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

AI Thread Summary
The Clausius-Clapeyron formula relates the change in pressure with temperature at a phase boundary between liquid and gas, expressed as dP/dT = L/(T(Vg - Vl)). In this context, Vl and Vg refer to the specific volumes of the liquid and gas, respectively, which are inversely related to density. The equation can be written using extensive or specific quantities, as long as consistency is maintained in the units used. The key is that L and V must be either both specific or both extensive to ensure correct dimensional analysis. Understanding this distinction is crucial for applying the formula accurately.
Sebas4
Messages
13
Reaction score
2
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.
 
Science news on Phys.org
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.
 
L and V's in your equation are per mole.
 
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.
 
  • Like
Likes vanhees71 and Chestermiller
Problem: You’re an Uber driver with a Tesla Model 3. Today’s low: 30F, high: 65F. You want to reach a USD$ profit target in the least number of hours, but your choices could have added cost. Do you preheat the battery only when you are headed to the charging station (to increase the charging rate by warming the battery — however the battery might not be “warm enough” when your reach the charger and thus slower charging rates), or do you always “navigate to the charger” the entire day (which...
Back
Top