Fusion and Specific Latent Heat of Fusion
Simple Explanation
Fusion (melting) is the change from solid to liquid. The specific latent heat of fusion is the energy needed to convert one kilogram of a solid into liquid at its melting point, with no temperature change.
Why Do We Need It?
Latent heat of fusion is generally smaller than latent heat of vaporization for the same substance, reflecting that melting requires less molecular rearrangement than fully separating molecules into a gas.
Formula
Latent Heat of Fusion
Q = mLf
The heat energy needed to convert a mass of solid into liquid (or vice versa) at a constant temperature (the melting point), with no temperature change during the process itself.
- Q
- — Heat energy required, in joules
- m
- — Mass of the substance changing state, in kg
- Lf
- — Specific latent heat of fusion of the substance, in J/kg
When to use it: Use to find the heat energy needed to melt (or freeze) a known mass of a substance at its melting point.
Worked Example
Finding energy to melt ice
Find the heat energy needed to melt 0.8 kg of ice already at 0°C (Lf of water = 334,000 J/kg).
Why Does This Work?
Melting only needs to loosen (not completely break) the rigid structure holding particles in fixed positions in a solid, allowing them to move past each other as a liquid — this requires less energy than fully separating molecules into a gas, which is why Lf is typically much smaller than Lᵥ for the same substance (for water, Lf ≈ 334,000 J/kg vs. Lᵥ ≈ 2,260,000 J/kg).
Real-Life Example
Ice used to cool drinks effectively
Adding ice to a drink cools it far more effectively than adding the same mass of cold water.
As ice melts, it absorbs a large amount of latent heat of fusion directly from the drink, cooling it significantly — plain cold water can only absorb heat via a temperature change (specific heat capacity), which is far less effective at removing the same amount of heat energy.
Practice
Find the heat energy needed to melt 0.3 kg of ice at 0°C (Lf = 334,000 J/kg).
MediumCommon mistake
Confusing latent heat of fusion with latent heat of vaporization — fusion refers to the solid↔liquid transition (smaller L value); vaporization refers to the liquid↔gas transition (much larger L value), even for the same substance.
Quick Review
- Q = mLf gives the heat needed to melt a mass of solid at its melting point.
- Lf is generally much smaller than Lᵥ for the same substance.
- Melting ice absorbs a large amount of latent heat, making it very effective for cooling.