Physics › 🔥 Thermodynamics

Phase Changes & Latent Heat

Why a melting ice cube and a boiling kettle both stall at a fixed temperature no matter how much heat you throw at them.

High schoolAP Physics 2 level
💡
The big idea: Temperature measures how fast molecules are jiggling, but melting and boiling are about breaking the bonds that hold molecules together — two completely different jobs for the same incoming energy. During a phase change, every joule you add goes entirely into breaking or forming bonds, so the thermometer holds perfectly still until the transition is finished.
🎯 By the end, you'll be able to
  • Explain, in terms of molecular bonds versus molecular motion, why temperature stays constant during melting and boiling.
  • Read a heating curve and identify which segments show temperature change and which show a phase change.
  • Calculate the heat required for a temperature change (Q = mcΔT) and for a phase change (Q = mL), including multi-step problems.
  • Explain why vaporization requires so much more energy than fusion for the same substance.
📎 You should already know
  • Temperature and the Kinetic Theory of Matter
  • Specific Heat Capacity and Q = mcΔT
  • Heat vs. Temperature: What's the Difference?

The Ice Cube That Refuses to Warm Up

Drop an ice cube into a glass of lemonade on a hot day and something strange happens: as it melts, the water right around it stays stubbornly at the same temperature — 0°C — until every last sliver of ice is gone. Crank the stove up under a pot of boiling water and hold it there for ten more minutes: the water never gets hotter than 100°C. It just boils away faster. So where is all that extra heat going, if not into raising the temperature?

This is the quiet secret of phase changes: heat flowing in doesn't always show up as a higher thermometer reading. Sometimes it's spent somewhere you can't see directly — prying apart the bonds that hold molecules to their neighbors.

🔑 Temperature Measures Motion. Phase Changes Cost Bonds.

Temperature tracks the average kinetic energy of jiggling, jostling molecules. But whether a substance is solid, liquid, or gas depends on something else entirely: how tightly its molecules are bound to their neighbors. Melting and boiling both require energy to break those bonds — and while that breaking is underway, every joule you add goes into separating molecules, not speeding them up. That's why the thermometer freezes in place at 0°C or 100°C until the whole sample has finished changing phase.

\[ Q = mc\Delta T \]
Heat needed to change temperature within a single phase — the same tool you already used for warming water or cooling metal, wherever nothing is melting or boiling.
\[ Q = mL \]
Heat needed for a phase change at constant temperature. \(L\) is the latent heat — 'latent' meaning hidden, since it produces no temperature rise you can measure. Use \(L_f\) for melting/freezing and \(L_v\) for boiling/condensing.
🎮 Interactive: Heat Ice into Steam and Watch the Temperature Curve LIVE
Add heat steadily and track the temperature as it goes. Watch it climb smoothly within a phase, then go completely flat while ice melts or water boils — the flat stretches are exactly where the latent heat is being spent.
✨ Reading the Heating Curve

Plot temperature against heat added for a block of ice starting below freezing, and you get a signature zig-zag: a rising slope (ice warming up), then a flat plateau (ice melting at 0°C), then another rising slope (liquid water warming up), then a second flat plateau (water boiling at 100°C), then a final rising slope (steam warming further). Notice the boiling plateau stretches much farther along the heat axis than the melting plateau — vaporizing water simply costs far more energy than melting it, because boiling has to fully separate molecules into a gas while melting only has to loosen their rigid, locked-in arrangement.

📝 Worked example: You have 20 g of ice at −10°C. How much total heat is needed to turn it completely into steam at 100°C? (Use \(c_{ice} = 2.09\ J/g°C\), \(c_{water} = 4.18\ J/g°C\), \(L_f = 334\ J/g\), \(L_v = 2260\ J/g\).)
  1. Step 1 — warm the ice from −10°C to 0°C: Q₁ = mcΔT = 20 g × 2.09 J/g°C × 10°C = 418 J.
  2. Step 2 — melt the ice at 0°C: Q₂ = mL_f = 20 g × 334 J/g = 6,680 J.
  3. Step 3 — warm the liquid water from 0°C to 100°C: Q₃ = mcΔT = 20 g × 4.18 J/g°C × 100°C = 8,360 J.
  4. Step 4 — boil the water into steam at 100°C: Q₄ = mL_v = 20 g × 2260 J/g = 45,200 J.
  5. Add all four stages: 418 + 6,680 + 8,360 + 45,200 = 60,658 J.
✓ About 60.7 kJ total — and notice that vaporizing the water (Step 4) alone eats up nearly three-quarters of that energy, even though it's the last and shortest-sounding step.
📝 Worked example: Which takes more energy: melting 100 g of ice at 0°C, or boiling away 100 g of water at 100°C?
  1. Melting: Q = mL_f = 100 g × 334 J/g = 33,400 J = 33.4 kJ.
  2. Boiling: Q = mL_v = 100 g × 2260 J/g = 226,000 J = 226 kJ.
  3. Compare: 226 kJ ÷ 33.4 kJ ≈ 6.8.
✓ Boiling the same mass of water takes roughly 6.8 times more energy than melting it — because turning liquid into gas means fully freeing molecules from each other, a far bigger job than just loosening a solid's rigid structure.
⚠️ Don't Mix Up the Two Formulas

Q = mcΔT and Q = mL solve different problems, and reaching for the wrong one is the most common mistake here. If the substance is actually melting or boiling, ΔT is zero — plugging that into Q = mcΔT just hands you zero, which is meaningless. Use Q = mL only for the phase-change stretch itself, and Q = mcΔT only for stretches where the substance stays in one phase and its temperature is genuinely rising or falling. Also watch your units: L and c values are specific to the substance (water's numbers won't work for, say, copper or ethanol), and it's easy to lose a factor of 1000 mixing up grams with kilograms or joules with kilojoules.

Check your understanding

1. While an ice cube is melting at 0°C, heat keeps flowing into it, yet its temperature doesn't rise. Why not?
Temperature reflects kinetic energy. During a phase change, added energy is spent breaking intermolecular bonds — raising potential energy — so kinetic energy, and therefore temperature, doesn't budge until melting is complete.
2. How much heat is required to melt 25 g of ice already at 0°C? (L_f = 334 J/g)
Q = mL_f = 25 g × 334 J/g = 8,350 J = 8.35 kJ. No ΔT is involved since the ice is already at its melting point.
3. Steam at 100°C causes far more severe burns than an equal splash of liquid water at 100°C. Why?
Steam and boiling water are the same temperature. But steam has to give up a huge amount of latent heat (2260 J/g) as it condenses back into liquid on your skin — energy that plain 100°C water doesn't carry, since it's already a liquid.
4. On a heating curve for a pure substance being heated at a steady rate, what does a flat, horizontal segment represent?
Flat segments mark phase changes (melting or boiling). Heat keeps flowing in at the same steady rate, but it's all going into breaking or forming bonds rather than raising kinetic energy, so temperature holds constant.
✅ Key takeaways
  • Temperature tracks molecular motion (kinetic energy); phase changes are about breaking or forming molecular bonds (potential energy) — the same heat can't do both jobs at once, which is why temperature holds constant during melting and boiling.
  • Use Q = mcΔT for heat that changes temperature within a single phase, and Q = mL for heat that drives a phase change at constant temperature — mixing the two up is the most common error.
  • Vaporization takes far more energy than fusion for the same substance (water's L_v is nearly 7 times its L_f) because turning liquid into gas fully separates molecules, while melting only loosens a solid's rigid structure.
  • A heating curve's flat plateaus mark phase changes; its sloped segments mark ordinary temperature rise or fall within one phase.