Can latent heat exist when both phases cannot exist at same temperature?

Question

This is my understanding (please tell me if i am going wrong anywhere):

During phase change (i.e. ice melting into water) the molecules absorb heat, gain more random kinetic energy, and spread apart (leading to weaker intermolecular bonds). When all the molecules are separated enough to become fluid, they turn into water. However, in a real life scenario some molecules become fluid earlier than the others. In this case, any heat added to the 'ice' goes into separating the bonds and the temperature stops rising. Latent heat is the energy required to sufficiently separate all the bonds enough to change phase.

My question is: If water and ice could not co-exist at the same temperature (0 degrees Celsius), would there still be a latent heat and the 'plateau regions' on a heating curve. If any of my reasoning is wrong, please explain why the temperature stops rising during phase change.

Answer 1

During phase change (i.e. ice melting into water) the molecules absorb heat, gain more random kinetic energy, and spread apart (leading to weaker intermolecular bonds).

During phase change there is no increase in temperature and so no increase in random kinetic energy. There is only an increase intermolecular potential energy causing breakage of bonds.

When all the molecules are separated enough to become fluid, they turn into water.

Ice is converted to water at constant temperature all during the phase transition. This requires 334 kJ of heat for each kg of ice melted (latent heat of fusion). When all the ice becomes water the change in phase is complete. Additional heating raises the temperature of the water until the next phase change begins.

My question is: If water and ice could not co-exist at the same temperature (0 degrees Celsius), would there still be a latent heat and the 'plateau regions' on a heating curve

But water and ice do in fact co-exist during phase transition. Liquid and gas also co-exist during the phase transition from liquid to gas. For the liquid to gas transition, at 1 atmosphere 2260 kJ of heat is required to convert each kg of water to water vapor (latent heat of vaporization).

Hope this helps.

Answer 2

I would answer this question with a quick introduction to thermodynamics.

In short, thermodynamics is the science of the most probable outcome - no more, no less. Imagine a very zoomed in view on a surface layer between water and steam. Sometimes, the wiggling of the molecules in the liquid will "interfere constructively" to give one of the outermost so much of a push that it will overcome surface tension and leave the liquid, becoming part of the vapor. Sometimes, an incoming molecule from the gas will hit the surface so slow that its energy can be dissipated on impact and it will stick, becoming part of the liquid.

How probable these events are, is measured by entropy - it tells you how many microscopic configurations of the molecules make up the same "state", with a configuration being defined by each molecule's position and velocity. The more possible configurations, the more probable it is, that your system will end up in one of them. Here "state" means whatever you want it to mean. It might be "all molecules being in one half of a container" or "more than 99% of the molecules being part of the liquid". Just count the amount of possible configurations of the system respecting your boundary configurations (usually a given total energy) and how many of those are favorable to your state. Entropy is just a fancy way to formulate, albeit a very smart one because it allows for easy quantitative calculations.

If you are uncomfortable with using the term "counting" when there is a continuous range of positions and speeds, just imagine binning your cooridnates so that only some values are allowed for both position and speed.

If you do not include an interaction energy of the molecules in your description of them, you will obviously find that it is not very probable that they all huddle up in one place. However, if they do not have an excessive amount of total energy to go around to begin with and more energy can be freed by molecules touching, it may well be the case that there are more possible states to clump and vibrate a lot than to just fly around slowly.

In case you are wondering why there are more posibilities if you move faster: Imagine a single molecule flying around with a fixed speed ${v}$ (to keep energy constant). If you draw a coordinate system for the velocity components in the x-, y- and z-directions, all allowed velocities lie on a sphere with radius ${v}$. To count the amount of possible configurations, you integrate over the surface area of this sphere and end up with ${4\pi v^2}$ (but you can also use the binning method again, count the bins that intersect the surface and end up with an approximate result), so quadratically more possibilities with increasing speed.

To balance this interplay of gaining energy by clumping together and being able to move around freely, different phases of matter arise, like vapor (completely free motion), water (some energy is freed by staying in close proximity) and ice (much energy is freed by staying in an order that almost perfectly minimizes potential).

Going back to your question, if you want to move your thought experiment to a point in parameter space where H${_2}$O can neither be water nor ice (e.g. by applying pressure, temperature, magnetic field, whatever), then you are really saying that there are more possible states to be in another phase, so the molecules will end up in one of those configurations. However, this also means that there will not be a point where there is a phase transition from water to ice, but from water to something else and then to ice if you vary some parameter even more. But still, conservation of energy still applies, of course, so if you look at the total energy difference of water at some starting temperature and vapor at some end temperature, you have to supply exactly that amount of energy to get there, no matter what path you take. It may involve adding latent heat at some phase transition(s), which would mean that the energy content of the the phases differs at that exact point, or it may mean you take a designed path through parameter space so there is a smooth transition (if that interests you, type "critical point" in your favorite search engine).

One additional thing: Why does thermodynamics get away with just looking at the most probable case? Imagine a box that you keep filling with non-interacting particles while watching if all of them ever end up on the left half of the box.

With 1 particle, this happens 50% of the time (${1/2^1}$), with 2 particles it's 25% (${1/2^2}$). With only 100 particles, this number (${1/2^{100}}$) is already smaller than ${10^{-30}}$. For comparison, the age of the universe in micro seconds is only about ${4*10^{23}}$, so if you set this experiment in motion right at the big bang with the particles moving so fast that you can claim that you see a new random configuration every micro second or even nano second, at present day you probably still would not have seen all of them on the same side for that fraction of a second even once. And that's just 100 particles - just a gramm of water has almost ${10^{20}}$ particles, so unless you look at just a handfull of particles, you can savely ignore any case that is not the most probable.

ADDED: If this is not perfectly clear yet: The temperature stops rising at the plateau, because energy coming into the system is stored as potential energy of molecules leaving the "energy well" of their neighbors in the liquid as they become gas and and not in kinetic energy going faster, i.e. being hotter.