Everyone has a memory of when they were a kid and the ice cream unexpectedly (and unintentionally) melted. Maybe you were on the beach trying to keep up with the splashes of melted ice cream, but then the whole ball landed in the sand. Maybe you've left a lollipop in the sun for too long and ended up back in a pool of colorful sugar water. Whatever your experience, most people have a clear memory of something in their mind.*solid phase*to make transition*liquid phase*and the consequences of this change.

Of course, physicists have a specific language to describe these phase changes between different states of matter. It should come as no surprise that different physical properties of materials determine their behavior, including the temperatures at which they undergo phase changes. Learning how to calculate the energy used in these phase changes and learning a little about the relevant physical properties is crucial to understanding everything from ice melting to more unusual processes like sublimation.

## phases of matter

Most people are familiar with the three main phases of matter: solid, liquid and gas. However, there is a fourth state of matter called plasma, which is briefly described later in this article. Solids are the easiest to understand; Matter in the solid state retains its shape and is not compressible to any appreciable extent.

Using water as an example, ice is the solid state and it is intuitively clear that ice would break before you could compress it to a smaller volume, and even then the broken ice would still occupy the same volume. As a possible counter-example, one could also think of a sponge, but in this case, when you "squeeze" you're really just removing any air pockets it contains in its natural state - real solids don't settle out.

Liquids take the shape of the container they are in, but cannot be compressed like solids. Again, liquid water is the perfect example of this because it's so familiar: you can put water in any shape of container, but you can't physically compress it so that it occupies less volume than it does in its natural state. Gases such as water vapor, on the other hand, fill the shape of the container they are in, but can be compressed.

The behavior of each is explained by its atomic structure. In a solid there is a regular lattice arrangement of atoms, so it forms a crystalline structure or at least an amorphous mass because the atoms are fixed in place. In a liquid, molecules or atoms are free to move but are partially connected by hydrogen bonds; hence it is free flowing but has some viscosity. In a gas, the molecules are completely separate and are not held together by intermolecular forces, which is why a gas can expand and compress much more freely than solids or liquids.

## latent heat of fusion

When you add heat to a solid, you increase its temperature until it reaches its melting point, at which point things change. The heat energy you add when it's at the melting point doesn't change the temperature; provides energy for the phase transition from the solid phase to the liquid phase, commonly referred to as melting.

The equation that describes the melting process is:

Q = ml_f

Wo*EU*_{F}is the latent heat of fusion of the material,*Metro*is the mass of the substance and*Q*is the extra heat. As the equation shows, the units of latent heat are energy/mass, or joules per kg, g, or other mass measure. The latent heat of fusion is sometimes called the enthalpy of fusion, or sometimes just the latent heat of fusion.

For any particular substance, for example if you are looking specifically at ice melts, there is a specific transition temperature at which this occurs. When ice melts into liquid water, the phase transition temperature is 0 degrees Celsius or 273.15 Kelvin. You can look up the latent heat of fusion for many common materials online (see Resources), but for ice it's 334 kJ/kg.

## latent heat of vaporization

The same melting process occurs when you vaporize a substance, except the temperature at which the phase transition occurs is the substance's boiling point. But for the same reason, the extra energy you give the substance at that point goes through the phase transition, in this case from the liquid phase to the gas phase. The term used here is latent heat of vaporization (or enthalpy of vaporization), but the concept is exactly the same as for latent heat of fusion.

The equation also has the same form:

Q = ml_v

Wo*EU*_{v}This time it's the latent heat of vaporization (see Resources for a table of values for common materials). Again, each substance has a specific transition temperature, and liquid water goes through this transition at 100 °C or 373.15 Kelvin. So if you heat a certain mass*Metro*Taking water from room temperature to the boiling point and then evaporating it, there are two calculation steps: the energy needed to bring it to 100 °C and then the energy needed to vaporize it.

## Sublimation

While solid-to-liquid (i.e., melting) and liquid-to-gas (evaporation) phase transitions are the most common, there are many other transitions that can occur. in particular,*Sublimation*is when a substance undergoes a phase transition from a solid phase directly into a gaseous phase.

The best-known example of this behavior is dry ice, which is actually solid carbon dioxide. At room temperature and atmospheric pressure, it sublimes directly to carbon dioxide, making it a common choice for theatrical fog effects.

The opposite of sublimation is*opinion*where a gas undergoes a change of state directly to a solid. This is another type of phase transition that is less commonly discussed but still occurs in nature.

## Effects of pressure on phase transitions

Pressure has a major impact on the temperature at which phase transitions occur. At higher pressures the vapor point is higher and at lower pressures it is reduced. This is why water boils at a lower temperature at higher altitudes because the pressure is lower and the boiling point is lower. This relationship is usually represented in a phase diagram, which has temperature and pressure axes and lines separating the solid, liquid, and gas phases of the substance in question.

If you look closely at a phase diagram, you will see that there is a certain point where the substance is at the intersection of the three main phases (i.e. gas, liquid and solid phase). This is called*triple point*or the critical point of the substance and occurs at a certain critical temperature and pressure.

## Plasma

The fourth state of matter is plasma. This is slightly different from other states of matter as technically it is an ionized gas (i.e. the electrons have been removed so the atoms have a net electric charge) so there is no phase transition in the same way as the other states of matter.

However, its behavior differs greatly from that of a typical gas because although it can be considered electrically "nearly neutral" (because it has the same number of protons and electrons in the*at*plasma), there are pockets of concentrated charge and resulting currents. Plasmas also respond to electric and magnetic fields in ways that a typical gas would not.

## The ranking of Ehrenfest

One of the best-known ways of describing transitions between different phases is the Ehrenfest classification system, which divides transitions into first- and second-order phase transitions, and the modern system relies heavily on it. The "order" of the transition refers to the lowest derivative of the thermodynamic free energy that exhibits a discontinuity. For example, transitions between solids, liquids, and gases are first-order phase transitions because latent heat creates a discontinuity in the free energy derivative.

A second-order phase transition has a discontinuity in the second derivative of the free energy, but no latent heat is involved in the process, so they are considered continuous phase transitions. Examples are the transition to superconductivity (that is, the point at which something becomes a superconductor) and the ferromagnetic phase transition (as described in the Ising model).

Landau theory is used to describe the behavior of a system, especially around a critical point. In general there is a symmetry breaking at the phase transition temperature and this is particularly useful for describing transitions in liquid crystals where the high temperature phase contains more symmetries than the low temperature phase.

## Examples of phase transitions: melting ice

Suppose you have a 1kg block of ice at 0°C and you want to melt the ice and raise the temperature to 20°C, just above the standard ambient temperature. As mentioned above, any calculation like this has two parts: you must calculate the phase shift, and then use the usual approach to calculate the energy required to raise the temperature by the specified amount.

The latent heat of fusion of water ice is 334 kJ/kg, so using the equation above:

\begin{aligned} Q &= mL_f \\ &= 1 \text{ kg} × 334 \text{ kJ/kg} \\ &= 334 \text{ kJ} \end{aligned}

Therefore, melting ice, specifically 1 kg, requires 334 kilojoules of energy. Of course, if you work with more or less ice, the 1kg is simply replaced by the appropriate value.

As this energy was now transferred to the ice, it changed phase.*But*It's still at 0°C. To calculate the amount of heat you would need to add to raise the temperature by 20°C, simply find the specific heat of water (*C*= 4.182 J/kg°C) and use the standard expression:

Q = mC∆T

wo ∆*T*represents the temperature change. This is easy to solve with the information we have: the required temperature change is 20°C, so the rest of the process is just plugging in the values and calculating:

\begin{alineado} Q &= mC∆T \\ &= 1 \text{ kg} × 4182 \text{ J / kg °C} × 20 \text{ °C} \\ &= 83,640 \text{ J} = 83,64 \text{kJ} \end{alineado}

So the whole process (i.e. melting the ice and heating the water) requires:

334 \text{ kJ} + 83.64 \text{ kJ} = 417.64 \text{ kJ}

Therefore, most of the energy comes from the melting process, not heating. Note that this calculation only worked because the units were consistent: the mass was always in kg and the energy was converted to kJ for the final addition, and you should always check this before attempting a calculation.

## Examples of phase transitions: Evaporation of liquid water

Now imagine you took 1kg of water at 20°C from the last example and you want to turn it into steam. Please try to solve this problem before reading further as the process is basically the same as before. First you need to calculate the amount of thermal energy required to boil the water and then calculate how much additional energy is required to vaporize the water.

The first stage is like the second stage in the previous example, except now ∆*T*= 80 C since the boiling point of liquid water is 100 C. So using the same equation gives:

\begin{alineado} Q &= mC∆T \\ &= 1 \text{ kg} × 4182 \text{ J / kg °C} × 80 \text{ °C} \\ &= 334,560 \text{ J} = 334,56 \text{kJ} \end{alineado}

From the point that this amount of energy has been added, the rest of the energy goes into vaporizing the liquid and you need to calculate this using the other expression. That is:

Q = ml_v

Wo*EU*_{v}= 2256 kJ/kg for liquid water. Considering that in this example there is 1 kg of water, you can calculate:

\begin{aligned} Q &= 1 \text{ kg} × 2256 \text{ kJ/kg} \\ &= 2256 \text{ kJ} \end{aligned}

The sum of both parts of the process gives the required total heat:

2256 \text{ kJ} + 334.56 \text{ kJ} = 2590.56 \text{ kJ}

Note again that the vast majority of the heat energy used in this process (like melting ice) is in the phase transition rather than the normal heating stage.