What is so magical about the melting and boiling points?

[Pranav Jha]

Melting and boiling explanation based on the kinetic-molecular model have always confused me. I am in grade 12 and still don't feel that I have got any real understanding of the process. Something that has always seemed odd to me is that the idea of increase in potential energy is only mentioned in books when they are discussing melting points? If the solid expands on heating, shouldn't the potential energy of the molecules increase as well all along, even before melting point is reached? Also, what is it with melting point? What "gives in" or breaks to allow the solid to suddenly change to liquid at that temperature for a given pressure?? What happens in terms of PE-KE equilibrium??

 

[Mapes]

A solid substance's energy certainly increases upon heating (and is quantified by the so-called heat capacity), but the increase for a few degrees or tens of degrees is small compared to the large increase in energy upon melting or boiling (the so-called latent heat).

Phase transitions like melting and boiling can be understood by looking at the Gibbs free energy G=U+PV-TS, a tradeoff between energy U and entropy S. Nature favors minimizing energy and maximizing entropy, and in general, the phase with the lowest value of G (e.g., G_liquid vs. G_solid) will be the stable one. Melting takes energy to break bonds (so U is higher for liquids vs. solids), but also increases entropy because more arrangements are possible when the molecules can move about in a liquid (so S is also higher in liquids). The minus sign above means that at a certain temperature, the liquid will have the same Gibbs free energy as the solid; we know this temperature as the melting temperature. The same argument applies for boiling. Does this make sense?

 

[sophiecentaur]

I think you want a more 'nuts and bolts explanation'.
Two molecules are held together by a (negative) binding energy (attractive force). Temperature is a measure of the average Kinetic Energy of the particles in a substance. Increasing the temperature will raise KE and, as you say, because of progressively more separation due to vibrations (increasing, or rather, less negative PE), the substance 'may' expand (if it is well behaved).

If the temperature is high enough, the average KE will be higher than the total binding energy - so the particles will part company because their KE is higher than the binding energy and the substance 'melts'. For a pure substance, the binding energy between all the particles is the same and the melting point will be at a well defined temperature. For mixtures, there is a range of binding energies and you can get partial melting when some particles will separate but others won't. This gives you a mixture which has a texture a bit like porrage (see the antifreeze in your car on a very cold morning).

A similar thing happens when a liquid boils; the KE is higher than the binding and molecules leave the surface and don't return. At lower temperatures, the more energetic molecules are constantly leaving the surface but they return because they haven't 'escaped' completely. Blowing on a wet item will lower its temperature because the most energetic molecules have been blown away and their KE is lost from the liquid.

 

[Studiot]

I don't know what grade 12 is (good idea to mention it though), but here is a non mathematical explanation.

I have sketched the essential points about solids, liquids and gasses and the changes between them. I have represented the particles (molecules if you like) by small circles.

You should bear in mind that when a solid changes to a liquid or a liquid changes to a gas there is no change in temperature during the change. I think you already know this.

So to concentrate on the kinetic explanation as to what happens to both the (latent) heat you have to put into effect change and the physical differences between solids, liquids and gasses.

In the solid the particles are arranged in a regular pattern - the crystal structure.
This posesses short range order because each particle is close to (even touching) a specific number of neighbours - 6 in my sketch ( there are other numbers possible).
A solid also posesses long range order because the same pattern repeats regularly.
The particles have no scope for free movement.

In the liquid we may still have short range order as most of the particles are still in touch with 4 or 5 or 6 of their fellows.
However we have lost the long range order in the transition from solid to liquid.
The particles are still packed close so there is little volume increase with this state change.
The particles still exert direct forces upon each other and have limited scope for free movement.

In the gas the particles are no longer touching, except when they collide, all forms of order have been lost.
The only forces the particles now exert on each other are impact forces. This is where the kinetic theory comes in.
There is a large volume change from liquid to gas.

The energy of state change goes directly into creating this disorder. The technical term is that the entropy increases, but I doubt that is a grade 12 issue.

go well

 

[sophiecentaur]

@studiot
Not all solids are regular in structure.
Only for pure substances does the temperature remain the same during phase change.
Your simplified 'kinetic' description gives no reason for the change of state, which is all to do with the kinetic energy distribution of the particles compared with the potential energy between them. As with most of Science, Energy is at the bottom of things.
The liquid state is an oddity which doesn't occur at all temperatures and pressures.

 

[Studiot]

Yes there are simplifications, I think are appropriate to the level of the enquiry.

Taken with your explanation and Mapes I don't think the offering is all that bad.

However you cannot just say that the energy you put in suddenly exceeds the binding energy, without explaining why it does not all fly apart, or why you do not get local melting in pure substances.

I think the explanation is a good start and Pranav Jha can ask for more when this is digested.

 

[sophiecentaur]

How can it "suddenly fly apart"? The binding energy I refer to is the energy for a single bond. As heat is added from outside, the KE of random molecules exceeds this binding energy and allows separation. The proportion of added energy that turns up as Potential will increase as more molecules acquire KE from outside. Part of the substance will be liquid and part will be solid. There will be a continual exchange from KE to PE and back but with an increasing amount of PE. any excess of KE will transfer to PE so temperature cannot rise. Only when all bonds have broken can there be an increase in KE / temperature.

 

[Studiot]

As heat is added from outside, the KE of random molecules exceeds this binding energy and allows separation.

This explanation does not say why this heat does is not then added to some of the molecules that have been separated, further increasing their KE and spearation.

Temperature is a measure of the average kinetic energy of the particles in a substance.

If this is true, how is heat energy being added without increase in temperature since these two statements appear in opposition?

 

[sophiecentaur]

They will collide with bound molecules. Ain't that obvious? There will, of course, be a distribution of velocities which is what Your kinetic theory tells us. But molecules with high KE will lose energy and so the mean Temperature will be limited until it's all melted.
The total PE not KE is increasing whilst not completely melted.

 

[Studiot]

So what about the entropy?

 

[sophiecentaur]

You'd need to expand on that question.
Have you any serious objection to the use of KE and PE in description of what happens? Kinetic Theory of real gases uses the same ideas. Remember, you have not given any reasons at all for your views - just a description of GCSE level states of matter.

 

[Studiot]

SC you should read this thread.

https://www.physicsforums.com/showthread.php?t=479978&highlight=entropy+fusion

 

[sophiecentaur]

I read it and you discuss entropy there.
Entropy is, however, a macroscopic quantity and that particular thread is discussing water, which is an rather special substance. It would surely be better to discuss a simpler, 'ideal' solid first.

The statement that Temperature only relates to translational KE is fair enough but that's only a nicety. The balance of energy between the degrees of freedom really implies that the vibrational KE gets its share of the internal energy.
I have to go now but I'll keep thinking about it.

 

[Studiot]

They will collide with bound molecules. Ain't that obvious?

No it's not obvious at all, in fact there is a difficulty with that view.

The heat input can only be made through the edge particles, it cannot miraculously appear within the material.

These edge particles are the very ones that have the freedom to gain kinetic energy and move away from the body of the mass.
That would imply temperature stratification, which (it is strongly taught) does not happen.
I think stratification occurs if the mass is large enough but that is another issue.

 

[Cleonis]

[...] any excess of KE will transfer to PE so temperature cannot rise. Only when all bonds have broken can there be an increase in KE / temperature. [...]

It seems the didactic question is as follows: in the case of an idealized substance, is it sufficiënt to explain melting and boiling purely in terms of (average) kinetic energy and potential energy?

I guestimate that a wax such as used for candles is close enough to an idealized substance. We readily see the candle stuff transitioning between solid, liquid and gaseous phase.


This is the question by the original poster:
"Melting and boiling explanation based on the kinetic-molecular model have always confused me."

- In the solid state: influx of thermal energy is absorbed as increase of average kinetic energy. There is a slight thermal expansion, so a fraction of the energy influx converts to potential energy, but just a fraction.
As long as the wax remains a solid there is (as yet) no capacity to build up a lot of potential energy.

- Melting sets in when there is (on average) enough kinetic energy to overcome the constraint of being bound in a solid. During melting the molecules gain a lot more freedom to move relative to each other, and the influx of energy is absorbed as increase of potential energy. That is why during melting the temperature remains the same while the energy influx continues.

- When all of the sample has turned liquid the capacity for building up potential energy is saturated, and from then on the ongoing influx of energy increases the temperature again.

- At some point the average kinetic energy is so high the liquid can go into vapor all at once. The reason that substances are slowly vaporizing all the time is that the kinetic energy of the molecules is a distribution with extremes, and there are always some molecules with enough velocity to escape. Boiling occurs when even the average velocity is enough to escape.


In general, about physics education:
The point of oversimplifying is reached, I think, when you lose more than you gain. An oversimplified explanation teaches warped concepts that the learner will have to unlearn later. I try to avoid that.

I feel a simplification is justifiable when it can serve as a lasting foundation. I'm OK with telling just part of the story, as long as the learner doesn't have to unlearn some of it later on.

 

[Studiot]

Any teacher should be explaining that the kinetic theory and the molecular theory are different theories about different things and not dependent upon each other.

 

[sophiecentaur]

They are contradictory?

 

[Studiot]

They are contradictory?

Not at all, they are complementary, although I'm sure you know this.

The kinetic theory is a purely mechanical theory (non electric) about the aggregate effects of particles in the sense of classical mechanics (dynamics).
These particles need only be small enough to be considered point masses in dynamics, but these can be several orders of magnitude larger than molecules.

The kinetic theory works rather well on a qualitative level explaining many mechanical and physical phenomenon of all three principal states.

It also works very well at a quantitative level (if this is in grade 12?) for gases, allowing calculations to be made about observable physical quantities.
However it is rather less successful in similar attempts on liquids and solids.

One of the founding and principle assumptions that is made in the quantitative kinetic theory is that

"The particles do not interact with each other, except in elastic collisions"

Enter the molecular theory.
Molecules modeled by non interacting mechanical balls are perfectly good candidates for kinetic theory particles.
However molecular theory is largely about the electrical interactions between and within molecules and does indeed provide explanation and sometimes quantitative calculations to modify the kinetic theory to bring it closer to observation.