---
title: "States of Matter and Changes of State"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 45
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state
---

# Chapter 45 — States of Matter and Changes of State

Six years of [solids](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) that keep their shape, [liquids](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) that lie level, gases that fill every corner — and never once did we ask *why*. This year, physics opens the lid. Underneath the three states hides one of the greatest ideas humans ever had: everything, absolutely everything, is made of particles too small to see. Grant that one idea, and the rules you have collected since childhood explain themselves in a single stroke.

## 45.1 The great idea

**Definition 45.1 (Molecules).**

All matter is made of *molecules*: unimaginably small particles, far below what any eye or school microscope can see. A single drop of water holds more molecules than there are drops of water in all the seas. Each pure substance is built of its own kind of molecule — water of water-molecules, iron of iron’s own particles — and a substance’s molecules are all identical.

**Remark 45.2 (Believing without seeing).**

No one has ever watched a single [molecule](#def-g7-states-of-matter-molecule) with the naked eye — so why believe in them? Because the idea *earns* belief: it predicts, correctly, everything this chapter contains, and mountains more. That is how physics accepts an invisible guest: not on faith, but on relentless usefulness. (Direct [images](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#prop-g5-mirrors-reflection-image) from marvelous modern instruments finally arrived a century ago — long after physicists were already sure.)

**Proposition 45.3 (The particle model of the three states).**

The three states are three arrangements of the same [molecules](#def-g7-states-of-matter-molecule):

1. *[solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid)* : [molecules](#def-g7-states-of-matter-molecule) packed tight in an orderly stack, each trembling in place but holding its position — hence the fixed shape;
2. *[liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid)* : [molecules](#def-g7-states-of-matter-molecule) still touching, but disordered and free to slide past one another — hence flowing, and the level surface;
3. *[gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas)* : [molecules](#def-g7-states-of-matter-molecule) far apart, flying fast in all directions, colliding and rebounding — hence filling every corner offered.

![One substance, three arrangements: the stacked solid, the sliding crowd of the liquid, the flying few of the gas.](https://one-course.com/images/onecourse/chapters/physics-1/g7-states-of-matter/fig-3fda475ae274.svg)

*One substance, three arrangements: the stacked [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid), the sliding crowd of the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid), the flying few of the [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas).*

**Example 45.4 (Six years of rules, one explanation).**

Run the old rules through the model. [Solids](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) keep their shape: every [molecule](#def-g7-states-of-matter-molecule) holds its post. [Liquids](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) take the container’s shape and lie level: the sliding crowd slumps until no [molecule](#def-g7-states-of-matter-molecule) can slide lower. Gases fill all the room offered: nothing holds the flyers back. The perfume crossing the room: [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) [molecules](#def-g7-states-of-matter-molecule) flying, colliding, spreading. Sand pouring like a [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid): not [molecules](#def-g7-states-of-matter-molecule) sliding, but grains — each grain itself a tiny orderly [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) of trillions of [molecules](#def-g7-states-of-matter-molecule).

## 45.2 The empty space test

**Method 45.5 (Two syringes).**

The model claims [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) [molecules](#def-g7-states-of-matter-molecule) fly far apart, [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) [molecules](#def-g7-states-of-matter-molecule) touch. Then [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) should squeeze, and [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) should not. Test it:

1. fill a plastic syringe with [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) , cap the nozzle with a fingertip, and push the plunger: it yields — you can halve the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) ’s room, feeling a springy fight-back;
2. fill the same syringe with water, cap, and push: the plunger stands like a wall — water refuses to shrink by even a hair;
3. release each plunger: the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) springs back; the water never moved.

**Proposition 45.6 (Gases squeeze; liquids and solids do not).**

A [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) can be *compressed* — forced into less room — because most of a [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) is empty space between flying [molecules](#def-g7-states-of-matter-molecule). [Liquids](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) and [solids](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) are practically *incompressible*: their [molecules](#def-g7-states-of-matter-molecule) already touch, and matter that touches cannot be packed tighter by any push a hand — or a hydraulic press — can give.

**Example 45.7 (Squeezed air at work).**

The bicycle pump squeezes room-fulls of [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) into the tire — possible only because [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) is mostly emptiness. The squeezed crowd, [molecules](#def-g7-states-of-matter-molecule) hammering the tire walls faster and thicker, holds the bicycle up: a [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas)’s push *is* its molecular hailstorm. Divers’ tanks pack an afternoon of breathing into a steel bottle; the incompressible brake fluid, meanwhile, carries your foot’s push to the wheels undiminished — each state hired for its own talent.

## 45.3 Changes of state, reread

**Example 45.8 (The doors, molecule by molecule).**

Warm a [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) and its trembling [molecules](#def-g7-states-of-matter-molecule) shake harder; at the [melting point](https://one-course.com/books/physics/1/en/chapter/21-melting-and-boiling-changes-of-state#def-g4-changes-of-state-melting-point) the shaking bursts the orderly stack — the crowd begins to slide: [melting](https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states#def-g6-water-states-changes). Warm the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) further and the fastest [molecules](#def-g7-states-of-matter-molecule) tear free of the crowd’s grip entirely and fly: evaporation — and at the [boiling point](https://one-course.com/books/physics/1/en/chapter/21-melting-and-boiling-changes-of-state#def-g4-changes-of-state-boiling-point) the escape becomes a stampede from within the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) itself. Cooling runs the film backward: flyers caught ([condensation](https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states#def-g6-water-states-changes)), sliders locking into ranks ([solidification](https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states#def-g6-water-states-changes)). The six doors of last year are one story of molecular grip against molecular shaking.

**Example 45.9 (Old laws for free).**

Two hard-won laws now come free of charge. *[Mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) survives changes of state*: [melting](https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states#def-g6-water-states-changes) rearranges [molecules](#def-g7-states-of-matter-molecule) but neither creates nor destroys a single one — same particles, same [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass). *[Temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) plateaus*: at the [melting point](https://one-course.com/books/physics/1/en/chapter/21-melting-and-boiling-changes-of-state#def-g4-changes-of-state-melting-point), incoming warmth is spent breaking the stack’s grip, [molecule](#def-g7-states-of-matter-molecule) by [molecule](#def-g7-states-of-matter-molecule), not on faster shaking — the [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) waits until the last rank is broken. What measurement discovered, the model explains.

**Remark 45.10 (Water’s odd swelling).**

Even water’s strange freeze-swelling joins in: [water-molecules](#def-g7-states-of-matter-molecule) happen to lock into an unusually *airy* stack — an open lattice with more empty space than the sliding crowd had. Airier stack, more room, lower [density](https://one-course.com/books/physics/1/en/chapter/44-density-why-things-float#def-g6-density-floating-density): ice [floats](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words) on its own [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid). Most substances stack tighter than they slide; water’s architecture is the beautiful exception.

![Condensation caught in the act: invisible water vapor from the room’s air turns liquid on the cold glass.](https://one-course.com/images/onecourse/chapters/physics-1/g7-states-of-matter/img-57fdc4c0c18b.jpg)

*[Condensation](https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states#def-g6-water-states-changes) caught in the act: invisible water vapor from the room’s [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) turns [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) on the cold glass.*

## 45.4 Heat, seen from inside

**Proposition 45.11 (Temperature and molecular motion).**

[Temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) the liveliness of molecular motion: the hotter a substance, the faster its [molecules](#def-g7-states-of-matter-molecule) tremble, slide or fly. [Heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) flowing from hot to cold is the lively crowd calming down as it stirs up the sluggish one — collision by collision — until both share one pace: one [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature). The old downhill law of [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) is molecular table tennis.

**Example 45.12 (Cold is not a stuff).**

The model retires an old temptation for good: nothing called “cold” ever flows. There is only slower and faster molecular motion; the lively lends liveliness, never the reverse. At the coldest imaginable — [molecules](#def-g7-states-of-matter-molecule) as still as nature permits — lies a true floor of [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature), far below any freezer; its strange and famous number belongs to the High School volume.

## 45.5 Exercises

**Exercise 45.1 ★.**

State the particle model’s picture of each of the three states, in one line each.

**Solution of Exercise 45.1.**

[Solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid): [molecules](#def-g7-states-of-matter-molecule) packed in an orderly stack, trembling in place. [Liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid): [molecules](#def-g7-states-of-matter-molecule) touching but disordered, sliding past one another. [Gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas): [molecules](#def-g7-states-of-matter-molecule) far apart, flying fast in all directions.

**Exercise 45.2 ★.**

Why does a [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) keep its shape while a [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) takes its container’s? Answer with [molecules](#def-g7-states-of-matter-molecule), not with rules.

**Solution of Exercise 45.2.**

In the [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) every [molecule](#def-g7-states-of-matter-molecule) holds its post in the stack, so the whole keeps its shape. In the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) the [molecules](#def-g7-states-of-matter-molecule) slide freely past each other while still touching: the crowd slumps to fit the container, until nothing can slide lower — the level surface.

**Exercise 45.3 ★.**

In the syringe test, why does the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) yield and spring back, while the water stands like a wall?

**Solution of Exercise 45.3.**

[Air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) is mostly empty space between flying [molecules](#def-g7-states-of-matter-molecule): pushing packs the flyers closer (and their hammering fights back — the spring). Water’s [molecules](#def-g7-states-of-matter-molecule) already touch; there is no emptiness to squeeze away, so the plunger meets a wall.

**Exercise 45.4 ★.**

A bicycle pump packs many room-fulls of [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) into one tire. What does this prove about the spacing of [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) [molecules](#def-g7-states-of-matter-molecule)? Could a pump do the same with water?

**Solution of Exercise 45.4.**

That [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) [molecules](#def-g7-states-of-matter-molecule) fly far apart with great emptiness between — room-fulls can be packed together. Water, its [molecules](#def-g7-states-of-matter-molecule) already touching, is incompressible: no pump packs it tighter.

**Exercise 45.5 ★.**

Tell the story of [melting](https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states#def-g6-water-states-changes) in molecular language: what does warmth do, and what breaks at the [melting point](https://one-course.com/books/physics/1/en/chapter/21-melting-and-boiling-changes-of-state#def-g4-changes-of-state-melting-point)?

**Solution of Exercise 45.5.**

Warmth makes the stacked [molecules](#def-g7-states-of-matter-molecule) tremble harder and harder; at the [melting point](https://one-course.com/books/physics/1/en/chapter/21-melting-and-boiling-changes-of-state#def-g4-changes-of-state-melting-point) the trembling overpowers the stack’s grip, the ranks break, and the [molecules](#def-g7-states-of-matter-molecule) begin to slide: the [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) has become [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid).

**Exercise 45.6 ★.**

Why does [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) survive every change of state, according to the model? What would have to happen to [molecules](#def-g7-states-of-matter-molecule) for [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) to be lost?

**Solution of Exercise 45.6.**

A change of state only rearranges the same [molecules](#def-g7-states-of-matter-molecule) — none are created or destroyed, so the [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) cannot change. Losing [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) would require [molecules](#def-g7-states-of-matter-molecule) to vanish (or escape the container — the uncapped bottle’s false alarm).

**Exercise 45.7 ★.**

What does [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) [measure](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring), in the model? Describe [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat)’s downhill flow as molecular table tennis.

**Solution of Exercise 45.7.**

The liveliness of molecular motion. When hot touches cold, the lively [molecules](#def-g7-states-of-matter-molecule) batter the sluggish ones, handing over liveliness collision by collision — the lively calm down, the sluggish quicken — until both crowds share one pace: equal [temperatures](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature).

**Exercise 45.8 ★.**

Perfume opened at one end of a still room is smelled at the other end a minute later. Explain the journey — and why a breeze [speeds](https://one-course.com/books/physics/1/en/chapter/35-speed-distance-and-time#def-g5-speed-distance-time-speed) it up.

**Solution of Exercise 45.8.**

Perfume [molecules](#def-g7-states-of-matter-molecule) fly, collide with [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) [molecules](#def-g7-states-of-matter-molecule), rebound, and wander — zigzag by zigzag across the room. A breeze carries whole crowds of them bodily: riding the [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind) beats staggering through the crowd.

**Exercise 45.9 ★★.**

Evaporation cools what it leaves behind: sweat chills your skin, and a wet finger held up feels the [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind)’s cold side. Explain with the escape of the *fastest* [molecules](#def-g7-states-of-matter-molecule) — what kind of crowd stays behind?

**Solution of Exercise 45.9.**

Only the *fastest* [molecules](#def-g7-states-of-matter-molecule) can tear free of the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid)’s grip, so evaporation is a tax on liveliness: the escapees carry away more than their share, and the crowd left behind is, on average, slower — that is, cooler. Sweat and the wet finger chill by exporting their liveliest.

**Exercise 45.10 ★★.**

A sealed balloon left in the summer sun swells; in the refrigerator it sags. The number of [molecules](#def-g7-states-of-matter-molecule) inside never changed. Explain both changes with molecular [speed](https://one-course.com/books/physics/1/en/chapter/35-speed-distance-and-time#def-g5-speed-distance-time-speed) and the hailstorm on the walls.

**Solution of Exercise 45.10.**

In the sun the trapped [molecules](#def-g7-states-of-matter-molecule) fly faster and hammer the skin harder and more often: the hailstorm inflates the balloon until the stretched skin balances it. In the cold the same [molecules](#def-g7-states-of-matter-molecule) slow, the hammering weakens, and the outside [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air)’s push squashes the balloon smaller.

**Exercise 45.11 ★★.**

Why does ice [float](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words), in molecular language? What is unusual about the stack [water-molecules](#def-g7-states-of-matter-molecule) build, and what would ponds do in winter if water stacked like ordinary substances?

**Solution of Exercise 45.11.**

Freezing water locks into an unusually airy, open stack — more empty space than the sliding crowd had — so ice takes more room for the same [molecules](#def-g7-states-of-matter-molecule): [density](https://one-course.com/books/physics/1/en/chapter/44-density-why-things-float#def-g6-density-floating-density) below the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid)’s, and it [floats](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words). Were water ordinary, ice would stack tight, [sink](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words) as it formed, and ponds would [freeze](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) from the bottom up — with no sheltered water left for the fish.

**Exercise 45.12 ★★★.**

A drop of ink released gently at the bottom of a glass of *still* water slowly spreads, over [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock), until all the water is faintly blue — no stirring, no currents. Explain what this patient spreading reveals about the [molecules](#def-g7-states-of-matter-molecule) of a [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) — both the water’s and the ink’s — and why the same drop spreads faster in warm water. (This humble observation was among the great early evidences for the whole molecular idea.)

**Solution of Exercise 45.12.**

Nothing stirred the water, yet the ink traveled: the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid)’s own [molecules](#def-g7-states-of-matter-molecule) are in ceaseless motion, jostling the ink [molecules](#def-g7-states-of-matter-molecule) step by random step through the crowd — both [liquids](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) are alive with motion at every instant, even when the glass looks perfectly still. Warmth quickens every jostle, so the spreading hurries. Patient ink thus made the invisible dance visible — evidence that convinced the doubters of [molecules](#def-g7-states-of-matter-molecule) themselves.

## 45.6 Problem: The Molecular Theater

**Problem 45.1.**

Weekend problem — the class stages the particle model in the gymnasium; pupils as molecules, states as choreography; the critics’ questions

The physics class stages matter itself: thirty pupils play the [molecules](#def-g7-states-of-matter-molecule) of one substance, and the gymnasium is the container.

**Part I — Three scenes.**

1. Scene one, the [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) : how should the thirty stand, and what small motion must each keep making? What may none of them do?
2. Scene two, the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) : what changes in the arrangement, and what new freedom appears? What must the pupils still keep doing that the [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) scene will abolish?
3. Scene three, the [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) : describe the choreography — and say why this scene needs the *whole* gymnasium while the first two huddle in a corner.
4. The audience asks: “Is it the same thirty pupils in all three scenes?” What law of last year does the answer stage?

**Part II — The critics test the play.**

5. A critic pushes gently on the [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) scene’s crowd, herding it into half the gym. Does the scene allow it? And the same push on the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) scene’s huddle? Name the proposition being staged.
6. To stage *[melting](https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states#def-g6-water-states-changes)* , the director turns up an imaginary [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) dial. What must the [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) ’s pupils do more and more of, and at what moment does the scene legally become the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) scene?
7. The play must show the [melting](https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states#def-g6-water-states-changes) plateau: while the change happens, what is the [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) dial’s [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) spent on — and what must the “ [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) critic” report about the pupils’ average liveliness during it?
8. Stage evaporation from the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) scene: which pupils leave the huddle — any at random, or a particular kind? What happens to the huddle’s average liveliness as they go, and what everyday chill does this explain?

**Part III — Special effects.**

9. The balloon effect: the [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) scene is fenced by pupils holding a rope-ring (the balloon’s skin). What do the molecular actors do to the rope, and what happens to the ring when the actors move faster?
10. Water’s odd freezing must be staged. What unusual instruction about *spacing* does the director give the [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) scene’s stack, and what floating fact does it explain?
11. The ink-drop finale: one pupil in a blue shirt starts in a corner of the *[liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid)* scene. Without any director’s push, how does the blue shirt end up far from its corner — and why faster if the [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) dial is up?
12. Write the program note: in three sentences, say what one idea the whole play stages, name two old laws it explains for free, and admit honestly what no scene can show (how *small* and how *many* the real actors are).

**Solution of Problem 45.1.**

**1.** In neat rows, shoulder to shoulder, each jiggling on the spot — and none may swap places or leave their post. **2.** Ranks dissolve: pupils stay shoulder to shoulder (touching!) but now weave and slide past one another. They must still keep contact with the crowd — no one may run free. **3.** Pupils scatter, running fast and straight until they collide or hit a wall, rebounding endlessly — and since nothing holds them together, only walls stop them: the crowd claims every corner the gym offers. **4.** Yes — the same thirty in every scene: [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) survives changes of state, staged. **5.** The [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) scene allows it — runners crowd into half the gym (and hammer the herders harder). The [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) huddle cannot shrink: the pupils already touch. Staged: gases squeeze, [liquids](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) do not. **6.** Jiggle harder and harder at their posts; the scene becomes the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) the moment jiggling bursts the ranks and pupils begin to slide past each other. **7.** The dial’s [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) is spent breaking the stack’s grip — rank by rank — not on faster motion: the [thermometer](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) critic must report the average liveliness *unchanged* until the last rank breaks. The plateau, staged. **8.** The *fastest* pupils — only they can tear free. The remaining huddle’s average liveliness drops: the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) cools itself by evaporating, exactly the chill of sweat and wet fingers. **9.** The actors keep colliding with the rope and shoving it outward; faster actors shove harder and more often, and the ring swells — the balloon in the sun. **10.** “Stack in *open* order — arms’ length, airy”: water’s [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) takes more room than its [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid), so the ice-scene raft would [float](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words) on the liquid-scene crowd. **11.** The blue shirt is jostled — bumped step by random step through the sliding crowd until it has wandered everywhere: ink diffusing. Turn the dial up and every jostle quickens, so the wandering hurries. **12.** For example: “Tonight’s play stages one idea: all matter is [molecules](#def-g7-states-of-matter-molecule) in motion. Granted, two old laws come free — [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) surviving every change of state, and the [melting](https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states#def-g6-water-states-changes) plateau. What we cannot stage is the scale: real actors are smaller than any seeing and more numerous than all the audiences of the world.”