A First Course in Physics · Ch. IV, §§ 92–98 · Chapter 4: Pressure in Air
11. Boyle's law and the ocean of air
Goal: Your student can contrast squeezing water and air, state Boyle's law (PV stays the same), and explain why the air thins out with height.
You'll need
- The book, open to these pages
- A plastic syringe with no needle (cap the tip with a finger)
- A balloon
- A bicycle pump and a ball, if you have them
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Water is almost incompressible; air is easily squeezed and springs back; why hollow bodies are not crushed; Boyle's J-tube experiment and Boyle's law; how far the atmosphere reaches, with the 1862 balloon ascent of Glaisher and Coxwell; the "homogeneous atmosphere"; air below sea level. Eleven questions and problems follow.
The lesson, step by step
Hook question
SayWhy does a sealed bag of chips puff up when you drive into the mountains?
Read together
Read §§ 92–98. Boyle's law in the book's words:
the pressure which a given quantity of air at constant temperature exerts against the walls of the containing vessel is inversely proportional to the volume occupied.
Try it: squeeze air, squeeze water
Pull the syringe plunger back to fill it with air, block the tip with a finger and push: the air squashes and springs back. Now fill it with water and try again: it won't budge. That is the difference § 92–93 describe.
Explain Boyle's law
Double the pressure on air and its volume halves; triple it and the volume is a third. So pressure × volume stays the same: P₁V₁ = P₂V₂ (as long as the temperature doesn't change).
That is why the air at the bottom of the atmosphere is squeezed dense, and why it thins out higher up: halfway up the atmosphere's weight (at Mont Blanc) it is half as dense.
Read the balloon story
Read the story of Glaisher and Coxwell aloud (§ 96; the book spells the name "Glasier"). Discuss: why did they faint? Why did Berson carry oxygen?
What we know now
The air has no sharp top; it fades out gradually. Space is usually said to begin about 100 km (62 miles) up. People have now flown far higher than 7 miles: jet airliners cruise at about 6–7 miles, and astronauts have gone to the Moon.
Say it back
Your student explains in their own words why a can or a bottle is not crushed by the air, even though air presses on it with great force.
Problems
Work questions 1–11 on book pages 70–71.
Afterwards
Take a closed, half-empty plastic water bottle on a hill drive or flight. Notice it puff up or crumple as the outside pressure changes.
Answers to the book's problems
1. About 1600 cc. 2. About 0.0006; about one half of the atmosphere is below him. 3. About 4.2 (76 ÷ 18). 6. The air pressing on the water in the dish holds up the water in the bottle. 8. Air must get in to take the place of the cider, or the pressure inside drops and the flow stops. 9. Air must bubble in to replace the water. 10. About 116.7 cm of mercury. 11. They get larger as the pressure on them falls.
Worked out for this site from the scan. If a number in your copy differs, trust the book.