Understanding the Boiling Point: Thermodynamic Proof

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Discussion Overview

The discussion revolves around the thermodynamic understanding of the boiling point of liquids, specifically addressing the behavior of a liquid at its boiling point when heat is added. Participants explore the concepts of phase changes, free energy, and the relationship between temperature and phase stability.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that adding heat at the boiling point can either increase temperature or cause a phase change, questioning why the temperature remains constant during the phase change.
  • Another participant suggests that the concept of free energy can explain this behavior, stating that below the boiling point, the free energy of the liquid is lower, while above it, the gas has lower free energy, with equality at the boiling point.
  • A question is raised about whether this explanation can be derived solely from thermodynamic laws without referencing ΔG values from tables.
  • A further response indicates that while the relationship between phases and free energy can be established, deriving the actual dependence of free energy on temperature may require statistical mechanics, implying that thermodynamics alone may not suffice.

Areas of Agreement / Disagreement

Participants express differing views on the sufficiency of thermodynamics for proving the behavior at the boiling point, with some asserting that statistical mechanics is necessary for a complete understanding. No consensus is reached on the best approach to prove the concepts discussed.

Contextual Notes

The discussion highlights potential limitations in deriving phase behavior solely from thermodynamic principles, suggesting a dependence on specific assumptions about free energy changes and the need for additional frameworks like statistical mechanics.

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If we add a small amount of heat δq to a liquid at its boiling point Tb, it could either increase its temperature a small amount dT = δq/Cv, or suffer a phase change into vapor.

Experimentally, we see that liquids remain at Tb until the phase change is complete, and only then continue increasing their temperature. Why is this?

I want to prove this macroscopically, that is, from thermodynamics, but I don't know where to start. Any leads?
 
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The way you do this is by looking at free energy. Bellow the Tb, the free energy of a liquid is lower. Above, free energy of gas is lower. At Tb, the free energy of the two phases is the same. So to get an absolute lowest free energy, the substance must convert part of liquid to vapor in response to added energy, until there is no more liquid left.
 


Can what you just said be proved from the laws of thermodynamics, without looking up ΔG values on tables?
 


Like I said, if you take for granted that different phases have different rate at which free energy changes with temperature, that's all you need to prove that phase transition happens at a specific temperature for pure substance.

If you want to derive the actual dependence of free energy on temperature, then you need statistical mechanics. As far as I know, thermodynamics by itself is insufficient.
 

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