---
title: "Melting and Boiling: Changes of State"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 21
exercises: 11
source: https://one-course.com/books/physics/1/en/chapter/21-melting-and-boiling-changes-of-state
---

# Chapter 21 — Melting and Boiling: Changes of State

You have known for years that warmth [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) ice and boils water. But now you own a [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) — and the [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) has something astonishing to report from inside the melting ice bucket: while the ice [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze), the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) *refuses to move*. Let us watch the old changes of state with new eyes.

## 21.1 The proper names

Water’s changes of state now get their grown-up names, good for every stuff, not just water. From [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) to [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid): *melting*. From [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) back to [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid): *freezing* (also called solidifying). From [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) to [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas): *boiling* when it happens fast with big bubbles, evaporation when it happens quietly from the surface. From [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) back to [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid): condensation. Every stuff in the world — water, chocolate, iron, gold — can play this game, each at its own [temperatures](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature).

**Definition 21.1 (Melting point).**

The *melting point* of a stuff is the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) at which it [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) — and also the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) at which the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) [freezes](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) back. For water it is $0\,{}^{\circ}\mathrm{C}$. Each stuff has its own: chocolate [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) near $34\,{}^{\circ}\mathrm{C}$ (mouth [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) — no accident, ask any chocolate maker), candle wax near $60\,{}^{\circ}\mathrm{C}$, iron only at $1538\,{}^{\circ}\mathrm{C}$.

**Definition 21.2 (Boiling point).**

The *boiling point* of a stuff is the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) at which it boils. For water it is $100\,{}^{\circ}\mathrm{C}$. Each stuff again has its own — which is why a careful cook can boil water away while the oil in the same pan stays quietly [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid).

**Example 21.3 (Reading the world with two numbers).**

Why is a chocolate bar [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) on the shelf ($20\,{}^{\circ}\mathrm{C}$) but [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) in your pocket on a summer hike ($35\,{}^{\circ}\mathrm{C}$)? Because its [melting point](#def-g4-changes-of-state-melting-point), near $34\,{}^{\circ}\mathrm{C}$, sits *between* the two. A stuff is [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) below its [melting point](#def-g4-changes-of-state-melting-point), [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) above it — up until its [boiling point](#def-g4-changes-of-state-boiling-point), where it leaves as [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas). Two numbers tell the whole story of any stuff at any [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature).

## 21.2 The stubborn thermometer

**Method 21.4 (Watching ice melt properly).**

1. Fill a bowl with crushed ice or snow and plant the [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) in it; wait and read: $0\,{}^{\circ}\mathrm{C}$ ;
2. bring the bowl into the warm kitchen and read the [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) every few minutes while the ice [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) ;
3. keep reading until long after the last sliver of ice has gone.

The report: all through the melting — water and ice together in the bowl — the [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) stands stubbornly at $0\,{}^{\circ}\mathrm{C}$. Only when the *last* piece of ice has melted does the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) begin to climb.

**Proposition 21.5 (The plateau law).**

While a stuff is changing state — melting or boiling — its [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) stands still at the milestone, however hard the stove works. All the incoming warmth is spent on the change of state itself, none on climbing. [Solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) and [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) live together at the [melting point](#def-g4-changes-of-state-melting-point); [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) and [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) at the [boiling point](#def-g4-changes-of-state-boiling-point).

![A pot of ice on a steady stove, told by the thermometer: the temperature climbs, halts at 0\, C while the ice melts, climbs again, and halts at 100\, C while the water boils away. (The last red climb belongs to the steam.)](https://one-course.com/images/onecourse/chapters/physics-1/g4-changes-of-state/fig-49bdb317bf8b.svg)

*A pot of ice on a steady stove, told by the [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature): the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) climbs, halts at $0\,{}^{\circ}\mathrm{C}$ while the ice [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze), climbs again, and halts at $100\,{}^{\circ}\mathrm{C}$ while the water boils away. (The last red climb belongs to the steam.)*

![A rolling boil: bubbles of water vapor form inside the liquid and burst at the surface — and all the while the thermometer stands still at the boiling point.](https://one-course.com/images/onecourse/chapters/physics-1/g4-changes-of-state/img-2d214253a51f.jpg)

*A rolling boil: bubbles of water vapor form inside the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) and burst at the surface — and all the while the [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) stands still at the [boiling point](#def-g4-changes-of-state-boiling-point).*

**Example 21.6 (The plateau in the kitchen).**

This is why gently boiling and furiously boiling water cook pasta equally fast: both pots stand at exactly $100\,{}^{\circ}\mathrm{C}$ — the furious one only wastes its extra warmth making steam faster. And it is why a drink with ice cubes stays at $0\,{}^{\circ}\mathrm{C}$ down to the last sliver: the melting ice pins the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) to the milestone.

**Remark 21.7 (A number the eye cannot see).**

Without a [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature), nobody would guess the plateau: the pot looks busier and busier, the ice bucket looks calmer and calmer, and the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) in both stands rock still. It is one more victory of measuring over seeming — and one of the first great surprises that instruments ever handed to science.

## 21.3 Each stuff keeps its milestones

**Proposition 21.8 (Milestones are identity marks).**

The [melting point](#def-g4-changes-of-state-melting-point) and [boiling point](#def-g4-changes-of-state-boiling-point) of a pure stuff never change: water [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) at $0\,{}^{\circ}\mathrm{C}$ today, tomorrow, in a palace or a tent. The milestones are part of the stuff’s identity — so well kept that a scientist can recognize an unknown stuff by measuring where it [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) and boils.

**Example 21.9 (The candle and the foundry).**

A candle by the fireplace slumps and drips: wax passes its [melting point](#def-g4-changes-of-state-melting-point) near $60\,{}^{\circ}\mathrm{C}$. In a foundry, workers pour glowing-orange [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) iron like soup — their furnace passed $1538\,{}^{\circ}\mathrm{C}$. Same game, wildly different milestones: what the fireplace does to wax, only a furnace can do to iron. And gold [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) at $1064\,{}^{\circ}\mathrm{C}$: goldsmiths have known that number, in their hands if not in degrees, for thousands of years.

![Milestones of some everyday stuffs, in degrees Celsius (the line is squeezed — iron’s mark truly stands fifteen times farther than water’s). Each stuff carries its own numbers, always.](https://one-course.com/images/onecourse/chapters/physics-1/g4-changes-of-state/fig-f9bee0594f70.svg)

*Milestones of some everyday stuffs, in [degrees Celsius](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) (the line is squeezed — iron’s mark truly stands fifteen times farther than water’s). Each stuff carries its own numbers, always.*

## 21.4 Exercises

**Exercise 21.1 ★.**

Give the proper name: [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) to [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid); [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) to [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid); [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) to [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) with big bubbles; [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) to [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) on a cold window.

**Solution of Exercise 21.1.**

Melting; freezing (solidifying); boiling; condensation.

**Exercise 21.2 ★.**

What are water’s two milestones, with their [temperatures](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature)? And chocolate’s [melting point](#def-g4-changes-of-state-melting-point), roughly?

**Solution of Exercise 21.2.**

[Melting point](#def-g4-changes-of-state-melting-point) $0\,{}^{\circ}\mathrm{C}$, [boiling point](#def-g4-changes-of-state-boiling-point) $100\,{}^{\circ}\mathrm{C}$. Chocolate [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) near $34\,{}^{\circ}\mathrm{C}$ — mouth [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature).

**Exercise 21.3 ★.**

A bowl holds ice and water together, well stirred. What does the [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) read? What will it read five minutes later, if some ice still remains?

**Solution of Exercise 21.3.**

$0\,{}^{\circ}\mathrm{C}$ — and still $0\,{}^{\circ}\mathrm{C}$ five minutes later: while ice and water live together, the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) is pinned to the [melting point](#def-g4-changes-of-state-melting-point).

**Exercise 21.4 ★.**

State the plateau law. Where does the stove’s warmth go while the water boils, since the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) no longer climbs?

**Solution of Exercise 21.4.**

While a stuff [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) or boils, its [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) stands still at the milestone. The warmth is all spent on the change of state itself — turning [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) into steam — not on climbing.

**Exercise 21.5 ★.**

Wax [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) near $60\,{}^{\circ}\mathrm{C}$. Is a candle [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) or [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid): in a $20\,{}^{\circ}\mathrm{C}$ living room? next to a flame that warms it to $80\,{}^{\circ}\mathrm{C}$? in a $35\,{}^{\circ}\mathrm{C}$ summer attic?

**Solution of Exercise 21.5.**

[Solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) at $20\,{}^{\circ}\mathrm{C}$ (below $60$); [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) at $80\,{}^{\circ}\mathrm{C}$ (above $60$); still [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) at $35\,{}^{\circ}\mathrm{C}$ — though a pocket chocolate bar would already have melted there.

**Exercise 21.6 ★.**

Pasta cooks in gently boiling water. Papa turns the flame to maximum and the pot boils furiously. Is the water now hotter? What does the extra warmth produce instead?

**Solution of Exercise 21.6.**

No hotter: both pots stand at $100\,{}^{\circ}\mathrm{C}$, the boiling plateau. The extra warmth only makes steam faster — wasted flame, same pasta.

**Exercise 21.7 ★.**

On the plateau graph of the chapter, how can you spot the two changes of state without reading a single word?

**Solution of Exercise 21.7.**

By the two flat stretches — the plateaus. Wherever the curve runs level while the stove keeps heating, a change of state is under way.

**Exercise 21.8 ★.**

Iron [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) at $1538\,{}^{\circ}\mathrm{C}$ and gold at $1064\,{}^{\circ}\mathrm{C}$. A furnace runs at $1200\,{}^{\circ}\mathrm{C}$: which of the two metals pours like soup in it, and which stays [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid)? By how many degrees does the furnace miss the other one?

**Solution of Exercise 21.8.**

Gold ($1064 < 1200$) pours; iron ($1538 > 1200$) stays [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid). The furnace misses iron’s milestone by $1538 - 1200 = 338$ degrees.

**Exercise 21.9 ★.**

Why does a drink with ice cubes stay just as cold down to the last sliver of ice — and only then start warming up?

**Solution of Exercise 21.9.**

Melting ice pins the drink to $0\,{}^{\circ}\mathrm{C}$: all incoming warmth is spent melting ice, none on warming the drink. Only when the last sliver is gone can the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) start to climb.

**Exercise 21.10 ★★.**

A scientist receives an unknown white [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid). She finds it [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) at exactly $0\,{}^{\circ}\mathrm{C}$ and its [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) boils at exactly $100\,{}^{\circ}\mathrm{C}$. What is her best guess about the stuff — and which law lets milestones serve as identity cards?

**Solution of Exercise 21.10.**

Her best guess: the stuff is ice — frozen water. The law that milestones are identity marks: a pure stuff’s melting and [boiling points](#def-g4-changes-of-state-boiling-point) never change, so matching water’s two numbers exactly is as good as a signature.

**Exercise 21.11 ★★.**

Mountain climbers report that high on great peaks, water boils while only *just* too hot to touch — and their tea never brews properly. What everyday certainty about boiling water breaks down up there? (The reason hides in the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) itself, and a later chapter on [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) pressure will catch it.)

**Solution of Exercise 21.11.**

The certainty that water always boils at $100\,{}^{\circ}\mathrm{C}$. High on a peak it boils well below that — hot but not $100\,{}^{\circ}\mathrm{C}$ — so the “boiling” water is too cool to brew tea properly. The culprit is the thinner [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) pressing less on the water, as the air-pressure chapter will show.