A First Course in Physics · Ch. IX, §§ 249–251 · Chapter 9: Work and Heat Energy
28. Specific heat and the method of mixtures
Goal: Your student can define specific heat, use "heat lost = heat gained" to find a final temperature or a specific heat, and explain why water warms and cools slowly.
You'll need
- The book, open to these pages
- Two insulated mugs or foam cups
- A kitchen scale (grams) and a thermometer
- Hot tap water and cold water
- A handful of metal objects (steel washers, coins or a metal spoon)
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Heating by work and by contact; specific heat defined; the experiment with hot lead, iron and aluminum dropped into water; the method of mixtures with a worked example; a table of specific heats. Ten problems follow.
The lesson, step by step
Hook question
SayOn a sunny day at the beach, why is the sand too hot to walk on while the water is still cool?
Read together
Read §§ 249–251. The definition:
The number of calories taken up by one gram of a substance when its temperature rises through 1° C., or given up when it falls through 1° C., is called the specific heat of that substance.
Try it: mixing water
Weigh 200 g of hot tap water into one cup and 100 g of cold water into the other. Take both temperatures. Pour together, stir and measure. Predict first with "heat lost = heat gained": 200 × (hot − x) = 100 × (x − cold). How close was the prediction? (An adult handles the hot water.)
Try it: metal versus water
Warm the metal objects in hot tap water for a few minutes, weigh them, and drop them into 100 g of cold water. The water warms only a little, because metals have small specific heats (iron about 0.11, from the table on page 185).
Explain the idea
Specific heat is how many calories one gram needs to warm 1°. Water's is 1, larger than almost anything else (question 6). That is why oceans keep islands mild and why water is used to cool engines.
In SI units, water's specific heat is about 4.18 joules per gram per degree.
Say it back
Your student explains the method of mixtures in their own words, using the book's lead-shot example.
Problems
Work problems 1–10 on book pages 185–186, using the table of specific heats.
Afterwards
Compare how fast a metal spoon and a wooden spoon in the same cup of hot tea warm up, and how long a pot of soup stays hot.
Answers to the book's problems
1. About 0.034. 2. 4,500,000,000 ergs; about 107 calories, which warms 10 g of lead (specific heat 0.0315) about 340° C. 3. About 135 m (0.315 calorie × 427 gram meters per gram). 4. About 56.7° C. 5. About 21.2° C. 6. Water warms and cools slowly, so the sea keeps the island from getting very hot or very cold. 7. 120 g. 8. The work of the blows turns to heat; the iron is heated less, since the hammer bounces back with much of its energy and iron's specific heat is greater. 9. About 11,900 calories per gram of the moon's mass; spread over twice that mass with specific heat 0.5, a rise of about 11,900° C. 10. About 1774° C.
Worked out for this site from the scan. If a number in your copy differs, trust the book.