---
title: "Water in All Its States"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 39
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/39-water-in-all-its-states
---

# Chapter 39 — Water in All Its States

You have chased water through its states since your second school year: ice, water, steam; [melting](#def-g6-water-states-changes) snowmen and misty windows. This year the chase becomes bookkeeping. When ice [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze), is any stuff lost? When water [freezes](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze), why do pipes burst? With balances and cylinders in hand, we audit all three of water’s states.

## 39.1 The three states, with proper labels

**Definition 39.1 (The six changes of state).**

Between its three states, water has six doors, each with its scientific name:

1. [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* ; [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) : *solidification* (freezing);
2. [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) : *vaporization* — roaring fast at the boil, quiet and cool as evaporation; [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) : *condensation* ;
3. [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) $\to$ [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) directly: *sublimation* , and [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) $\to$ [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) directly — rarer doors, but real: frost feathers on a freezing window grow straight from invisible vapor, skipping the [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) entirely.

![Water’s six doors, with their proper names. Warmth drives the red doors; cold drives the blue.](https://one-course.com/images/onecourse/chapters/physics-1/g6-water-states/fig-a3fed1ba35c1.svg)

*Water’s six doors, with their proper names. Warmth drives the red doors; cold drives the blue.*

**Example 39.2 (Doors all around you).**

Morning frost [melting](#def-g6-water-states-changes) off the grass; laundry evaporating on the line; a cold [mirror](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#def-g5-mirrors-reflection-reflection) condensing your shower’s vapor; the freezer solidifying tomorrow’s ice cubes; frost feathers grown overnight on the pane. One substance, six doors, all within a day of ordinary life — name them and you own them.

## 39.2 The audit: is stuff lost?

**Method 39.3 (Weighing a change of state).**

Put the question to the balance:

1. pour some water into a small plastic bottle, screw the cap tight, dry the outside;
2. weigh it: say $368\,\mathrm{g}$ — write it down;
3. lay it in the freezer overnight: [solidification](#def-g6-water-states-changes) ;
4. weigh the frozen bottle at once (dry off any frost).

The balance answers: $368\,\mathrm{g}$, to the [gram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units). [Melt](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) it back on the windowsill and weigh again: $368\,\mathrm{g}$. The state changed twice; the stuff never blinked.

**Proposition 39.4 (Mass survives changes of state).**

A change of state changes a substance’s appearance, not its amount: the [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) before equals the [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) after, exactly. [Melting](#def-g6-water-states-changes), freezing, boiling in a sealed pot, condensing — through every door, the balance reads the same. (Leave the cap off, though, and vapor drifts away with its [grams](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units): the stuff still exists, but your audit no longer contains it.)

**Example 39.5 (Where the puddle’s grams went).**

A $300\,\mathrm{g}$ puddle dries up. Vanished? Weighed nothing? No: $300\,\mathrm{g}$ of water now ride the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) as invisible vapor, every [gram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) intact — some to fall as next week’s rain. Evaporation fools the eye, never the bookkeeping. The chalk line of your childhood puddle experiment was an audit; now it has numbers.

## 39.3 The audit: is room kept?

**Proposition 39.6 (Water swells as it freezes).**

[Mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) survives the doors — [volume](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) does not. Water is a curious substance: turning [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid), it *expands*. A [litre](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) of water makes about $1.1$ [litres](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) of ice: same [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass), about a tenth more room. Most substances shrink when they solidify; water swells — and that oddity redraws landscapes.

![The frozen bottle: the balance unchanged, the level higher. Freezing keeps the stuff and demands more room.](https://one-course.com/images/onecourse/chapters/physics-1/g6-water-states/fig-027767663485.svg)

*The frozen bottle: the balance unchanged, the level higher. Freezing keeps the stuff and demands more room.*

**Example 39.7 (The burst pipe and the cracked mountain).**

Forgotten in the freezer, a full glass bottle of water cracks: the swelling ice needs its extra tenth of room and takes it, glass or no glass. Winter does the same to plumbing — water freezing in a pipe bursts it as surely as a hammer — and to mountains: rain seeps into rock cracks, [freezes](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) at night, swells, and wedges the crack wider. Year by year, [freeze](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) by [freeze](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze), the odd little swelling of [Proposition 39.6](#prop-g6-water-states-volume) splits boulders and crumbles peaks.

**Remark 39.8 (Why ice floats).**

The same oddity answers a question you asked years ago at bath time. Ice holds a [litre](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume)’s stuff in $1.1$ [litres](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) of room: for equal room, ice is *lighter* than water — so 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). Icebergs ride the sea, ponds [freeze](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) from the top down (saving the fish beneath), and your lemonade’s cubes bob instead of sinking. Few substances [float](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words) on themselves; life on frozen ponds is glad water does.

## 39.4 The water cycle, audited

**Example 39.9 (The great round trip, with vocabulary).**

The childhood story of sea, cloud and rain now reads like a ledger. The Sun’s warmth drives *[vaporization](#def-g6-water-states-changes)* from the seas — tonnes upon tonnes rise invisibly. High and cold, the vapor *[condenses](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-evapcond)* into cloud droplets; colder still, droplets [freeze](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) into snow. Snow piles into glaciers; glaciers *[melt](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze)* into rivers; rivers return every [gram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) to the sea. Around the whole circuit, [Proposition 39.4](#prop-g6-water-states-mass) holds: the [planet](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-planet) neither gains nor loses a drop — the water in your glass has sailed this loop since before the dinosaurs.

![Frost feathers on a freezing pane: water from the air built this ice overnight, straight onto the glass.](https://one-course.com/images/onecourse/chapters/physics-1/g6-water-states/img-a20594e51b2a.jpg)

*Frost feathers on a freezing pane: water from the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) built this ice overnight, straight onto the glass.*

## 39.5 Exercises

**Exercise 39.1 ★.**

Name the six doors of [Definition 39.1](#def-g6-water-states-changes), each with one everyday sighting.

**Solution of Exercise 39.1.**

[Melting](#def-g6-water-states-changes) (frost off the morning grass); [solidification](#def-g6-water-states-changes) (the freezer’s ice cubes); [vaporization](#def-g6-water-states-changes) (laundry drying, the boiling pot); [condensation](#def-g6-water-states-changes) (mist on the cold [mirror](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#def-g5-mirrors-reflection-reflection)); [sublimation](#def-g6-water-states-changes) (a snowbank shrinking in dry frost); [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) to [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) directly (frost feathers on the pane).

**Exercise 39.2 ★.**

Which door: dew forming on cold grass at dawn? a snowman shrinking on a sunny $-5\,{}^{\circ}\mathrm{C}$ day, with no puddle appearing? ice cubes clouding the freezer with “smoke”?

**Solution of Exercise 39.2.**

Dew: [condensation](#def-g6-water-states-changes). The puddle-less shrinking snowman: [sublimation](#def-g6-water-states-changes) — [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) straight to vapor in the cold dry [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air). The freezer’s “smoke”: [condensation](#def-g6-water-states-changes) — room vapor condensing into a little cloud in the cold [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) (droplets, not [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas)).

**Exercise 39.3 ★.**

A sealed bottle of water weighs $412\,\mathrm{g}$. It [freezes](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) overnight. What does it weigh now, and which proposition answers?

**Solution of Exercise 39.3.**

Still $412\,\mathrm{g}$: [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) survives changes of state — the sealed bottle lost and gained nothing.

**Exercise 39.4 ★.**

In [Method 39.3](#met-g6-water-states-weigh), why must the bottle be capped — and why dried before each weighing?

**Solution of Exercise 39.4.**

Capped, so no vapor can drift off with its [grams](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) (the audit must stay closed); dried, because clinging water or frost from outside would add foreign [grams](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) that belong to the room, not the audit.

**Exercise 39.5 ★.**

A pot of water boils uncovered for ten minutes and its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) drops by $200\,\mathrm{g}$. Was [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) destroyed? Where are those [grams](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units)?

**Solution of Exercise 39.5.**

Not destroyed: $200\,\mathrm{g}$ of water left as vapor through the kitchen [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) — [vaporization](#def-g6-water-states-changes) moved the [grams](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) out of the pot, not out of the world.

**Exercise 39.6 ★.**

One [litre](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) of water goes into the freezer. About what [volume](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) of ice comes out? Same question for the [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass).

**Solution of Exercise 39.6.**

About $1.1\,\mathrm{L}$ of ice — a tenth more room. The [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) is unchanged: $1\,\mathrm{kg}$ going in, $1\,\mathrm{kg}$ coming out.

**Exercise 39.7 ★.**

Why do water pipes burst in hard winters — and why do gardeners drain their outdoor taps in autumn?

**Solution of Exercise 39.7.**

Water trapped in a pipe swells as it [freezes](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze), and the pipe, like the glass bottle, gives way. Gardeners drain autumn taps so there is nothing left inside to swell.

**Exercise 39.8 ★.**

Why does ice [float](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words) on water? Connect [Proposition 39.6](#prop-g6-water-states-volume) to the floating rule — lighter or heavier for the same room?

**Solution of Exercise 39.8.**

Ice packs a [litre](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume)’s stuff into $1.1$ [litres](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) of room: lighter than water for the same room — and lighter-for-the-same-room is exactly what [floats](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words).

**Exercise 39.9 ★★.**

Tell the water cycle as a ledger: follow $1\,\mathrm{kg}$ of sea water around the full loop, naming each door it passes and stating its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) at every stage.

**Solution of Exercise 39.9.**

Sea ($1\,\mathrm{kg}$, [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid)) — [vaporization](#def-g6-water-states-changes) — vapor ($1\,\mathrm{kg}$) — [condensation](#def-g6-water-states-changes) — cloud droplets ($1\,\mathrm{kg}$) — [solidification](#def-g6-water-states-changes) — snow ($1\,\mathrm{kg}$) — [melting](#def-g6-water-states-changes) — meltwater ($1\,\mathrm{kg}$) — river to sea ($1\,\mathrm{kg}$). Six stages, one unchanging [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass).

**Exercise 39.10 ★★.**

A lemonade glass is filled to the very brim, ice cubes bobbing. A guest worries it will overflow as the ice [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze). Use the two audits ([mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) kept, ice’s extra room given back) to reassure — or alarm — the guest, with your reasoning.

**Solution of Exercise 39.10.**

Reassure. The bobbing ice already displaces its own *[weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight)* of lemonade; [melting](#def-g6-water-states-changes) returns exactly that water, shrunk back by the tenth it had swollen — it slips into the room the cube was already using below the surface. The glass stays brim-full, overflowing not a drop.

**Exercise 39.11 ★★.**

Frost feathers appear on a freezing window pane overnight in a dry room, with no rain and no wet pane at bedtime. Which door did the water take, from where, and why is this door’s name not “freezing”?

**Solution of Exercise 39.11.**

The gas-to-solid door: invisible 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) touched the freezing pane and built ice directly, skipping [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid). It is not “freezing” because nothing [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) ever existed on the pane — the water arrived straight from the vapor state.

**Exercise 39.12 ★★★.**

Ponds [freeze](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) from the top down. Explain the whole chain: why the coldest water’s ice forms *at the surface* and stays there, what the floating lid does to the [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) flow beneath (an insulation idea from last year), and why the fish below owe their winters to water’s strange swelling.

**Solution of Exercise 39.12.**

The pond loses [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) to the winter [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) at its surface, so surface water reaches $0\,{}^{\circ}\mathrm{C}$ first and its ice forms there — and [floats](https://one-course.com/books/physics/1/en/chapter/5-floating-and-sinking#def-g1-floating-and-sinking-words), being lighter than water for the same room, so it stays on top. The lid of ice (and snow) is a slow lane: it insulates the water beneath, whose [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) now leaks only slowly upward. The deep water hovers above freezing all winter, and the fish swim under a roof their strange, swelling water built for them.

## 39.6 Problem: A Kilogram Around the World

**Problem 39.1.**

Weekend problem — one kilogram of sea water on its grand tour; six doors, three mountains, one unbroken ledger

We stamp an imaginary label on $1\,\mathrm{kg}$ of sea water and follow it for a year.

**Part I — Up.**

1. June: the Sun warms the sea surface and our [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) rises into the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) , invisibly. Name the door it took.
2. What is the [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) of our (now invisible) [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) of water? Which proposition guarantees it?
3. At $3000\,\mathrm{m}$ , the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) is cold: the water becomes a cloud of droplets. Name this door.
4. Colder still, the droplets become snowflakes. Name that door — [solidification](#def-g6-water-states-changes) — and state the [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) at which cloud droplets of pure water begin to [freeze](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) .

**Part II — The glacier’s ledger.** Our [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) lands on a glacier and is pressed into glacier ice.

5. As water, our [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) occupied $1\,\mathrm{L}$ . About what [volume](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) does it occupy as ice?
6. The glacier’s snout [melts](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-meltfreeze) in summer. Our [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) becomes meltwater: what is its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) now, and its [volume](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) (back as [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) water)?
7. On the way down the mountain, $250\,\mathrm{g}$ of our [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) [evaporates](https://one-course.com/books/physics/1/en/chapter/9-ice-water-steam#def-g2-ice-water-steam-evapcond) from a sunlit waterfall pool. How much of the labeled water continues as [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid) in the stream?
8. Has the evaporated quarter left the audit? Say where its $250\,\mathrm{g}$ are, and what door they will most likely take next.

**Part III — Home, and the books balanced.**

9. The stream’s $750\,\mathrm{g}$ reach the sea in October. The evaporated $250\,\mathrm{g}$ fell as rain over the coast in August and ran to the sea in September. Add up what the sea got back of our [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) .
10. Along the whole tour, our [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) was weightless exactly never — but it was *invisible* twice. At which stages, and in which state?
11. A classmate objects: “Snow is fluffy and [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) — surely the [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) weighed less as snow.” Untangle the mix-up with the right pair of words from this year.
12. Write the tour as a chain of doors, in order, using only the six proper names of [Definition 39.1](#def-g6-water-states-changes) .

**Solution of Problem 39.1.**

**1.** [Vaporization](#def-g6-water-states-changes) (evaporation from the warm surface). **2.** Still $1\,\mathrm{kg}$ — [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) survives changes of state. **3.** [Condensation](#def-g6-water-states-changes). **4.** At $0\,{}^{\circ}\mathrm{C}$. **5.** About $1.1\,\mathrm{L}$. **6.** [Mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) $1\,\mathrm{kg}$; [volume](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume) back to $1\,\mathrm{L}$. **7.** $1000 - 250 = 750\,\mathrm{g}$ continue in the stream. **8.** No: the $250\,\mathrm{g}$ ride the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) as vapor, intact; their likeliest next door is [condensation](#def-g6-water-states-changes) — into cloud, then rain. **9.** $750 + 250 = 1000\,\mathrm{g}$: the whole [kilogram](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units) came home. **10.** Twice invisible: as vapor just after leaving the sea, and as vapor again over the waterfall pool — both in the [gas](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-gas) state. **11.** Fluffy is about *[volume](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume)*: snow is ice crystals laced with [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air), taking generous room. The *[mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass)* of our labeled water stayed exactly $1\,\mathrm{kg}$ — light-per-room is not light-in-stuff: the pair of words is [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) and [volume](https://one-course.com/books/physics/1/en/chapter/38-mass-and-volume#def-g6-mass-and-volume-volume). **12.** [Vaporization](#def-g6-water-states-changes), [condensation](#def-g6-water-states-changes), [solidification](#def-g6-water-states-changes), [melting](#def-g6-water-states-changes) — and for the evaporated quarter: [vaporization](#def-g6-water-states-changes), [condensation](#def-g6-water-states-changes) (rain), rejoining as [liquid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-liquid). Four doors used; [sublimation](#def-g6-water-states-changes) and the gas-to-solid door were not needed on this tour.