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

In summary, the Clausius-Clapeyron formula, which calculates the phase boundary between liquid and gas, is represented by the equation dP/dT = L / (T(V_g - V_l)). V_l and V_g refer to specific volumes for gas and liquid, respectively, as defined by the equation nu = rho^-1. The equation can be written in terms of extensive, specific, or molar quantities as long as consistency is maintained.
  • #1
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)
[tex] \frac{dP}{dT} = \frac{L}{T\left(V_{g} - V_{l} \right)} [/tex].

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

My question is, is [itex]V_{l}[/itex] and [itex]V_{g}[/itex] 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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  • #2
Sebas4 said:
What is [itex]V_{l}[/itex] or [itex]V_{g}[/itex]? 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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  • #3
L and V's in your equation are per mole.
 
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  • #4
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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Related to Understanding the Clausius-Clapeyron Formula: V_{l} and V_{g}

1. What is the Clausius-Clapeyron formula?

The Clausius-Clapeyron formula is a thermodynamic equation that relates the vapor pressure of a substance to its temperature. It is expressed as ln(P2/P1) = -(ΔHvap/R) x (1/T2 - 1/T1), where P1 and P2 are the vapor pressures at temperatures T1 and T2, ΔHvap is the enthalpy of vaporization, and R is the gas constant.

2. What is the significance of the Clausius-Clapeyron formula?

The Clausius-Clapeyron formula is important because it helps us understand the relationship between temperature and vapor pressure. It is also used to predict the boiling point of a substance at different pressures, and to calculate the enthalpy of vaporization.

3. How does the Clausius-Clapeyron formula apply to liquid and gas phases?

The Clausius-Clapeyron formula can be applied to both liquid and gas phases. In the formula, P1 and P2 represent the vapor pressures of the liquid and gas phases, respectively. By plugging in the appropriate values, we can calculate the change in vapor pressure with respect to temperature for both phases.

4. What factors affect the accuracy of the Clausius-Clapeyron formula?

Several factors can affect the accuracy of the Clausius-Clapeyron formula. These include the assumption of ideal gas behavior, the assumption of constant enthalpy of vaporization, and the presence of impurities in the substance. In addition, the formula may not be accurate for substances with very high or very low vapor pressures.

5. How is the Clausius-Clapeyron formula used in real-world applications?

The Clausius-Clapeyron formula has many practical applications, including in the design of refrigeration and distillation systems, in weather forecasting, and in the study of phase transitions in materials. It is also used in the production of pharmaceuticals and in the chemical industry to control the boiling point of substances.

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