# Why does melting and boiling occur at a specific temperature?

• sgstudent

#### sgstudent

When a solid is heated, its kinetic and potential energies increases. Up to a certain point, the kinetic and potential energy is so high that any heating done to it would only increase the potential energy and not the kinetic energy of the solid anymore. When this happens, some of the intermolecular forces are weakened and so the average distance between particles increase (the potential energy increases) while the kinetic energy remains the same.

I'm not sure why there is a certain threshold of KE and PE then melting occurs actually. Why is this so?

Then after the solid is fully melted and heated, the kinetic energy will increase with the potential energy. This goes on until a certain point where only the potential energy increases (boiling). When boiling occurs, now the intermolecular forces are completely broken and so the average distance between particles continue to increase (PE increases) while the kinetic energy remains the same.

Again I'm not sure what determined the threshold of KE and PE to which boiling occurs. Why don't the KE continue increasing with the PE until the bonds are weakened such that a liquid is forms. In other words, why can't it be a gentle increase in both energies so that the change from one state to another isn't indicated by the constant KE and increasing PE and instead the gradual change from solid to liquid cannot be pinpointed at one specific level of KE and PE.

Could anyone explain why must the KE be constant during any of this processes?

Temperature is not equal to kinetic energy. There was a recent thread on temperature that might help clear things up: https://www.physicsforums.com/showthread.php?t=713354

That helped me understand what temperature really is but I still don't get why there is even such a thing as melting or boiling.

Because if we just took a object and heated it, initially the kinetic energy and potential energy would increase until it reaches a point where only the potential energy increases. But I don't really get why this happens. I thought that if we continued to heat up the object, then why not the kinetic and potential energy continues to increase. This way the particles gets further from each other as well as they receive more and more energy too.

I don't really see why in nature, there is a point where the kinetic energy just stop increasing when we apply heat to it and just have the potential energy to increase. I don't really visualize any reason for the kinetic energy to simply just stop increasing.

I'll try to answer this using my own understanding in a rather crude manner. I'm sure the senior mentors will reply to your question soon. I'm going to answer for boiling case.

First of all boiling point is defined according to Wikipedia and I believe in many standard textbooks as when the vapor pressure of the liquid is equal to the atmospheric pressure. So in this definition we can infer that pressure plays an important role in this process, and that the boiling point of a substance can change depending on the atmospheric pressure. You should know for instance the case that liquid boils at lower temperature in mountains.

Reading from your question I want to make it clear also that phase transition of a substance, that is to say the change from liquid to gas or others, occurs not only when the substance is at boiling or melting point. In fact they happen all the time. When a glass of water is at 20C for example, there is always a fraction of it which turns to gas. You know this as evaporation. If you are referring to this process, then there is no specific temperature when the liquid starts to turn to gas. The process is similar to an equilibrium process in chemical reaction. There is though this point when the majority of the liquid particles has the energy to create a pressure equivalent to that of atmospheric pressure.

When a liquid is not at boiling point, it doesn't mean that it's staying still. Boiling point is not a point where a liquid starts to change to gas.

Returning to discussion in terms of PE and KE, we can explain why KE stays constant during the process with the help of atmospheric pressure. You need to apply heat to overcome not only the bond between molecules but also the pressure from the air molecules pushing on the liquid molecules. If we want to boil water in vacuum certainly the boiling point will change, but this does not mean that the hydrogen bond strength between water molecules are suddenly weakened when we are in vacuum doesn't it?

I'll try to answer this using my own understanding in a rather crude manner. I'm sure the senior mentors will reply to your question soon. I'm going to answer for boiling case.

First of all boiling point is defined according to Wikipedia and I believe in many standard textbooks as when the vapor pressure of the liquid is equal to the atmospheric pressure. So in this definition we can infer that pressure plays an important role in this process, and that the boiling point of a substance can change depending on the atmospheric pressure. You should know for instance the case that liquid boils at lower temperature in mountains.

Reading from your question I want to make it clear also that phase transition of a substance, that is to say the change from liquid to gas or others, occurs not only when the substance is at boiling or melting point. In fact they happen all the time. When a glass of water is at 20C for example, there is always a fraction of it which turns to gas. You know this as evaporation. If you are referring to this process, then there is no specific temperature when the liquid starts to turn to gas. The process is similar to an equilibrium process in chemical reaction. There is though this point when the majority of the liquid particles has the energy to create a pressure equivalent to that of atmospheric pressure.

When a liquid is not at boiling point, it doesn't mean that it's staying still. Boiling point is not a point where a liquid starts to change to gas.

Returning to discussion in terms of PE and KE, we can explain why KE stays constant during the process with the help of atmospheric pressure. You need to apply heat to overcome not only the bond between molecules but also the pressure from the air molecules pushing on the liquid molecules. If we want to boil water in vacuum certainly the boiling point will change, but this does not mean that the hydrogen bond strength between water molecules are suddenly weakened when we are in vacuum doesn't it?

Hmm yes I think pressure is a big part of boiling. It is when the vapour pressure of water is equal to the atmospheric pressure so it can expand and do work against the atmosphere. But I don't really know how to fit it into the simple kinetic energy and potential energy increasing as heat is supplied to it. To me they sound like two different explanations and I don't really know how to fit them together. Because when water heats up at 10°C it also experiences 1 atm of pressure and at 100°C it also experiences the same external pressure. So at 10°C and heat is applied, the heat goes into the KE, PE and some work against the atmosphere as it does expand a little? But then at 100°C, the heat just goes into the PE and work against atmosphere seems strange to me. I feel like I'm clueless to why only at 100°C, then the heat doesn't go into the KE component anymore.

Hope you can clear out this problem I have with understanding this.

Thanks so much for the help :)

When the kinetic energy is enough to overcome the attractive force between molecules it becomes a gas. But you probably already knew that. The details are described nicely in the page.

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html

Especially this section:
Some energy details related to heating water

When the kinetic energy is enough to overcome the attractive force between molecules it becomes a gas. But you probably already knew that. The details are described nicely in the page.

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html

Especially this section:
Some energy details related to heating water

Hi thanks for the great link :)

But even if we knew that at a certain kinetic energy at 100°C boiling occurs to continue to increase the potential energy (as the bar graph shows) it still doesn't explain why boiling occurs only at that level of kinetic energy and why would the potential energy change only at that particular temperature. So I'm quite confused about that part actually.

Thanks :)

I don't really see why in nature, there is a point where the kinetic energy just stop increasing when we apply heat to it and just have the potential energy to increase. I don't really visualize any reason for the kinetic energy to simply just stop increasing.
It doesn't. Again: temperature is not kinetic energy. Because temperature is constant doesn't mean that kinetic energy is constant.

If you insist in thinking in terms of PE and KE, which I don't think is the best way to look at the phenomenon, consider the following example. Take a solid to be a set of classical atoms held together by springs, and look at what happens when it sublimates. As you heat up the substance, the oscillation amplitude of the atoms goes up, which increases both KE and PE. At the point of sublimation, the springs are barely holding up, and the tiniest extra energy will break a spring and an atom will escape from the solid and become part of the gas.

But to really understand what happens during phase transitions, you will need to understand what is happening in terms of entropy, and look at the change in Gibbs free energy for the different phases as a function of temperature.

Hi thanks for the great link :)

But even if we knew that at a certain kinetic energy at 100°C boiling occurs to continue to increase the potential energy (as the bar graph shows) it still doesn't explain why boiling occurs only at that level of kinetic energy and why would the potential energy change only at that particular temperature. So I'm quite confused about that part actually.

Thanks :)

Not sure I understand the PE part, but, roughly speaking, for any material the attractive forces between molecules is defined and "constant" so the amount of vibration it takes to break it loose is fixed and consistent. Are you asking why the amount of vibration needed to break them loose always happens at a specific temperature? At a certain amount of "joules per mole"?

It doesn't. Again: temperature is not kinetic energy. Because temperature is constant doesn't mean that kinetic energy is constant.

If you insist in thinking in terms of PE and KE, which I don't think is the best way to look at the phenomenon, consider the following example. Take a solid to be a set of classical atoms held together by springs, and look at what happens when it sublimates. As you heat up the substance, the oscillation amplitude of the atoms goes up, which increases both KE and PE. At the point of sublimation, the springs are barely holding up, and the tiniest extra energy will break a spring and an atom will escape from the solid and become part of the gas.

But to really understand what happens during phase transitions, you will need to understand what is happening in terms of entropy, and look at the change in Gibbs free energy for the different phases as a function of temperature.

I agree with DrClaude, it would be a bit difficult to see the phenomenon with PE and KE approach. But unfortunately I also believe this is the way used by some introduction physics books or curriculum. I can remember this concept being used when I studied for A Level and it got pretty murky there when you decide to explain non-ideal gas with this approach. On the other hand I'm not sure if advance concept like Gibbs free energy or entropy are even taught to students.

Hi thanks for the great link :)

But even if we knew that at a certain kinetic energy at 100°C boiling occurs to continue to increase the potential energy (as the bar graph shows) it still doesn't explain why boiling occurs only at that level of kinetic energy and why would the potential energy change only at that particular temperature. So I'm quite confused about that part actually.

Thanks :)

Well boiling occurs because if you follow the definition of boiling point, it is at that particular energy does the liquid molecules has the ability to create a vapor pressure equivalent to the atmospheric pressure. Indeed in different atmospheric pressure you will as I stated before have different boiling point.

It doesn't. Again: temperature is not kinetic energy. Because temperature is constant doesn't mean that kinetic energy is constant.

If you insist in thinking in terms of PE and KE, which I don't think is the best way to look at the phenomenon, consider the following example. Take a solid to be a set of classical atoms held together by springs, and look at what happens when it sublimates. As you heat up the substance, the oscillation amplitude of the atoms goes up, which increases both KE and PE. At the point of sublimation, the springs are barely holding up, and the tiniest extra energy will break a spring and an atom will escape from the solid and become part of the gas.

But to really understand what happens during phase transitions, you will need to understand what is happening in terms of entropy, and look at the change in Gibbs free energy for the different phases as a function of temperature.

Hi thanks for the reply :)

But I thought as the hyperlink article shown the kinetic energy of the ice at 0°C is the same as water at 0°C? For the example, is it because the after the spring snaps the atoms would just travel at the velocity just before snapping?

I'm not too sure how to use Gibbs free energy for this actually. I thought we used the idea that temperature stays constant during any phase change for Gibbs free energy. Where is a good start to learn and understand more about this in the recommended sense?

I agree with DrClaude, it would be a bit difficult to see the phenomenon with PE and KE approach. But unfortunately I also believe this is the way used by some introduction physics books or curriculum. I can remember this concept being used when I studied for A Level and it got pretty murky there when you decide to explain non-ideal gas with this approach. On the other hand I'm not sure if advance concept like Gibbs free energy or entropy are even taught to students.

Well boiling occurs because if you follow the definition of boiling point, it is at that particular energy does the liquid molecules has the ability to create a vapor pressure equivalent to the atmospheric pressure. Indeed in different atmospheric pressure you will as I stated before have different boiling point.

Hmm but how does the pressure let us know that the boiling would occur at a constant temperature rather than to increase during the process too? Because even if the vapour pressure of water=external vapour pressure, I still don't really see why the kinetic energy of the liquid must remain constant. Because if if we just use the graph of the vapour pressure of water against temperature, then I would think that if we increase the temperature to 101°C, then the water would boil faster as now the vapour pressure of the water is greater than of the atmosphere. But we know using the first concept that when water boils at 100°C its temperature would not increase anymore. So I feel that that graph that tells us about the pressure and boiling point doesn't really explain why temperature must remain constant.

Thanks so much for the help guys :)

But I thought as the hyperlink article shown the kinetic energy of the ice at 0°C is the same as water at 0°C? For the example, is it because the after the spring snaps the atoms would just travel at the velocity just before snapping?
I'm not sure where you see that the kinetic energies are the same. It doesn't make sense to talk about the KE of a harmonic oscillator at constant total energy as the energy keeps changing from KE to PE and back.

I'm not too sure how to use Gibbs free energy for this actually. I thought we used the idea that temperature stays constant during any phase change for Gibbs free energy. Where is a good start to learn and understand more about this in the recommended sense?
My comment was more to answer the question as to why the phase change occur. When you plot G vs T for both phases, you will see them cross at the temperature of the phase transition. So going from low T to high T, you will find that for instance the solid phase has a lower G than the liquid phase until Tmelt is reached, after which the liquid has the lower G. So basically the system is always in the state of lowest G.

The way to see it, I think, is to think of energy only. As the substance heats up, the energy added to the system raises its temperature, increasing the relative motion of the molecules composing the substance. At the the temperature of the phase transition, additional heat goes into actually transforming the substance from one phase to another, and therefore temperature does not increase. One the phase transition is complete, heat supplied once again goes into relative and internal motion, and the temperature goes up.

I'm not sure where you see that the kinetic energies are the same. It doesn't make sense to talk about the KE of a harmonic oscillator at constant total energy as the energy keeps changing from KE to PE and back.

My comment was more to answer the question as to why the phase change occur. When you plot G vs T for both phases, you will see them cross at the temperature of the phase transition. So going from low T to high T, you will find that for instance the solid phase has a lower G than the liquid phase until Tmelt is reached, after which the liquid has the lower G. So basically the system is always in the state of lowest G.

The way to see it, I think, is to think of energy only. As the substance heats up, the energy added to the system raises its temperature, increasing the relative motion of the molecules composing the substance. At the the temperature of the phase transition, additional heat goes into actually transforming the substance from one phase to another, and therefore temperature does not increase. One the phase transition is complete, heat supplied once again goes into relative and internal motion, and the temperature goes up.

Hi thanks for the reply. :)

kinetic energy and potential energy keeps converting from one form to another. So what actually happens during a phase change since they keep changing? I think I read somewhere which said that the maximum KE=total internal energy as they keep oscillating from PE to KE. So what is meant when they say during a temperature increase both the KE and PE increase since they are actually the same thing? So actually during a phase change is the kinetic energy actually constant or does it change around too? Because I thought if temperature is constant, and it is proportional to the average particle's kinetic energy the kinetic energy should also be constant during heating.

Lastly do you have a link to that graph and explanation? I couldn't get much results when searching for the G against T graph for the phase changes.

Thanks so much for the help :)

kinetic energy and potential energy keeps converting from one form to another. So what actually happens during a phase change since they keep changing? I think I read somewhere which said that the maximum KE=total internal energy as they keep oscillating from PE to KE. So what is meant when they say during a temperature increase both the KE and PE increase since they are actually the same thing? So actually during a phase change is the kinetic energy actually constant or does it change around too? Because I thought if temperature is constant, and it is proportional to the average particle's kinetic energy the kinetic energy should also be constant during heating.
Again, please please please stop thinking of temperature as KE. For an ideal gas, there is a simple relation between the two, and for gases in general higher temperature means higher kinetic energy, but mixing the two concepts will get you in trouble later.

Going from solid/liquid to gas, basically you are transforming the energy that was stored in the inter-molecular interaction, so both PE and KE in the harmonic oscillator approximation, into kinetic energy in the gas, if you neglect the interaction between molecules in the gas.

Lastly do you have a link to that graph and explanation? I couldn't get much results when searching for the G against T graph for the phase changes.
I good textbook should have such a figure. The figs. from Schrpeder's An Introduction to Thermal Physics are available online: http://physics.weber.edu/thermal/figures.pdf
There isn't exactly the figure I mentioned, but Fig. 5.15 shows the principle for the conversion of graphite to diamond as pressure changes.

Hmm but how does the pressure let us know that the boiling would occur at a constant temperature rather than to increase during the process too? Because even if the vapour pressure of water=external vapour pressure, I still don't really see why the kinetic energy of the liquid must remain constant. Because if if we just use the graph of the vapour pressure of water against temperature, then I would think that if we increase the temperature to 101°C, then the water would boil faster as now the vapour pressure of the water is greater than of the atmosphere. But we know using the first concept that when water boils at 100°C its temperature would not increase anymore. So I feel that that graph that tells us about the pressure and boiling point doesn't really explain why temperature must remain constant.

Thanks so much for the help guys :)

The boiling point is defined as the temperature when the vapor pressure of the liquid is equal to the atmospheric pressure, which generally is constant unless you're changing the pressure intentionally. So from this point on we know that boiling point is constant if the atmospheric pressure is constant. You can measure the vapor pressure of the liquid at various temperatures to check this fact experimentally. Of course the vapor pressure will increase but there will only be one point where it's the same as the current atmospheric pressure.

Regarding kinetic energy I think it's been made clear by DrClaude that if you have a substance at constant temperature, it doesn't always that the particles have constant kinetic energy.

You can imagine that when boiling occurs you will not have constant mass in your container as the liquid is transformed to gas to the surrounding and we cannot consider it as one isolated system. There's no change in the temperature of water that are currently in 100C because they are in the process of changing phase. It takes time and energy to convert a certain mass of liquid to gas completely. The temperature is constant during the process for the water in liquid phase that has not yet had the energy to break free and become gas, but the fact is if you keep on adding heat on the water that is now in gas phase, the gas will eventually gain kinetic energy. Note also at same temperature gas will generally have greater kinetic energy than its liquid counterpart.

The temperature is constant during the process for the water in liquid phase that has not yet had the energy to break free and become gas, but the fact is if you keep on adding heat on the water that is now in gas phase, the gas will eventually gain kinetic energy.
Just to make things clear: during the phase change, both phases have the same temperature. (Under the usual conditions that internal equilibrium is maintained at all times.)

Again, please please please stop thinking of temperature as KE. For an ideal gas, there is a simple relation between the two, and for gases in general higher temperature means higher kinetic energy, but mixing the two concepts will get you in trouble later.

Going from solid/liquid to gas, basically you are transforming the energy that was stored in the inter-molecular interaction, so both PE and KE in the harmonic oscillator approximation, into kinetic energy in the gas, if you neglect the interaction between molecules in the gas.

I good textbook should have such a figure. The figs. from Schrpeder's An Introduction to Thermal Physics are available online: http://physics.weber.edu/thermal/figures.pdf
There isn't exactly the figure I mentioned, but Fig. 5.15 shows the principle for the conversion of graphite to diamond as pressure changes.

Hi thanks for the reply :)

I think you're right I shouldn't relate them together. But actually why is it possible for the KE of a gas to be greater than of the liquid while they are at the same temperature?

Sorry but I don't quite understand "Going from solid/liquid to gas, basically you are transforming the energy that was stored in the inter-molecular interaction, so both PE and KE in the harmonic oscillator approximation, into kinetic energy in the gas" could you explain this to me again? Sorry about that.

I managed to find a graph of molar gibbs energy, Gm against temperature, T. They said Gm(liquid)=Gm(solid) at Tm and the text box for the graph was "at low temperatures solids have the lowest atm and so form the stable phase. At higher temperatures, gases are the most stable phase. Liquids are stable at intermediate temperatures."

So for this I would think at the intersection between the solid line and liquid line is where both the solid and liquid can exist as they both have the same level of stability. From the graph I can see that at Tm if we apply more heat and raise the temperature it would become a liquid. But at exactly that temperature what is happening?

Thanks so much for the help :)

I think you're right I shouldn't relate them together. But actually why is it possible for the KE of a gas to be greater than of the liquid while they are at the same temperature?
What does it mean to have the same kinetic energy? Are you thinking that all molecules in a gas at a given temperature have the same speed? Because they don't.

Sorry but I don't quite understand "Going from solid/liquid to gas, basically you are transforming the energy that was stored in the inter-molecular interaction, so both PE and KE in the harmonic oscillator approximation, into kinetic energy in the gas" could you explain this to me again? Sorry about that.
Think of two classical atoms held together by a spring, just below the breaking point. The system has both PE and KE. Add an epsilon of energy, the bond breaks, at your are left with only KE. So the total energy, which included a PE component, is now converted to KE.

I managed to find a graph of molar gibbs energy, Gm against temperature, T. They said Gm(liquid)=Gm(solid) at Tm and the text box for the graph was "at low temperatures solids have the lowest atm and so form the stable phase. At higher temperatures, gases are the most stable phase. Liquids are stable at intermediate temperatures."

So for this I would think at the intersection between the solid line and liquid line is where both the solid and liquid can exist as they both have the same level of stability. From the graph I can see that at Tm if we apply more heat and raise the temperature it would become a liquid. But at exactly that temperature what is happening?
You have an equilibrium between the two. Molecules are constantly going from one phase to the other. If you start with a solid and increase its temperature to exactly the melting point, you still have a solid. Any additional energy you add will be used to overcome the strong attraction in the solid and put molecules in the liquid phase. Stop adding energy, and the mixture of solid and liquid will keep the same proportions, but some molecules are constantly going from one phase to the other at the interface. Continue adding energy and the fraction of liquid will increase up to the point where it is all liquid, still at the melting temperature. Additional energy will then increase the temperature of the liquid.

Melting does not happen at a specific temperature. Except when special conditions are met:

1: Slow heating
2: Stuff that is heated must not be asphalt or butter or other similar stuff.

Melting does not happen at a specific temperature. Except when special conditions are met:

1: Slow heating
As I mentionned earlier, we are of course considering that the system is considered to always be in internal equilibrium. That said, even if not all parts of the system are at the same temperature, it is those parts where the melting temperature is reached that will melt.

2: Stuff that is heated must not be asphalt or butter or other similar stuff.
We are obviously talking only about pure substances, not mixtures.

At a microscopic level, molecules are constantly evaporating and condensing. These are reverse reactions. The concept of boiling only exists at a larger scale, since it is a thermodynamics concept, which deals with statistical averages. When the temperature is raised, the rate of evaporation increases since more molecules have the energy to escape the surface. The rate of condensation increases with the partial pressure of the vapor since more pressure = more molecules of the vapor hitting the surface and getting stuck.

In a closed vessel, the liquid and vapor will reach some kind of equilibrium. But in an open vessel, the atmosphere is assumed to be an infinite reservoir. Depending on atmospheric humidity, which depends on the partial pressure of the vapor and the temperature, the liquid will eventually evaporate completely or the vapor will condense as dew. You don't have to reach the boiling point for all the liquid to evaporate away. But evaporation only happens at the surface, so it is a relatively slow process.

Something special happens at the boiling point. This is the point where the pressure of the atmosphere is low enough that the vapor pressure matches the atmospheric pressure. Slightly above this point, bubbles can expand in the liquid because the gas generated by the reaction has enough pressure to push the liquid up and out of the way. Therefore, evaporation can occur throughout a large volume of the liquid, not just the surface. If the liquid is in a tall vessel, the bottom of the liquid is at a higher pressure than the top of the liquid and requires a higher temperature for the bubbles to grow.

Someone correct me if I'm wrong: I think the dew point and the boiling point are essentially the same thing when the atmosphere consists completely of one type of vapor.

The melting point conceptually similar to the boiling point, except that it is less sensitive to pressure since the density of the liquid phase and solid phase are similar. You can still have a concept analogous to partial pressure in the liquid if it's a mixture (like salt water). I suppose there should be two kinds of melting points for a mixed liquid: one analogous to the dew point and one analogous to the boiling point. But I might be totally wrong on this.

Melting does not happen at a specific temperature. Except when special conditions are met:

1: Slow heating
2: Stuff that is heated must not be asphalt or butter or other similar stuff.

We are obviously talking only about pure substances, not mixtures.

2: Stuff that is heated must not be asphalt or butter or other similar stuff.
Neither may it be glass (silicon dioxide, not a mixture).
But bronze, which is a mixture of copper and tin, it may be.
Also water has a sharp freezing point, although lot of energy is released when water molecules start sticking more tighly togerher, when water is cooled from 10 C to 5 C, for example.

What does it mean to have the same kinetic energy? Are you thinking that all molecules in a gas at a given temperature have the same speed? Because they don't.

Think of two classical atoms held together by a spring, just below the breaking point. The system has both PE and KE. Add an epsilon of energy, the bond breaks, at your are left with only KE. So the total energy, which included a PE component, is now converted to KE.

You have an equilibrium between the two. Molecules are constantly going from one phase to the other. If you start with a solid and increase its temperature to exactly the melting point, you still have a solid. Any additional energy you add will be used to overcome the strong attraction in the solid and put molecules in the liquid phase. Stop adding energy, and the mixture of solid and liquid will keep the same proportions, but some molecules are constantly going from one phase to the other at the interface. Continue adding energy and the fraction of liquid will increase up to the point where it is all liquid, still at the melting temperature. Additional energy will then increase the temperature of the liquid.

Hi thanks again for the response :)

I was thinking the kinetic energy of the particles would be about the same not speed. So the 1/2mv2 would be roughly the same? And that value would be proportional to the temperature. But u guess that's a wrong way to look at it.

So for the liquid to gas case, the KE of the gas is greater than the liquid at the same temperature?

Lastly, I think I'm understanding it already. But I was wondering when the ice has partially melted can the water part rise is temperature or are we assuming that thermal equilibrium is always maintained so if the water gains any excess heat it would immediately transfer it to the ice such that the temperatures are always fixed at Tm?

Thanks so much for the help :)

I was thinking the kinetic energy of the particles would be about the same not speed. So the 1/2mv2 would be roughly the same? And that value would be proportional to the temperature. But u guess that's a wrong way to look at it.
Look up the Maxwell-Boltzmann distribution.

So for the liquid to gas case, the KE of the gas is greater than the liquid at the same temperature?
Yes, average KE for a gas is higher because it has less PE.

Lastly, I think I'm understanding it already. But I was wondering when the ice has partially melted can the water part rise is temperature or are we assuming that thermal equilibrium is always maintained so if the water gains any excess heat it would immediately transfer it to the ice such that the temperatures are always fixed at Tm?
Yes, such a theoretical description assumes internal equilibrium: exchange of heat within the system is much faster than exchange of heat with the environment.

Of course, reality is hardly ever ideal. If you have an open container that is heated on all sides, then that container can heat up directly the gas once boiling has started, and you can get the gas hotter than the liquid. Likewise, since it is open some gas molecules will escape the container, and they tend to be the ones with the most energy (those going the fastest). In a previous post, Khashishi also pointed out some other things to consider for a real system.

Look up the Maxwell-Boltzmann distribution.

Yes, average KE for a gas is higher because it has less PE.

Yes, such a theoretical description assumes internal equilibrium: exchange of heat within the system is much faster than exchange of heat with the environment.

Of course, reality is hardly ever ideal. If you have an open container that is heated on all sides, then that container can heat up directly the gas once boiling has started, and you can get the gas hotter than the liquid. Likewise, since it is open some gas molecules will escape the container, and they tend to be the ones with the most energy (those going the fastest). In a previous post, Khashishi also pointed out some other things to consider for a real system.

Hi thanks for the reply :)

I read about this before and it shows that some molecules have more KE than others but most have a moderate amount while few has either a lot or very little KE?

So the gas at the same temperature of boiling point has a greater KE than the liquid but does the gas have a greater total internal energ? If so does it mean now the KE the gas has is like the KE of the liquid +PE of liquid + extra energy from the heating?

Oh I think I understand the Gibbs free energy explanation better now but as I was reading my book, it shows that dG=0 so dH=TdS and for dH and dS they used the dH naught and dS naught to solve for T. But I thought when dG=0 the composition of solid and liquid is varied? Like it can be 100% solid and 0% liquid so how can we use the dH naught and dS naught which assumes 100% change?

or is it because even at 100% liquid and 0% solid the dG can still be zero as long as we do not increase the temperature and let it stay at melting point then the dG would still be zero? But in this case when we use the dGo=-RTlnKeq to solve for our Keq our Keq would be a constant but at 100% solid isn't the Keq 0?

thanks so much for the help :)

So the gas at the same temperature of boiling point has a greater KE than the liquid but does the gas have a greater total internal energ? If so does it mean now the KE the gas has is like the KE of the liquid +PE of liquid + extra energy from the heating?
The gas has to have slightly higher total energy, coming from the breaking of the bonds between the molecules. But the difference will be small.

Oh I think I understand the Gibbs free energy explanation better now but as I was reading my book, it shows that dG=0 so dH=TdS and for dH and dS they used the dH naught and dS naught to solve for T. But I thought when dG=0 the composition of solid and liquid is varied? Like it can be 100% solid and 0% liquid so how can we use the dH naught and dS naught which assumes 100% change?

or is it because even at 100% liquid and 0% solid the dG can still be zero as long as we do not increase the temperature and let it stay at melting point then the dG would still be zero? But in this case when we use the dGo=-RTlnKeq to solve for our Keq our Keq would be a constant but at 100% solid isn't the Keq 0?
I'm sorry, but I don't undertsand what you mean here.

The gas has to have slightly higher total energy, coming from the breaking of the bonds between the molecules. But the difference will be small.

I'm sorry, but I don't undertsand what you mean here.