Interactive Thermodynamics Laboratory
Latent Heat of Fusion
The latent heat of fusion is the heat energy required to transition a substance from a solid to a liquid at its melting point without changing its temperature. Explore this phase boundary using the simulator tabs below to run melting labs, view wiggling molecular lattices, analyze heating curve plateaus, and perform live energy equations.
Latent Heat of Fusion Laboratory
What is Latent Heat of Fusion?
When thermal energy is added to a solid substance, its temperature generally increases because the kinetic energy of its molecules rises. However, when the solid reaches its melting point, a unique thermodynamic phenomenon occurs: the temperature remains completely constant. Even if you continue to add heat, a thermometer placed in the substance will read exactly the same value until the solid has transitioned entirely into a liquid.
This heat energy absorbed during the melting phase is called the latent heat of fusion. The word latent means "hidden", as this thermal energy does not register as a temperature rise. Instead of increasing the molecular kinetic energy, the added thermal energy is used to overcome the intermolecular attractive forces holding the molecules in their rigid, solid crystal lattice.
m = Mass of the substance undergoing phase change (kilograms, kg)
Lf = Specific latent heat of fusion of the material (Joules/kilogram, J/kg)
Melting Points and Latent Heats of Fusion
Every substance has a unique melting point and specific latent heat of fusion, reflecting the strength of its internal atomic bonds:
| Material | Melting Point (°C) | Specific Latent Heat of Fusion (Lf) | Bonding Character |
|---|---|---|---|
| Water (Ice) | 0°C | 334,000 J/kg (3.34 × 105 J/kg) | Strong intermolecular Hydrogen bonds |
| Copper | 1,085°C | 205,000 J/kg (2.05 × 105 J/kg) | Moderate metallic bonds |
| Iron | 1,538°C | 247,000 J/kg (2.47 × 105 J/kg) | Strong metallic lattice structure |
| Lead | 327°C | 24,500 J/kg (2.45 × 104 J/kg) | Weak metallic bonds |
| Gold | 1,064°C | 63,700 J/kg (6.37 × 104 J/kg) | Moderate metallic bonds |
Understanding the Heating Curve
A heating curve represents how the temperature of a substance changes as heat is added at a constant rate. For a sample starting as ice below freezing, the curve goes through three distinct stages of interest for fusion:
- Solid Warmup (Slanted Line): Below 0°C, added heat increases molecular kinetic energy. The temperature rises. The formula is Q = m × cice × ΔT.
- Melting Plateau (Flat Line): At exactly 0°C, the temperature stays constant. Heat goes into breaking lattice bonds. Both solid and liquid phases coexist. The formula is Q = m × Lf.
- Liquid Warmup (Slanted Line): Once all ice is melted, added heat again increases kinetic energy. The water warms up. The formula is Q = m × cwater × ΔT.
Real-World Thermodynamics
Ice Coolers & Drinks
Ice is exceptionally good at cooling drinks because of its high latent heat of fusion. A single gram of ice at 0°C absorbs 334 Joules of heat from your drink just to melt into water, keeping the drink at 0°C far longer than the same mass of cold water at 0°C would.
Freezing of Lakes
As lakes freeze in winter, they release a massive amount of latent heat of fusion directly into the surrounding air. This thermal release prevents the local climate around lakes from dropping rapidly, cushioning local ecosystems from extreme cold shocks.
Glaze Ice Preservation
Budding fruit trees are sometimes sprayed with water during cold snaps. As the water freezes on the branches, the latent heat released by the freezing process keeps the temperature of the buds right at 0°C, preventing them from falling below freezing.
Solved Examples
Example 1 — Find the heat energy required to completely melt 0.75 kg of ice at 0°C. (Specific Latent Heat of Fusion of ice, L_f = 334,000 J/kg)
• Identify the given values: mass (m) = 0.75 kg, latent heat of fusion (L_f) = 334,000 J/kg.
• Recall the phase transition formula: Q = m * L_f.
• Substitute the values: Q = 0.75 kg * 334,000 J/kg.
• Calculate the result: Q = 250,500 Joules = 250.5 kJ.
• Verify: The energy required is positive as melting is an endothermic process absorbing heat from the surroundings.
Final Answer: Q = 250.5 kJ (2.51 × 10^5 J)
Example 2 — A solid copper sample at its melting point (1085°C) is heated with 410,000 Joules of thermal energy. How much copper is converted into liquid copper? (Latent Heat of Fusion of copper, L_f = 205,000 J/kg)
• Identify the given values: heat energy supplied (Q) = 410,000 J, latent heat of fusion (L_f) = 205,000 J/kg.
• State the formula and rearrange to solve for mass: Q = m * L_f => m = Q / L_f.
• Substitute the parameters: m = 410,000 J / 205,000 J/kg.
• Calculate the mass: m = 2.0 kg.
• Verify: 2 kg of copper will melt completely under this thermal load.
Final Answer: m = 2.0 kg
Example 3 — Calculate the total heat energy needed to warm a 0.20 kg ice block from -15°C to liquid water at 0°C. (Specific heat of ice = 2,220 J/kg·K, latent heat of fusion of ice = 334,000 J/kg)
• Break down the thermodynamic process into two steps:
• Step 1: Warm the solid ice from -15°C to 0°C. Q_1 = m * c_ice * ΔT = 0.20 kg * 2,220 J/kg·K * 15 K = 6,660 J.
• Step 2: Melt the ice at 0°C into water. Q_2 = m * L_f = 0.20 kg * 334,000 J/kg = 66,800 J.
• Sum the values: Q_total = Q_1 + Q_2 = 6,660 J + 66,800 J = 73,460 Joules = 73.46 kJ.
• Verify: The sensible heating step requires much less energy (~9%) compared to the latent melting transition (~91%).
Final Answer: Q_total = 73.46 kJ
Common Mistakes to Avoid
❌ Using Q = mcΔT during melting
The most common error is trying to apply specific heat capacity during a phase transition. Because ΔT is zero, you would get Q = 0. Use Q = m × Lf instead for the horizontal regions of the heating curve.
❌ Forgetting unit conversions
Make sure your mass (m) is in kilograms if your Latent Heat of Fusion (Lf) is given in J/kg. If mass is in grams, convert it (divide by 1000) before multiplying.
❌ Neglecting step-by-step sums
When heating a substance across a phase change boundary (e.g. ice at -10°C to water at 15°C), you cannot calculate the energy in one equation. You must calculate each segment separately and add them.
Quick Summary
- Latent heat of fusion is the energy required to change a solid to a liquid at constant temperature.
- Formula: Q = m × Lf. It applies to both melting (absorbing heat) and freezing (releasing heat).
- For water ice, the specific latent heat of fusion is Lf ≈ 3.34 × 105 J/kg.
- During a phase transition, temperature remains constant because energy is used for bond breaking rather than kinetic speed.
- The melting process represents a flat plateau on a temperature-energy heating curve graph.
Practice Questions
- Question: Define "Specific Latent Heat of Fusion". What is its SI unit?
Reveal Answer & Explanation
Specific Latent Heat of Fusion (L_f) is the amount of heat energy required to change 1 kilogram of a substance from solid to liquid at its melting point without any change in temperature. Its SI unit is Joules per kilogram (J/kg).
- Question: Why does temperature remain constant when ice is melting at 0°C, despite heat being added continuously?
Reveal Answer & Explanation
The added thermal energy does not increase the average kinetic energy of the molecules (which determines temperature). Instead, it is used entirely to break and loosen the rigid intermolecular hydrogen bonds holding the solid ice lattice structure together, allowing it to transition to the liquid state.
- Question: How much heat is released to the surroundings when 0.50 kg of liquid water at 0°C freezes into solid ice? (L_f = 334,000 J/kg)
Reveal Answer & Explanation
Using Q = m * L_f: Q = 0.50 kg * 334,000 J/kg = 167,000 Joules = 167 kJ. Since freezing is exothermic, this energy is released.
- Question: Compare the heat energy needed to melt 1 kg of ice (L_f = 334,000 J/kg) with the energy needed to melt 1 kg of lead (L_f = 24,500 J/kg). Why is water's value so much higher?
Reveal Answer & Explanation
Water needs 334,000 J, while lead needs only 24,500 J (about 13 times less). Water's latent heat is high because of strong hydrogen bonds between water molecules, which require significant energy to break compared to the metallic bonds in lead.
- Question: In a laboratory experiment, a student heats ice at 0°C. They write "Q = m * c * ΔT" in their lab report to calculate the melting heat. Explain the mistake.
Reveal Answer & Explanation
During melting, the temperature remains constant, meaning ΔT = 0. Using Q = m * c * ΔT would incorrectly give Q = 0. The correct formula for phase changes is Q = m * L_f.
- Question: Explain how spraying orange trees with water protects them from frost damage in winter.
Reveal Answer & Explanation
When temperatures drop below 0°C, the sprayed water on the oranges freezes. As it freezes (transitions from liquid to solid), it releases its latent heat of fusion (334,000 J/kg) onto the oranges, keeping their skin at 0°C and preventing them from freezing.
- Question: A heater of 500 W is used to melt ice. How long will it take to completely melt 0.30 kg of ice at 0°C?
Reveal Answer & Explanation
Total energy needed: Q = m * L_f = 0.30 * 334,000 = 100,200 J. Since Power (P) = Q / t, the time t = Q / P = 100,200 / 500 = 200.4 seconds (approx. 3.34 minutes).
Frequently Asked Questions
What does "latent" mean in latent heat of fusion?
The word "latent" comes from Latin meaning "hidden". It is called hidden heat because adding heat energy during a phase transition does not cause a temperature rise on a thermometer—the energy is hidden in the changing state of the bonds.
What is the formula for Latent Heat of Fusion?
The formula is Q = m * L_f, where Q is the heat energy absorbed or released in Joules (J), m is the mass in kilograms (kg), and L_f is the specific latent heat of fusion in Joules per kilogram (J/kg).
What is the melting point of water?
The melting point of water is 0°C (32°F or 273.15 K) at standard atmospheric pressure.
Is melting an endothermic or exothermic process?
Melting is an endothermic process, meaning the substance absorbs heat energy from its surroundings to break its solid structures. Freezing is the reverse process and is exothermic, releasing heat.
Why does ice float on water?
Ice floats because it is less dense than liquid water. The molecular structure of ice forms a rigid hexagonal crystal lattice with hollow spaces, which occupies more volume than the disorganized liquid water molecules.
What is the latent heat of fusion value for ice?
For water ice, the specific latent heat of fusion is approximately 334,000 J/kg (or 3.34 × 10^5 J/kg, which can also be written as 334 J/g or 80 cal/g).
Does pressure affect the latent heat of fusion?
Yes, changes in pressure alter the melting point and slightly affect the latent heat of fusion, though for most general physics laboratory calculations, we assume standard pressure (1 atm).
What is the difference between specific heat capacity and latent heat of fusion?
Specific heat capacity is the energy needed to change the temperature of a substance without a phase change (slanted lines on a heating curve). Latent heat of fusion is the energy needed to change state between solid and liquid at a constant temperature (flat plateau on the curve).
How does the molecular structure of ice change when it melts?
In ice, water molecules are held in a fixed, open hexagonal lattice by strong hydrogen bonds. When it melts, thermal energy wiggles molecules enough to break some hydrogen bonds, causing the rigid lattice to collapse into a more compact, fluid arrangement.
Why does it take so much energy to melt ice compared to warming it?
Warming ice only wiggles molecules slightly faster in their fixed lattice. Melting requires breaking a significant number of strong intermolecular hydrogen bonds, which requires a much larger amount of energy.