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

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SUMMARY

The Clausius-Clapeyron formula, as presented in Daniel v. Schroeder's textbook, is defined as \(\frac{dP}{dT} = \frac{L}{T(V_{g} - V_{l})}\), where \(V_{g}\) and \(V_{l}\) represent the specific volumes of gas and liquid, respectively. Specific volume is calculated as \(\nu = \rho^{-1}\). The discussion clarifies that \(V_{g}\) and \(V_{l}\) can be interpreted as either specific or extensive quantities, provided that the units remain consistent throughout the equation. The units of the expression are confirmed to be J m-3 K-1 or equivalently Pa K-1.

PREREQUISITES
  • Understanding of the Clausius-Clapeyron equation
  • Knowledge of specific volume and its calculation
  • Familiarity with extensive vs. specific quantities
  • Basic thermodynamics concepts
NEXT STEPS
  • Study the derivation of the Clausius-Clapeyron equation in thermodynamics
  • Learn about specific volume calculations in different states of matter
  • Explore the implications of extensive vs. specific quantities in thermodynamic equations
  • Investigate applications of the Clausius-Clapeyron formula in phase transitions
USEFUL FOR

Students of thermodynamics, physicists, and engineers interested in phase transitions and the behavior of substances under varying temperature and pressure conditions.

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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