The heat of fusion (\(\Delta H_{fus}\)) is a fundamental thermodynamic quantity describing the energy involved when a substance changes phase between a solid and a liquid. It represents the latent heat absorbed during melting or released during freezing, occurring without a change in temperature. This latent heat is used entirely to overcome the intermolecular forces holding the solid structure together, enabling the transition to the liquid state.
Calculating the Energy Required for Phase Change
Calculating the heat energy (\(Q\)) involved in a simple phase change uses a formula that incorporates the mass of the substance and its specific constant. The fundamental relationship for this process is expressed as \(Q = m L_f\), where \(Q\) is the heat energy transferred. This calculation applies only during the exact moment of melting or freezing, when the temperature remains constant at the substance’s melting point.
In this formula, \(m\) represents the mass of the substance undergoing the phase change, typically measured in grams or kilograms. The term \(L_f\) (or \(\Delta H_{fus}\)) is the Latent Heat of Fusion, which is a fixed property unique to each substance. For water, the Latent Heat of Fusion is approximately 334 Joules per gram (J/g), meaning 334 Joules of energy are required to melt one gram of ice at \(0^\circ \text{C}\) into one gram of water at \(0^\circ \text{C}\).
To illustrate this, imagine you want to melt 10 grams of ice at \(0^\circ \text{C}\) into water at \(0^\circ \text{C}\). You would multiply the mass (10 g) by the Latent Heat of Fusion for water (334 J/g). The resulting calculation, \(Q = 10 \text{ g} \times 334 \text{ J/g}\), yields 3,340 Joules of energy required for this specific phase transition.
Calculating Total Heat Transfer in Multi-Step Problems
Real-world scenarios often involve heating a substance across a temperature range that includes a phase change, requiring a multi-step calculation to find the total heat energy transferred. This process combines the energy needed to change the substance’s temperature with the latent heat required for the phase transition itself. The first step in these multi-step problems is calculating the heat required to change the temperature of a substance while it is in a single phase, which uses the formula \(Q = mc\Delta T\).
In this equation, \(c\) is the specific heat capacity, representing the energy needed to raise one unit of mass by one degree of temperature, and \(\Delta T\) is the change in temperature. When a substance reaches its melting point, the heat calculation must switch to the latent heat formula, \(Q = m L_f\), because the temperature stops rising during the phase change. Once the entire mass has converted to the new phase, the calculation reverts to the \(Q = mc\Delta T\) formula, but it must use the specific heat capacity appropriate for the new state of matter.
A common example is heating ice from below freezing to liquid water above freezing, which involves three distinct steps. The total heat energy absorbed (\(Q_{total}\)) is the sum of the heat calculated for each step: \(Q_{total} = Q_1 + Q_2 + Q_3\).
- \(Q_1\): Heating the ice from its initial temperature up to \(0^\circ \text{C}\) using \(Q_1 = m c_{ice} \Delta T\).
- \(Q_2\): Melting the ice at \(0^\circ \text{C}\) using the latent heat formula, \(Q_2 = m L_f\).
- \(Q_3\): Heating the resulting liquid water from \(0^\circ \text{C}\) up to the final temperature using \(Q_3 = m c_{water} \Delta T\).
Essential Constants and Unit Management
Accurate calculation of the heat of fusion and related heat transfer problems depends on using the correct physical constants and maintaining consistency in units. Heat energy (\(Q\)) is commonly expressed in Joules (J), which is the standard international unit, but it may also be given in kilojoules (kJ) or calories (cal). The specific Latent Heat of Fusion (\(L_f\)) for water is equivalent to approximately 80 calories per gram (cal/g).
For the temperature-change calculations (\(Q = mc\Delta T\)), the specific heat capacity (\(c\)) must match the phase of the substance being heated. For instance, the specific heat of ice (\(c_{ice}\)) is around 2.09 J/g\(\cdot^\circ \text{C}\), while the specific heat of liquid water (\(c_{water}\)) is much higher, approximately 4.18 J/g\(\cdot^\circ \text{C}\).
Ensure all units are consistent before performing any mathematical operation. If the Latent Heat of Fusion (\(L_f\)) is provided in Joules per gram (J/g), then the mass (\(m\)) must be in grams (g) to ensure the units cancel correctly and the final energy answer is in Joules (J). Similarly, the specific heat capacity (\(c\)) must be aligned with the units used for mass and temperature change.