Latent heat

The latent heat is the amount of energy required by a substance to change phase, from solid to liquid (heat of fusion) or from liquid to gas (heat of vaporization). It must be taken into account that this energy in the form of heat is invested for the phase change and not for a temperature increase.

Latent, from the Latin latens, or hidden, name referring to not noticing a change in temperature of the system while a phase change occurs (despite adding or subtract energy). The idea comes from the time when heat was believed to be a fluid substance called caloric. On the contrary, the heat that is applied when the substance does not change phase and the temperature increases, is called sensible heat.

When there is heat towards a piece of ice, its temperature increases until it reaches the Melting Point (temperature of change from solid to liquid state); from that moment on, although heat continues to flow, the energy supplied is inverted to the change of state of the system. Only when the entire system has reached the new state (in this example the gaseous state) will an increase in the temperature of the system begin to be observed.

The concept was introduced around 1762 by the Scottish chemist Joseph Black.

This quality is used in cooking, refrigeration, heat pumps and is the principle by which sweat cools the body.

Latent heat of some substances

Each substance has its own latent heats of fusion and vaporization.

When latent heat is given, it is necessary to also give the temperature at which it is produced, because, to a lesser extent, there is also evaporation or fusion at other temperatures (for example, the evaporation of sweat on the skin occurs at temperatures lower than 100 °C), with different values of latent heat.

Water has a high heat of vaporization since, in order to break the hydrogen bonds that link the molecules, it is necessary to supply a lot of energy; it also has a high heat of fusion. One of the advantages of the high heat of vaporization of water is that it allows certain organisms to lower their body temperature. This cooling is due to the fact that, in order to evaporate, water from the skin (for example, sweat) absorbs energy in the form of heat from the body, which lowers the surface temperature. Another good example of the latent heat of vaporization of water is when the soil is irrigated: the water evaporates and absorbs energy, thus cooling the environment.

It is important to know that not all material systems have the same latent heat, but each substance has its own latent heat of fusion and vaporization.

Status changes

Normally, a substance undergoes a temperature change when it absorbs or gives up heat to the surrounding environment. However, when a substance changes phase, it absorbs or gives up heat without a change in its temperature. The heat Q that is necessary to provide for a mass m of a certain substance to change phase is equal to

Q=mL{displaystyle Q=mL}

where L is called the latent heat of the substance and depends on the type of phase change.

For example, for water to change from a solid (ice) to a liquid, at 0 °C it takes 334000 J/kg or 334 kJ/kg. For it to change from a liquid to a vapor at 100 °C requires 2260000 J/kg.

The changes of state can be explained qualitatively as follows:

In a solid, the atoms and molecules occupy the fixed positions of the knots of a crystal lattice. A solid has in the absence of external forces a fixed volume and a certain shape.

Atoms and molecules vibrate around their positions of stable equilibrium, each time with greater amplitude as the temperature increases. There comes a time when the attractive forces that hold the atoms in their fixed positions are overcome and the solid becomes a liquid. Atoms and molecules are still held together by attractive forces, but they can move relative to each other, causing liquids to conform to the container that contains them but maintain a constant volume.

When the temperature is increased further, the attractive forces that hold the atoms and molecules together in the liquid are overcome. The molecules are far from each other, they can move throughout the container that contains them and they only interact when they are very close to each other, at the moment they collide. A gas takes the shape of the container that contains it and tends to occupy all the available volume.

A classic example in which the concepts of specific heat and latent heat are used is the following:

Determine the heat required to convert 1g of ice at -20°C to steam at 100°C. The data is the following:

Specific heat of ice ch=2090 J/(kg K)

Heat of fusion of ice Lf=334000 J/kg

Specific heat of water c=4180 J/(kg K)

Heat of vaporization of water Lv=2260000 J/kg

Stages:

The temperature of 1g of ice is raised from -20 °C (253 K) to 0 °C (273 K)

Q1=0.001 2090 (273-253)=41.8 J

The ice melts

Q2=0.001 334000=334 J

The water temperature is raised from 0 °C (273 K) to 100 °C (373 K)

Q3=0.001 4180 (373-273)=418 J

1 g of water at 100 °C is converted into steam at the same temperature

Q4=0.001 2260000=2260 J

The total heat Q=Q1+Q2+Q3+Q4=3053.8 J.

If we have a heat source that supplies energy at a constant rate of q J/s we can calculate the duration of each of the stages

The figure, which has not been made to scale, shows how the temperature increases as heat is added to the system. The vaporization of water requires a large amount of heat as we can see in the graph and in the calculations made in the example.

The figure below is made to scale with the Microsoft Excel program, taking the data from the table Heat, Q Temperature, T 0 -20 41.8 0 375.8 0 793.8 100 3053.8 100

Measurement of the latent heat of fusion

A thermos is filled with ice and closed. A long glass tube with a small section S is passed through the stopper and two cables are connected to a resistor through which an electric current circulates that heats the ice to turn it into water at 0 °C.

Water is added through the tube to refill the bottle and the tube itself.

On the left side of the figure, the initial situation is shown. On the right side, the situation after a certain time t after connecting the resistor to a battery.

The electrical resistance heats the ice, it melts and the volume of the system decreases, as a consequence, water passes from the glass tube to the thermos. We measure the variation in height of the water in the vertical graduated tube.

The experiment consists of measuring the energy required to reduce the volume of the system by a certain amount at constant temperature and constant pressure.

In the initial state we have a mass M of ice of density ρh=0.917 g/cm³ in a volume V0.

M= ρh V0

After a certain time t, a mass Δm of ice has turned into water of density ρa=1.0 g/cm³, the volume V of the system decreases

The change in volume, in absolute value, is

To melt a mass Δm of ice and turn it into water, an amount of heat is needed

Q=Lf Δm

where Lf is the latent heat of fusion

As the volume of the system decreases, the water from the standpipe enters the thermos, decreasing the height by ΔV=SΔh

We can measure the heat Q supplied by the electrical resistance at time t.

Q=i2 R t

We measure the variation of the height Δh of water in the vertical glass tube and solve for the latent heat of fusion Lf

Example:

The section of the vertical tube is worth S=0.1782 cm²

The density of ice ρh=0.917 g/cm³

The density of water ρa=1.0 g/cm³

Q=13140 J is required for the water level in the standpipe to decrease by Δh=20 cm. All these processes are used in the matter that is. That is to say, it is everything that occupies a place in space, can be touched, can be felt, can be measured, etc.