A First Course in Physics · Ch. V, §§ 113–120 · Chapter 5: Molecular Motions
13. Molecules in motion: the kinetic theory of gases
Goal: Your student can explain the evidence that gas molecules are always moving, and use the kinetic theory to explain gas pressure, Boyle's law, and why a warm gas pushes harder.
You'll need
- The book, open to these pages
- A bottle of perfume, vanilla or an orange to peel
- An empty plastic bottle and a balloon (for warming air)
- A bowl of hot tap water and a bowl of ice water
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Matter made of molecules; smells spreading across a room and gases mixing (diffusion); gas pressure as the blows of moving molecules; Boyle's law explained; molecular speeds of hundreds of meters per second; diffusion through a porous cup; temperature as molecular speed. Six problems follow, with a portrait and short life of James Clerk Maxwell.
The lesson, step by step
Hook question
SayIf I peel an orange in the kitchen, how does the smell get to the far end of the house, even with no breeze?
Read together
Read §§ 113–120. The heart of the chapter:
To increase the temperature is to increase the average velocity of the molecules, and to diminish the temperature is to diminish this average molecular velocity.
Try it: smell races
Stand at one end of a room while a helper opens perfume or peels an orange at the other. Time how long until you smell it. The molecules have wandered across the room, bumping into air molecules all the way (diffusion).
Explain the idea
Gas molecules are far apart and moving very fast, faster than a rifle bullet. Their blows on the walls are what we call pressure (§ 116). Squeeze the gas into half the space and twice as many blows land each second: twice the pressure (that is Boyle's law, § 117). Heat it and the molecules move faster and hit harder (§ 120).
Try it: warm air pushes
Stretch a balloon over the mouth of an empty plastic bottle. Stand the bottle in a bowl of hot tap water: the balloon starts to fill up. Move it to ice water: the balloon goes limp again. Nothing went in or out; the molecules just sped up and slowed down.
What we know now
In 1906 some scientists still doubted that atoms and molecules were real. Einstein's 1905 explanation of Brownian motion (the jiggling of tiny specks in water) and Jean Perrin's experiments soon after settled it. Today we can even take pictures of single atoms with special microscopes. The book's speeds are about right: air molecules at room temperature average roughly 500 m per second.
Say it back
Your student explains, using molecules, why a bicycle tire feels harder after a ride on a hot day.
Problems
Work problems 1–6 on book page 88. They use Boyle's law (P₁V₁ = P₂V₂) from Chapter IV.
Afterwards
Put a drop of food coloring in a glass of cold water and one in hot water, without stirring. Which spreads faster, and why?
Answers to the book's problems
1. About 176.7 cm (76 × 1000 ÷ 430). 2. About 246.7 g. 3. About 784,000 cc (784 liters). 4. 75 cm (the air above has a pressure of 2 cm; doubling its volume halves it to 1 cm). 5. 201 ft. = 6126 cm of water = 450.5 cm of mercury, so about 525.5 cm of mercury in all (about 7 atmospheres); the air density is about 0.0083. 6. About 7 times.
Worked out for this site from the scan. If a number in your copy differs, trust the book.