Understanding the Boiling Point: Thermodynamic Proof

[Termotanque]

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

Experimentally, we see that liquids remain at T_b 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?

 

[K^2]

The way you do this is by looking at free energy. Bellow the T_b, the free energy of a liquid is lower. Above, free energy of gas is lower. At T_b, 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.

 

[Termotanque]

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

 

[K^2]

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.

 

[sardar]

I would like to start by stating that boiling point is a fundamental property of a substance and is determined by its thermodynamic properties. It is the temperature at which the vapor pressure of a liquid equals the atmospheric pressure surrounding it.

Now, let's consider the scenario where we add a small amount of heat δq to a liquid at its boiling point Tb. This heat energy is used to overcome the intermolecular forces holding the liquid molecules together and facilitate the phase change from liquid to vapor. This process is known as vaporization and it requires a significant amount of energy.

According to the first law of thermodynamics, the heat added to the system (liquid) is equal to the change in internal energy (ΔU) and the work done (W) by the system. Mathematically, it can be expressed as δq = ΔU + W.

In this case, as the liquid is at its boiling point, there is no change in temperature (dT = 0) and therefore, there is no change in internal energy (ΔU = 0). This means that all the heat energy added to the system is used to do work (W) in the form of overcoming intermolecular forces and facilitating the phase change from liquid to vapor.

Hence, experimentally, we see that liquids remain at their boiling point until the phase change is complete because all the added heat energy is being used for the phase change process and not for increasing the temperature. Once the phase change is complete, any additional heat energy added will result in an increase in temperature, as expressed by the equation dT = δq/Cv, where Cv is the heat capacity at constant volume.

In conclusion, the understanding of boiling point and its behavior can be explained by thermodynamics, specifically the first law of thermodynamics. By considering the change in internal energy and work done, we can see why liquids remain at their boiling point until the phase change is complete. Further research and experimentation can help us gain a deeper understanding of this phenomenon.