Heat of fusion (also called latent heat of fusion) is the amount of energy required to change a unit mass of a substance from solid to liquid (melting) or from liquid to solid (freezing) at its melting point temperature. During this phase change, temperature remains constant even though energy is being added or removed. The energy goes into breaking or forming the intermolecular bonds that hold the solid structure together. Different materials have vastly different heats of fusion, reflecting the strength of their molecular bonds and crystal structures.
The concept was first developed by Scottish chemist Joseph Black around 1762, who distinguished between 'sensible heat' (which changes temperature) and 'latent heat' (which causes a phase change at constant temperature). This discovery was a cornerstone in the development of thermodynamics.
Heat of fusion, also known as latent heat of fusion, is the thermal energy required to change the state of a substance between solid and liquid at a constant temperature. This energy is absorbed during melting and released during freezing, without changing the substance's temperature.
| Property | Details |
|---|---|
| Nature | Heat of fusion is a scalar quantity, as it describes an amount of energy per unit mass and has no associated direction. |
| SI Units | The standard SI unit for heat of fusion is Joules per kilogram (J/kg). Other common units include kilojoules per kilogram (kJ/kg) or calories per gram (cal/g). |
| Magnitude | The magnitude is a positive, intrinsic property specific to each substance. For example, the latent heat of fusion for water is approximately 334,000 J/kg. |
| Governing Principle | The concept is governed by the law of conservation of energy. The energy absorbed by a melting solid is equal to the energy released when the same mass of liquid freezes. |
| Dimensional Formula | The dimensional formula is [M⁰L²T⁻²], representing energy ([ML²T⁻²]) per mass ([M]). |
| Symbol | Quantity | SI Unit | Description |
|---|---|---|---|
| Q | Heat Energy | Joule (J) | The amount of heat absorbed or released during the phase change. |
| L | Specific Latent Heat of Fusion | Joule per kilogram (J/kg) | An intrinsic property of a substance; the energy required to melt one unit of mass. |
| m | Mass | kilogram (kg) | The mass of the substance undergoing the phase change. |
| T_melting | Melting Point Temperature | Kelvin (K) or Celsius (°C) | The specific temperature at which the phase change occurs; it remains constant throughout the process. |
The formula for latent heat is empirical, derived from calorimetry experiments rather than a first-principles mathematical proof. However, it can be explained conceptually through thermodynamics. The total internal energy (E) of a system is the sum of its kinetic and potential energies.
Temperature is a measure of the average kinetic energy of the molecules. During a phase change, the added energy (Q) does not increase the speed of the molecules but instead works to break the intermolecular bonds holding the solid crystal lattice together. This increases the potential energy of the system while the kinetic energy remains constant.
Therefore, all the heat added goes into changing the potential energy. The total change in potential energy is proportional to the mass (m) of the substance, with the constant of proportionality being the specific latent heat of fusion (L).
The application of the heat of fusion concept is distinguished by the direction of the phase change and the conditions under which it occurs. The fundamental formula remains the same, but the interpretation of energy flow changes.
| Type / Case | Description | When to Use |
|---|---|---|
| Melting (Fusion) | The process of changing a substance from a solid to a liquid state. Energy, equal to the heat of fusion, is absorbed by the substance from its surroundings. | Use when calculating the energy required to melt a solid at its melting point. The heat transfer (Q) is considered positive, representing energy input. |
| Freezing (Solidification) | The process of changing a substance from a liquid to a solid state. Energy, equal to the heat of fusion, is released by the substance into its surroundings. | Use when calculating the energy released as a liquid freezes at its freezing point. The heat transfer (Q) is considered negative, representing energy output. |
| Pressure-Dependent Fusion | The value of the latent heat of fusion and the melting point temperature can vary with changes in ambient pressure. For most substances, increased pressure raises the melting point. | This case is important in high-pressure environments, such as in geological processes or specialized industrial applications. For most introductory physics problems, pressure is assumed to be constant. |
The concept of heat of fusion is critical in many fields:
Ice Cooling a DrinkWhen you add ice to a warm drink, the ice absorbs a large amount of heat energy from the liquid to undergo the phase change from solid to liquid. Because of water's high latent heat of fusion, a small amount of ice can absorb significant heat, effectively cooling the drink without a large temperature change in the ice-water mixture until all the ice is melted.
Road Salt in WinterSpreading salt on icy roads lowers the freezing point of water. This causes the ice to melt even at temperatures below 0°C because the ambient temperature is now above the new, lower melting point. The melting process still requires absorbing the latent heat of fusion from the surroundings.
Fruit Farmers and FrostOn a night when a frost is expected, fruit farmers may spray their crops with water. As the water freezes on the fruit, it releases its latent heat of fusion (Q = -Lm). This released energy helps keep the surface of the fruit at or near 0°C, preventing the plant cells inside from freezing and being damaged by colder air temperatures.
| Quantity | Symbol | SI Unit | Dimensions |
|---|---|---|---|
| Heat Energy | Q | Joule (J) | [M][L]²[T]⁻² |
| Mass | m | kilogram (kg) | [M] |
| Specific Latent Heat of Fusion | L | Joule per kilogram (J/kg) | [L]²[T]⁻² |
Dimensional analysis confirms the formula's consistency: The dimensions of L multiplied by the dimensions of m are \( [L]^2[T]^{-2} \times [M] = [M][L]^2[T]^{-2} \), which are the dimensions of energy (Q).
The formula is Q = mL. It calculates the amount of heat energy (Q) that must be absorbed to melt a substance (fusion) or released to freeze it (solidification) at a constant temperature. This energy is known as latent heat because it changes the phase, not the temperature.
In this equation, 'Q' represents the heat energy transferred, measured in Joules (J). The variable 'm' is the mass of the substance undergoing the phase change, measured in kilograms (kg). 'L' is the specific latent heat of fusion, a constant unique to each substance, measured in Joules per kilogram (J/kg).
The formula Q = mL is used specifically for the moment a substance is changing state between solid and liquid at its melting or freezing point. It is applied only when the temperature is constant during this phase transition. It is often used as one step in a multi-part problem that also involves temperature changes before or after the phase change.
A frequent error is forgetting to account for the energy of the phase change in problems that involve both heating/cooling and melting/freezing. Students often calculate the energy for the temperature change using Q = mcΔT but omit the Q = mL calculation for the phase transition itself. Another common mistake involves unit conversion, such as failing to convert the latent heat (L) from kilojoules per kilogram (kJ/kg) to Joules per kilogram (J/kg).
In metallurgy, engineers use the heat of fusion to calculate the exact amount of energy required to melt a specific mass of metal for casting into molds or for welding processes. This calculation is critical for designing furnaces and managing energy costs efficiently. The reverse process, solidification, is equally important for understanding how alloys form and cool.
These two formulas describe different parts of a substance's thermal energy journey. Q = mcΔT calculates the heat required to change a substance's temperature while it remains in a single phase (solid, liquid, or gas). In contrast, Q = mL calculates the heat required to change its phase at a constant temperature. To find the total energy to melt a block of ice and then heat the resulting water, you must use both formulas sequentially.