from original form to the reduce form.

 

[dRic2]

What's a "reduce form" ? Sorry I don't know. Btw https://en.wikipedia.org/wiki/Redlich–Kwong_equation_of_state
you just need the formula in that article. You have to find $a$ and $b$ for the particular substance you are studying. You could get those from any good engineering /chemical engineering handbook. It's been a while since I last check one of those so I can't help you much further.

 

[ReuvenD10]

What's a "reduce form" ? Sorry I don't know. Btw https://en.wikipedia.org/wiki/Redlich–Kwong_equation_of_state
you just need the formula in that article. You have to find $a$ and $b$ for the particular substance you are studying. You could get those from any good engineering /chemical engineering handbook. It's been a while since I last check one of those so I can't help you much further.

I saw wikipedia page, but the equation not clear. I think some sign is missing.

from wikipedia: