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Lesson: Chapter 9 — Heat

Putting the chapter together 2 of 3

The exercise

Worked answers to exercise 9.3.

Question 1 — fill the blanks

Fill the blanks

  1. The international unit of temperature is ______ and of quantity of heat is ______.
  2. Absolute zero equals ______ Celsius.
  3. While latent heat is taken in, the ______ does not change but the ______ changes.
  4. Heat travels with no medium taking part by ______.
  5. Objects with low specific heat capacity ______, and those with high specific heat capacity ______.

The answer

  1. The kelvin (K); the joule (J)
  2. −273 °C (−273.15 °C)
  3. temperature; state
  4. radiation
  5. heat up quickly; heat up slowly

Question 2 — two cups of tea cooling

Two cups of the same shape and size, made of different materials, are filled with equal amounts of hot tea and left to cool. In the graph cup A is the solid line, cup B the dashed curve, and the flat dashed line is room temperature, 20 °C.

t (min) 5 15
T (°C) 55.2 32.9

Read the graph

  1. The temperature of the tea in cup A after 5 minutes?
  2. How long does the tea in cup B take to fall to 30 °C?
  3. The temperature difference between the cups after 15 minutes?
  4. Which cup is made of the better insulator?
  5. Why?
  6. What will the final temperature of the tea in both cups be?

The answer

  1. About 55 °C
  2. About 10 minutes
  3. About 9 °C (about 33 °C against about 24 °C)
  4. Cup A
  5. Its tea cools more slowly, so less heat escapes through its walls.
  6. Room temperature, 20 °C

Readings from our redrawing of the graph, so approximate — as readings from any graph are.

Question 3 — the vacuum flask

Figure to be added

A cross-section of a vacuum flask: stopper, vacuum, silvered inner wall, hot water, outer case.

A vacuum flask (thermos)

  1. Give two different uses of the flask.
  2. 500 ml of water at 100 °C is kept hot. What features stop heat loss?
  3. How much heat is lost as 500 ml of water at 100 °C cools to 25 °C? (c = 4200 J kg-1 K-1)
  4. Why should cold water not be poured in straight after hot water is emptied out?

The answer

  1. Keeping hot drinks hot, and keeping cold drinks cold.
  2. The vacuum between the walls stops conduction and convection; the silvered walls reflect radiation; the stopper stops convection and evaporation from the top.
  3. 500 ml of water has a mass of 0.5 kg. Q = 0.5 × 4200 × (100 − 25) = 157 500 J.
  4. The hot glass would suddenly cool and contract unevenly, and it could crack.

Question 4

Water and steam

  1. Find the heat given out as 10 g of water at 100 °C cools to 25 °C.
  2. Explain why a scald from steam at 100 °C is worse than one from boiling water at 100 °C.

The answer

  1. Q = 0.01 × 4200 × 75 = 3150 J
  2. Steam condensing on the skin first gives out its latent heat of vaporization — 2.26 × 106 J for every kilogram, about 22 600 J for 10 g — and only then cools like the water. So steam delivers far more heat to the skin than the same mass of boiling water.

Question 5 — heating wax

A piece of wax at room temperature is heated, and its temperature is plotted against time.

t (min) 0 2 3 4
T (°C) 25 55 55 70

Read the graph

  1. What is room temperature?
  2. What is the melting point of the wax?
  3. How long after heating began did the wax start to melt?
  4. Why is the temperature constant from 2 to 3 minutes?
  5. If heating stopped at 4 minutes, sketch how the temperature would change after that.

The answer

  1. 25 °C
  2. 55 °C
  3. 2 minutes
  4. The heat supplied is the latent heat of fusion, used to melt the wax rather than raise its temperature.
  5. It falls from 70 °C to 55 °C, stays at 55 °C while the wax solidifies, then falls towards room temperature, ever more slowly.
t (min) 4 5 7
T (°C) 70 55 55