A First Course in Physics · Ch. VII, §§ 193–201 · Chapter 7: Thermometry; Expansion Coefficients
21. Expansion of liquids and solids; water's strange behavior
Goal: Your student can explain why water is densest at 4° C and why lakes freeze from the top, use the linear coefficient of expansion, and explain compensated pendulums, bimetal strips and bridge rollers.
You'll need
- The book, open to these pages
- A glass jar with a tight metal lid, and hot tap water
- A strip of aluminum foil glued to a strip of paper (a homemade bimetal strip) and a hair dryer
- Ice cubes and a glass of water
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Liquids expand irregularly and differently; measuring their expansion; water's maximum density at 4° C (Hope's experiment); how a lake cools in winter; linear coefficients of solids and a table of them; compensated pendulums and balance wheels; the bimetal strip and dial thermometer; rollers under iron bridges. Eight problems follow.
The lesson, step by step
Hook question
SayWhy do fish survive the winter under the ice of a frozen pond?
Read together
Read §§ 193–201. The book's conclusion about lakes:
Thus, before any ice whatever can form on the surface of a lake, the whole mass of water to the very bottom must be cooled to 4° C.
Explain the idea
Most things shrink as they cool. Water does too, down to 4° C; below that it expands again, and ice is lighter still. So in autumn the cold surface water sinks until the whole lake is at 4°; then colder water stays on top and freezes there (§ 196).
For solids, the linear coefficient is the fraction of its length a bar grows per degree: iron about 0.000012. A 100 ft iron bridge grows about ¾ inch from winter to summer (§ 201).
Try it: the stuck lid
Run hot tap water over a tight metal jar lid for half a minute: it now twists off more easily, because metal expands more than glass (question 1 is the same idea).
Try it: a bimetal strip
Glue foil to a paper strip and warm it with a hair dryer (on low, held back a bit). It curls, because the two layers expand differently (§ 199, Fig. 142). The dial thermometer in Fig. 143 works this way, and so do many thermostats.
Watch only: heated ball and ring
The ball-and-ring demonstration (back in § 147) and the heated brass-and-iron bar (§ 199) use a gas flame and very hot metal. Look up a video of a teacher doing the "ball and ring" demonstration instead.
Say it back
Your student explains why railroad rails and bridges need gaps or rollers.
Problems
Work problems 1–8 on book page 145, using the table of coefficients on page 142 (iron 0.000012, steel 0.000011, copper 0.000017, platinum and glass 0.000009).
Afterwards
Look for expansion joints in sidewalks, bridges and highway overpasses.
Answers to the book's problems
1. The hot water warms and expands the neck before the stopper. 2. 60.072 ft. 3. About 2.9 ft. 4. About 0.37 ft. (about 4.5 in.). 5. About 0.000012. 6. 0.018 ft. (about 0.22 in.). 7. About 1.41 m (2 × 12/17). 8. Platinum expands at the same rate as glass (0.000009), so the seal does not crack as it heats and cools.
Worked out for this site from the scan. If a number in your copy differs, trust the book.