A First Course in Physics · Ch. VII, §§ 191–192 · Chapter 7: Thermometry; Expansion Coefficients
20. The gas laws: Charles and Boyle together
Goal: Your student can use V₁/V₂ = T₁/T₂ with absolute temperatures, combine it with Boyle's law, and solve the book's gas problems.
You'll need
- The book, open to these pages
- A balloon and a freezer (or a bowl of ice water)
- A tape measure or string
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Gay-Lussac's volume coefficient of a gas (1/273 per degree); volume, pressure and density proportional to absolute temperature. Twelve problems follow, mixing Charles's law and Boyle's law.
The lesson, step by step
Hook question
SayWhy does a bag of chips puff up in a hot car, and why do car tires look low on a cold morning?
Read together
Read §§ 191–192. The key result:
the volume of a gas at constant pressure is directly proportional to the absolute temperature.
Try it: shrink a balloon
Blow up a balloon and measure around its middle with string. Put it in the freezer for 20 minutes, then measure again quickly. It has shrunk. Let it warm up and measure once more.
Explain the method
Always change to absolute temperature first (add 273). Then:
At constant pressure, V₁/V₂ = T₁/T₂.
At constant volume, P₁/P₂ = T₁/T₂.
At constant temperature, P₁V₁ = P₂V₂ (Boyle).
When both pressure and temperature change, do it in two steps, as problem 6 suggests: first the pressure change, then the temperature change. (Today we write this as one "combined gas law": PV/T stays the same.)
Work an example together
Problem 3: a tire at 150 cm of pressure warms from 10° C (283° A) to 30° C (303° A). New pressure = 150 × 303/283 ≈ 160.6 cm.
Say it back
Your student explains why we must use absolute temperatures and not Centigrade ones (try doubling 10° C to 20° C and see that the volume does not double).
Problems
Work problems 1–12 on book page 139. For divers, every 34 ft (about 1033 cm) of water adds one atmosphere (76 cm of mercury).
Afterwards
Check car tire pressure on a cold morning and again after a drive (with an adult) and see the difference.
Answers to the book's problems
1. 273° C. 2. 30/293, about one tenth. 3. About 160.6 cm. 4. Each winter breath holds 303/253 ≈ 1.2 times as much oxygen as a summer breath. 5. 19 cc; then about 24.6 cc. 6. About 620 cc (500 × 76/70 = 543 cc, then × 323/283). 7. 100 ft. of water = 224 cm of mercury, so about 299 cm (about 4 atmospheres); density about 0.0049. 8. About 4.4 times (299/75 × 303/277). 9. About 0.00028. 10. About 185,000 liters (100,000 × 75/37 × 263/288). 11. 181.5° C (454.5° absolute). 12. About 0.00109 on the summer day; about 0.00148 on the cold day.
Worked out for this site from the scan. If a number in your copy differs, trust the book.