Spinodal and Isotherms graph on P-V diagram

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Discussion Overview

The discussion revolves around the process of plotting spinodal and isothermal lines on a P-V diagram for water, including the necessary calculations and equations of state required for this task. Participants explore various equations of state and seek clarification on specific terms and methodologies.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about how to draw spinodal and isothermal lines on a P-V diagram, expressing confusion and a lack of resources.
  • Another participant suggests that the spinodal line is defined by the condition where the second derivative of free energy with respect to volume equals zero, and outlines a method for plotting it using an equation of state.
  • There is a request for alternative equations of state suitable for fluids beyond the Van der Waals equation.
  • Redlich–Kwong and Redlich–Kwong-Soave equations are proposed as potential alternatives, with a note that RKS may be more applicable to organic compounds.
  • A participant seeks a reduced form of the Redlich-Kwong equation and asks for resources to develop it from the original form.
  • Clarification is sought regarding the term "reduced form," with a reference to a Wikipedia article that provides the necessary formula, though some participants express uncertainty about the clarity of the equation presented there.

Areas of Agreement / Disagreement

Participants express varying degrees of uncertainty about the definitions and applications of different equations of state. There is no consensus on the best approach or equation to use for plotting the spinodal line, and the discussion remains unresolved regarding the clarity of the reduced form of the Redlich-Kwong equation.

Contextual Notes

Participants mention the need for specific parameters (like ##a## and ##b##) for the equations of state, indicating a dependence on the particular substance being studied. There are also indications of missing clarity in the equations referenced, which may affect the discussion.

ReuvenD10
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Homework Statement
During my work I have to show on a P-V diagram certain points on the spinodal for water
Relevant Equations
//
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.
 
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*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.
 
Thank for the answer.
Besides Van Der Waals, do you have a suggestion for another equation of state that is suitable for fluid?
 
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
 
Thank, I want to find a development for a state equation to get points on the spinodal for fluid (except a VDW state equation).
 
There's a nice explanation on spinodal diagram and also binodal in Principles of Condensed Matter Physics of Chaikin and Lubensky.
 
dRic2 said:
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.
 
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.
 
dRic2 said:
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:
1608550749820.png
 

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