A First Course in Physics · Ch. X, §§ 264–274 · Chapter 10: Change of State
30. Melting and freezing: the heat of fusion
Goal: Your student can explain why melting ice stays at 0° C, use the heat of fusion of ice (80 calories per gram) in mixing problems, and explain why water's expansion on freezing matters so much.
You'll need
- The book, open to these pages
- Ice cubes, a kitchen scale (grams), a thermometer and an insulated cup
- Warm tap water
- A plastic bottle filled to the top with water and capped loosely (for the freezer)
- Two ice cubes
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
The thermometer stays at 0° C while snow melts; the heat of fusion of ice (about 80 calories per gram), measured by mixing ice and warm water; freezing gives out heat; latent heat; fixed melting points of crystals and a table of them; glass and wax soften instead; water expands on freezing; pressure lowers the melting point of ice, and regelation (a wire cutting through ice). Seven problems follow.
The lesson, step by step
Hook question
SayIf you heat a pot of ice slowly, the thermometer stops at 0° C until all the ice is gone. Where is the heat going?
Read together
Read §§ 264–274. The definition:
The number of calories of heat energy required to melt one gram of any substance without producing any change in its temperature is called the heat of fusion of that substance.
Try it: measure the heat of fusion
Weigh about 200 g of warm water (near 40° C) in an insulated cup and record the temperature. Dry an ice cube with a paper towel, weigh it, drop it in and stir until it melts; record the final temperature.
Work it like § 265: heat lost by the warm water = ice mass × x + ice mass × final temperature. Solve for x. You should get somewhere near 80.
Explain the idea
Melting does not speed up the molecules; it pulls them apart, so the temperature stays put. The same 80 calories come back out when the water freezes (§ 266). In SI units the heat of fusion of ice is about 334 joules per gram.
Try it: ice that sticks
Press two ice cubes firmly together for half a minute, under water if you like: they freeze together (§ 273). Pressure melts a thin film where they touch; when you let go, it freezes again. This is regelation.
Water expands when it freezes
Leave the full, loosely capped plastic bottle in the freezer overnight (plastic only, never glass). It bulges. The book points out that if ice sank instead of floating, lakes would freeze solid from the bottom up (§ 272).
Say it back
Your student explains why ice at 0° C cools a drink much better than the same weight of water at 0° C (question 1).
Problems
Work problems 1–7 on book page 202. Use 80 calories to melt a gram of ice and 427 gram meters of work per calorie.
Afterwards
Watch an ice cube melt in a glass of water with a thermometer in it. The water stays near 0° C until the ice is gone.
Answers to the book's problems
1. The ice, because each gram must take in 80 calories to melt before it begins to warm. 2. 80° C. 3. About 66.7 g. 4. About 34,000 m (80 calories × 427 gram meters per gram). 5. Ice would sink as fast as it formed, and lakes and rivers would freeze solid from the bottom. 6. Pressing melting snow melts it a little at the points of contact, and it refreezes when released (regelation); very cold snow does not melt under the pressure of your hands. 7. 20° C.
Worked out for this site from the scan. If a number in your copy differs, trust the book.