Phase changes

Matter can exist in three aggregate states, i.e., solid, liquid and gas. The passages from one state to another (by adding or removing heat) are known as phase changes. The transformation from the solid state to the liquid state is said fusion or melting, the inverse is said solidification. The transformation from the liquid state to the vapor state is said vaporizzation, the inverse is said condensation. Some substances can pass from the solid state directly to the vapor state (i.e., without passing from the liquid state) and viceversa. The term sublimation is used to indicate such transormations.

Fusion is the passage from the solid state to the liquid state and it requires heat (energy) to take place.

Let's consider the heating of ice (1 atm) from -10 ^oC to 0 ^oC, at beginning we can observe an increase of temperature and when the temperature reach 0 ^oC, fusion (melting) begins (formation of liquid water). The temperature at which fusion begins (0 ^oC and 1 atm, in the case of water) is said fusion (melting) temperature. By further addition of heat, until ice and water coexists, no change of temperature is observed (line B-C in figure). Once all ice is transformed into water (point C) the temperature starts to increase again.

The heat which does not produce a temperature change is said latent heat of fusion (it is used to breakdown attractive forces between molecules and no temperature change is observed). On the contrary, the heat which produces a temperature change is said sensible heat (line A-B).

Notes on fusion 1. Not all substances has a constant temperature of fusion, in fact a constant temperature is observed only for crystalline solids but not for amorphs (not crystalline) solids such as glass, wax, etc. 2. For some substances (e.g., wood, bones) no fusion can be observed, they just decompose whe heat is supplied. 3. For most substances the volume of the liquid phase is greater than that of the solid phase. Water is an important exception. 4. The fusion temperature depends on pressure. When the volume of the liquid phase is greater than that of the solid phase, an increase of pressure leads to an increase of the fusion temperature. Otherwise (e.g., water) an increase of pressure lead to a diminution of the fusion temperature. The effect of pressure on the fusion temperature can be explained on thermodynamics base (see later, equation of Clausius-Clapeyron)

A simple experiment can demonstrate that the fusion temperature of ice decreases when pressure increases. Consider a block of ice on which is placed a very thin string of steel having at the extremities two big weights (see figure). Since the surface of contact between ice and steel is very small, weights will generate a considerable increase of pressure at surface contact. Since an increase of pressure leads to a decrease of the fusion temperature ice becomes liquid and the string moves down. Liquid water is now above the string and it experiences the normal pressure and solidification occurs. Therefore the string will pass through the ice block without dividing it in two parts.

The process of solidification can be illustrated with the same graph used for fusion. Consider the cooling of liquid water (any point on the line CD), we will observe a decrease of temperature until we reach point C at which water begin to solidify (the corresponding temperature is the temperature of solidification which matches the temperature of fusion). By further cooling, the temperature will remain constant untill all liquid water is transformed in ice. The heat needed to transform all water in ice is said latent heat of solidification which is equal to the latent heat of fusion.

For some substances, when cooled slowely, it is possible to exceed the solidification temperature (at a given pressure) without observing the formation of the solid. Such liquids are said subcooled and are very unstable, in fact by means of a light shaking it solidify reaching the solidification temperature (it warm up).

Vaporization

Vaporization is the passage from the liquid state to the gas (vapor) state and it requires heat (energy) to take place.

Vaporization in a close container.

When the evaporation takes place in a closed evacuated container at constant temperature, we can observe that

only part of the liquid evaporates;

the pressure exerted by vapor molecules increases with time until to reach a constant value.

These observations can be explained by considering that vapor molecules can return to the liquid state (condensation) and the rate at which vapor molecules condense depends on pressure (the higher the pressure the higher the rate of condensation). At the beginning the rate of evaporation is greater than the rate of condensation and we observe a net formation of vapor but as the pressure increases the rate of condensation increases until to matches the rate of evaporation and no more vapor is formed. When the liquid-vapor equilibrium is reached we have that evaporation rate = condensation rate and the pressure exerted by vapor is constant. This equilibrium pressure is known as the vapor pressure. The concept of vapor pressure will be deepen later on these pages. Here we just note that vapor pressure measures the tendency of a liquid to enter the vapor state (the higher the vapor pressure the higher the rate of evaporation) and it depends only on temperature (the higher the temperature the higher the vapor pressure).

As an example of this last point we can compare the vapor pressure of three commonly encountered liquids (values in torr at 30°C):

Water (the less volatile)	Ethyl alcohol	Acetone (the most volatile)
31.82	78.8	282.7

Vaporization in a open container.

A common experience is that liquids of relative low boiling temperature, placed in a container open to the atmosphere, will ultimately evaporate entirely. This can be explained by considering that

in order to enter vapor state, molecules need energy to break-down the attractive forces of their neighbors molecules. In fact, when a volatile liquid, e.g. ether, is applied on the skin we can determine the cooling of the skin. This due to the fact that the energy needed for evaporation is taken  from the skin thus producing a diminution of temperature. Some liquids, such as ethyl chloride can be used as local anesthetics for they freeze the skin upon evaporation. 

the energy of molecules in a liquid is distributed according to Maxwell-Boltzmann law which can be briefly summarized as follows:

If E is the energy molecules should have to evaporate, the number of molecules having an energy greater than E is proportional to e^-E/kT.

At a given temperature, some molecule exist having enough energy to enter the vapore state (red molecules). Once these molecules are lost in the atmosphere, in the remaining liquid there will be a redistribution of the energy (according to Boltzmann factor) and new molecules will have an energy greater than E and evaporation continues until no liquid is left.

Boiling process

Normally, for a liquid in a container open to the atmosphere the pressure above the liquid is due to the vapor molecules and to air. We can imagine that, on the surface of the liquid there exists an envelope containing vapor molecules and air. Suppose that the atmospheric pressure is 1 atm (101.3 kPa). In 'absence' of vaporization the pressure exerted by air is 101.3 kPa and it is due only to air molecules. But, when vaporization occurs part of air molecules are pushed out, by water molecules, from the envelope above the liquid. The total pressure will be always 101.3 kPa but now it is due both to vapor and air molecules. According to Dalton' law, we have that

Total pressure = P_air + P_vapor = 101.3 kPa

In the following table is reported the vapor pressure of water at different temperatures along with the pressures of air calculated according to Dalton's law:

As can be seen, at 100^oC, the vapor pressure of water is exactly 101.3 kPa and thus only water molecules will be in the space over the liquid. At this temperature, known as boiling point, the liquid starts to boil and a further administration of heat will not increase the temperature until all water is evaporated.

The boiling process is characterized by the formation and the growt of bubbles of vapor throughout the bulk of a liquid. The initiation of a bubble in a liquid is a very difficult process, in fact it requires that many molecules of energy greater than that needed for vaporization must be close one other. Thus, it is not always guaranteed that a liquid starts to boil at its boiling temperature. In such condition, the administration of further heat will produce a superheated liquid, i.e. a liquid having a temperature greater than its boiling point. When the formation of bubbles in a superheated liquid eventually occur, it can be very violent and dangerous. In fact, since the vapor pressure in bubbles greatly exceeds atmospheric pressure, the bubbles tend to expand rapidly. The violent boiling (said bumping) can be avoided by introducing materials which initiate bubbles in the liquid as soon as the boiling point is reached. For example, porous pieces of ceramic which evolve small bubbles of air into which evaporation can occur.

Notes: The pressure and temperature at which a phase change takes place are said saturation pressure and saturation temperature respectively. When a substance occurs in the liquid state at its saturation conditions, it is said saturated liquid. As an example, liquid water at 100 oC and 1 atm water starts to boil and it is a saturated liquid. On the other hand the term saturated vapor is used to indicate a substance that occurs in vapor state at its saturation temperature and saturation pressure. Steam at 100 oC and 1 atm is a saturated vapor. If, after the complete transformation into vapor, further heat is administered we obtain a vapor with a temperature greater than its saturation temperature, i.e. a superheated vapor.