Understanding the Clausius-Clapeyron Formula: V_{l} and V_{g}

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Discussion Overview

The discussion revolves around the interpretation of variables in the Clausius-Clapeyron formula, specifically focusing on the meanings of V_{l} and V_{g}. Participants explore whether these variables represent specific volumes for liquid and gas or if they are extensive quantities. The scope includes theoretical understanding and clarification of the formula's components.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether V_{l} and V_{g} are specific volumes for gas and liquid, seeking confirmation.
  • Another participant asserts that V_{l} and V_{g} are indeed volumes, noting that the equation can be expressed in terms of extensive quantities.
  • A third participant clarifies that L and V's in the equation are per mole, suggesting a molar interpretation.
  • A later reply emphasizes the importance of consistency in units, stating that L and V can be either specific, molar, or extensive, as long as they match in type.

Areas of Agreement / Disagreement

Participants express differing views on whether V_{l} and V_{g} should be interpreted as specific volumes or extensive quantities, indicating that multiple competing interpretations remain unresolved.

Contextual Notes

The discussion highlights potential ambiguities in the definitions of specific and extensive quantities, as well as the need for clarity regarding the units used in the Clausius-Clapeyron formula.

Sebas4
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Hey, I have a question about the meaning of a variable in the Clausius-Clapeyron formula.

My textbook (Daniel v. Schroeder) says that the Clausius-Clapeyron formula is (for phase boundary between liquid and gas)
\frac{dP}{dT} = \frac{L}{T\left(V_{g} - V_{l} \right)}.

What is V_{l} or V_{g}? It's not volume. I looked on Wikipedia, they say that V_{g} - V_{l} is the difference in specific volume of gas and liquid.
Specific volume is defined as \nu = \rho^{-1}.

My question is, is V_{l} and V_{g} specific volumes for gas and liquid, or I mean is it correct?
I want to ask just to be sure.

Thank you in advance for responding,

-Sebas4.
 
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Sebas4 said:
What is V_{l} or V_{g}? It's not volume.
It is volume. Schroeder writes the equation in terms of extensive quantities (total latent heat for a given system of a given size) whereas in Wikipedia the equation is written in terms of the specific latent heat and the specific volume.
 
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L and V's in your equation are per mole.
 
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It doesn't matter as long as you are consistent, i.e. L and V are both specific (J/kg and m3/kg), or both molar (J/mol and m3/mol), or both extensive (J and m3). In each case the expression has units J m-3 K-1 ≡ Pa K-1.
 
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