What is a maxwell construction.?

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Discussion Overview

The discussion revolves around the concept of Maxwell construction, particularly in the context of van der Waals isotherms. Participants seek to clarify its definition and application, especially regarding phase equilibrium and the behavior of fluid and gaseous phases.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks for a clear definition of Maxwell construction and its application to van der Waals isotherms, expressing confusion about the topic.
  • Another participant provides a link to a Wikipedia page on Maxwell relations, suggesting it as a reference for further reading.
  • A participant explains that the Maxwell isotherm assumes spatial homogeneity but acknowledges the presence of unstable regions that can separate into fluid and gaseous phases. They clarify that Maxwell construction is a method to determine phase equilibrium in these inhomogeneous regions.
  • Further elaboration is provided on the requirement for equal chemical potential in liquid and gas phases at phase equilibrium, noting that this necessitates the signed area under the curve of pressure versus volume to be zero, achieved by making opposing areas equal.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and interpretations of Maxwell construction, with some clarifying its application while others provide references. The discussion does not reach a consensus on the best way to explain or understand the concept.

Contextual Notes

There is a mention of the assumption of spatial homogeneity and the implications of phase instability, which may not be fully explored or agreed upon by all participants.

misslondonuk
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what is a maxwell construction...?

What is a maxwell construction when applied to van der Waals isotherms??

please help, i really don't understand it.

Thanks in advance
 
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The Maxwell isotherm is based on the assumption that the system is spatially homogeneous. However, there are regions of the isotherm which are unstable and tend to segregate into fluid and gaseous phases. The Maxwell construction is a method to determine the phase equilibrium in the inhomogeneous region.
It is not related to the Maxwell relations in contrast to the answer of nbo10.
 


To expand on DrDu's excellent answer, in phase equilibrium, we need the chemical potential of the liquid and gas phases to be equal. In particular, since [tex]d\mu = -s dT + v dp[/tex], to have equal [tex]\mu[/tex] at equal temperature requires the integral of v dp to be zero, i.e. the signed area under the curve to be zero. We arrange for this by making the opposing areas equal.
 

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