KAHIBARO
Table of Contents
Hidden energy in phase changes
Latent heat is the energy transferred as heat during a change of phase, such as melting, freezing, boiling, or condensation, while the temperature stays constant. This idea is important because not all heat added to a substance makes it hotter. Sometimes the energy goes into changing the arrangement of particles instead of increasing their average kinetic energy.
When ice melts into water, the temperature of the ice-water mixture remains at $0^\circ \mathrm{C}$, if the pressure is normal atmospheric pressure, until all the ice has melted. Likewise, when water boils at $100^\circ \mathrm{C}$ under normal atmospheric pressure, the temperature stays constant until the liquid has fully turned into vapor. During these processes, heat is still being transferred, but the temperature does not rise.
Why temperature does not change
Temperature is related to the average kinetic energy of particles. During a phase change, the added heat is mainly used to overcome intermolecular forces or to rearrange the structure of the substance. Because the energy is not going into increasing particle speed, the temperature remains constant.
For melting, the substance absorbs energy so that particles can move more freely than they could in the solid state. For boiling, even more energy is needed so that particles can separate widely and form a gas.
During a phase change at constant pressure, heat can be added or removed without changing the temperature.
Latent heat and its types
The word latent means hidden. The energy is called latent because it does not appear as a temperature change.
There are two main latent heats commonly studied.
| Process | Name | Symbol | Meaning |
|---|---|---|---|
| Solid to liquid | Latent heat of fusion | $L_f$ | Energy per unit mass needed to melt a substance |
| Liquid to gas | Latent heat of vaporization | $L_v$ | Energy per unit mass needed to vaporize a substance |
The reverse processes use the same amount of energy per unit mass, but heat is released instead of absorbed. So freezing releases the same amount per kilogram as melting absorbs, and condensation releases the same amount per kilogram as vaporization absorbs.
The latent heat formula
If a mass $m$ of substance changes phase, the heat transferred is
$$
Q = mL
$$
where $Q$ is the heat transferred, $m$ is the mass, and $L$ is the specific latent heat of the phase change.
If the process is melting or freezing, then
$$
Q = mL_f
$$
If the process is boiling or condensation, then
$$
Q = mL_v
$$
In SI units, latent heat is measured in joules per kilogram, $\mathrm{J/kg}$.
Important formula:
$$
Q = mL
$$
Here, $L$ is the latent heat per unit mass, not a length.
Sign of heat transfer
The sign of $Q$ depends on whether heat is absorbed or released.
If the substance melts or vaporizes, it absorbs heat, so $Q$ is positive. If it freezes or condenses, it releases heat, so $Q$ is negative when using the convention that heat added to the substance is positive.
| Phase change | Heat flow |
|---|---|
| Melting | absorbed |
| Freezing | released |
| Vaporization | absorbed |
| Condensation | released |
Common examples
Water is a very important example because its latent heats are large. A lot of energy is needed to melt ice or boil water, and a lot of energy is released when water freezes or condenses.
Approximate values for water are:
| Quantity | Value |
|---|---|
| Latent heat of fusion of water | $L_f \approx 3.34 \times 10^5 \, \mathrm{J/kg}$ |
| Latent heat of vaporization of water | $L_v \approx 2.26 \times 10^6 \, \mathrm{J/kg}$ |
This means that changing liquid water into steam requires much more energy per kilogram than changing ice into liquid water.
For water at standard atmospheric pressure:
$$
L_f \approx 3.34 \times 10^5 \, \mathrm{J/kg}
$$
$$
L_v \approx 2.26 \times 10^6 \, \mathrm{J/kg}
$$
Example calculation
Suppose $2.0 \, \mathrm{kg}$ of ice at its melting point melts completely into water at the same temperature. The required heat is
$$
Q = mL_f
$$
so
$$
Q = (2.0)(3.34 \times 10^5) = 6.68 \times 10^5 \, \mathrm{J}
$$
So $6.68 \times 10^5 \, \mathrm{J}$ of heat must be added.
Now suppose $0.50 \, \mathrm{kg}$ of water at its boiling point turns completely into steam. Then
$$
Q = mL_v
$$
$$
Q = (0.50)(2.26 \times 10^6) = 1.13 \times 10^6 \, \mathrm{J}
$$
Even for a smaller mass, vaporization can require a very large amount of energy.
Heating curve and flat regions
A heating curve shows how temperature changes as heat is added. During ordinary heating, temperature rises. During a phase change, the graph becomes flat because heat is being used as latent heat.
The horizontal parts represent latent heat. The sloping parts represent temperature increase within a single phase.
Microscopic picture
In a solid, particles are closely packed and mainly vibrate about fixed positions. In a liquid, particles are still close together but can move around each other. In a gas, particles are much farther apart.
When a solid melts, energy loosens the structure. When a liquid vaporizes, energy separates particles much more strongly. This is why the latent heat of vaporization is usually larger than the latent heat of fusion.
Latent heat in everyday life
Latent heat appears in many common situations. Ice cools drinks because it must absorb heat to melt. Sweat cools the body because evaporation requires energy, and that energy comes from your skin. Steam can cause severe burns because when it condenses on skin, it releases a large amount of latent heat. Clouds and weather are also strongly affected by evaporation and condensation.
Distinguishing latent heat from specific heat
Latent heat and specific heat are different ideas. Specific heat describes how much heat is needed to change temperature within one phase. Latent heat describes how much heat is needed to change phase at constant temperature.
| Quantity | Used for | Formula |
|---|---|---|
| Specific heat capacity | temperature change | $Q = mc\Delta T$ |
| Latent heat | phase change | $Q = mL$ |
A real thermal problem can involve both. For example, heating ice below $0^\circ \mathrm{C}$ to steam above $100^\circ \mathrm{C}$ requires several separate steps, some using $Q = mc\Delta T$ and others using $Q = mL$.
Use $Q = mc\Delta T$ when temperature changes.
Use $Q = mL$ when phase changes at constant temperature.
Summary
Latent heat is the heat absorbed or released during a phase change without temperature change. The main formula is
$$
Q = mL
$$
For melting and freezing, use the latent heat of fusion, $L_f$. For boiling and condensation, use the latent heat of vaporization, $L_v$. Latent heat explains why phase changes can involve large energy transfers even when a thermometer shows no temperature change.