Conceptual Physics

Paul G. Hewitt

Chapter 15

Temperature, Heat, and Expansion

Educators


Problem 1

What is meant by temperature? What is the underlying cause of warmth produced by matter?

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Problem 2

What are the temperatures for freezing water and boiling water on the Kelvin temperature scale?

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Problem 3

What happens to kinetic energy at absolute zero?

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Problem 4

Which forms of energy determine temperature: translational kinetic energy, rotational kinetic energy, vibrational kinetic energy, or all of these?

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Problem 5

Why should a thermometer be small in comparison with an object the temperature of which needs measurement?

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Problem 6

Is there a distinction between thermal energy and internal energy? Which term do physicists prefer?

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Problem 7

What is internal energy? What are the different constituents of internal energy?

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Problem 8

Does a hot object contain internal energy, or does it contain heat?

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Problem 9

How does heat differ from internal energy, or are they two terms for the same thing?

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Problem 10

What role does temperature have in the direction of internal energy flow?

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Problem 11

How is the energy value of foods determined?

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Problem 12

How is the unit of heat known as a ‘calorie’ defined?

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Problem 13

What is the relationship between calories and joules?

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Problem 14

How many joules are needed to change the temperature of 1 gram of water by 1°C?

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Problem 15

Why does iron warm faster than water upon the application of heat?

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Problem 16

Does a substance that heats up quickly have a high or a low specific heat capacity?

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Problem 17

Why is it appropriate to think of specific heat capacity as thermal inertia?

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Problem 18

Why is water the preferred choice as a cooling agent in the cooling systems of automobiles and engines?

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Problem 19

Northeastern Canada and much of Europe receive about the same amount of sunlight per unit area. Why, then, is Europe generally warmer in the winter?

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Problem 20

According to the law of conservation of energy, if ocean water cools, then something else should warm. What is it that warms?

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Problem 21

Why do islands and peninsulas surrounded by water not experience extremes of temperatures?

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Problem 22

Why do most substances contract when they are cooled?

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Problem 23

Why does a bimetallic strip bend with changes in temperature?

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Problem 24

What would happen if the glass of a thermometer were to expand as much as the mercury within it?

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Problem 25

When the temperature of ice-cold water is increased slightly, does it undergo a net expansion or a net contraction?

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Problem 26

Mention the temperature range within which water doesn’t expand upon heating.

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Problem 27

Does “microscopic slush” in water tend to make it more dense or less dense?

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Problem 28

What happens to the amount of “microscopic slush” in cold water when its temperature is increased?

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Problem 29

At what temperature do the combined effects of contraction and expansion produce the smallest volume for water?

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Problem 30

Why does all the water in a lake have to be cooled to $4^{\circ} \mathrm{C}$ before the surface water can be cooled below $4^{\circ} \mathrm{C} ?$

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Problem 31

How much energy is in a nut? Burn it and find out. The heat from the flame is energy released when carbon and hydrogen in the nut combine with oxygen in the air (oxidation reactions) to produce $\mathrm{CO}_{2}$ and $\mathrm{H}_{2}$ O. Pierce a nut (pecan or walnut halves work best) with a bent paper clip that holds the nut above the table surface. Above this, secure a can of water so that you can measure its temperature change when the nut burns. Use about $10^{3} \mathrm{cm}(10 \mathrm{mL})$ of water and a Celsius thermometer. As soon as you ignite the nut with a match, place the can of water above it and record the increase in water temperature once the flame burns out. The number of calories released by the burning nut can be calculated by the formula $Q=\mathrm{cm} \Delta T$ , where $c$ is its specific heat $\left(1 \mathrm{cal} / \mathrm{g} \cdot^{\circ} \mathrm{C}\right), m$ is the mass of water, and $\Delta T$ is the change in temperature. The energy in food is expressed in terms of the Calorie, which is 1000 of the calories you'll measure. So to find the number of Calories, divide your result by 1000 . (See Think and Solve $\# 36 . )$

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Problem 32

Write a letter to your grandparents describing how you’re learning to see connections in nature that have
eluded you until now, and how you’re learning to distinguish related ideas. Use temperature and heat as examples.

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Problem 33

How much energy in calories is required to raise the temperature of 200 g of water from 20°C to 30°C? For the specific heat capacity c, use 1 cal/g?°C.

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Problem 34

Use the same formula to calculate the heat required in joules to raise the temperature of the same mass $(0.2 \mathrm{kg})$ of water through double the temperature interval. For the specific heat capacity $c$ , use 4190 $\mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$ .

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Problem 35

Show that 3000 cal = 12,570 J, the same quantity of thermal energy in different units.

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Problem 36

Will Maynez burns a 0.6 -g peanut beneath 50 $\mathrm{g}$ of water, which increases in temperature from $22^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C} .$ The specific heat capacity of water is 1.0 $\mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C} . )$
a. Assuming that 40$\%$ of the heat released by the burning peanut makes its way to the water $(40 \% \text { efficiency })$ show that the peanut's food value is 3500 calories (equivalently, 3.5 Calories).
b. Then show how the food value in calories per gram is 5.8 $\mathrm{kcal} / \mathrm{g}(\text { or } 5.8 \mathrm{Cal} / \mathrm{g})$

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Problem 37

If you wish to warm 50 $\mathrm{kg}$ of water by $20^{\circ} \mathrm{C}$ for your bath, show that the amount of heat needed is 1000 $\mathrm{kcal}$ $(1000 \mathrm{Cal}) .$ Then show that this is equivalent to about 4200 $\mathrm{kJ}$

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Problem 38

The specific heat capacity of steel is 450 $\mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C}$ . Show that the amount of heat needed to raise the temperature of a 10 -kg piece of steel from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ is $450,000 \mathrm{J}$ . How does this compare with the heat needed to raise the temperature of the same mass of water through the same temperature difference?

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Problem 39

A bar that is 1 $\mathrm{m}$ in length expands by 0.3 $\mathrm{cm}$ when heated. If a 200 -m bar of the same material is heated to the same temperature, calculate its final length.

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Problem 40

Suppose that the $1.3-\mathrm{km}$ main span of steel for the Golden Gate Bridge had no expansion joints. Show that for an increase in temperature of $20^{\circ} \mathrm{C},$ the bridge would be nearly 0.3 $\mathrm{m}$ longer.

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Problem 41

Imagine a $40,000$ -km steel pipe that forms a ring to fit snugly entirely around the circumference of Earth. Suppose that people along its length breathe on it so as to raise its temperature by $1^{\circ} \mathrm{C}$ . The pipe gets longer- and is also no longer snug. How high does it stand above ground level? Show that the answer is an astounding 70 m higher! (To simplify, consider only the expansion of
its radial distance from the center of Earth, and apply the geometry formula that relates circumference $C$ and radius $r : C=2 \pi r$ .

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Problem 42

Rank the magnitudes of these units of thermal energy from greatest to least:
a. 1 calorie
b. 1 Calorie
c. 1 joule

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Problem 43

Three blocks of metal at the same temperature are placed on a hot stove. Their specific heat capacities are listed below. Rank them from greatest to least in how quickly each warms up.
a. Steel, 450 $\mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$
b. Aluminum, 910 $\mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$
c. Copper, 390 $\mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$

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Problem 44

How much the lengths of various substances change with temperature changes is given by their coefficients of linear expansion, $\alpha .$ The greater the value of $\alpha,$ the greater the change in length for a given change in temperature. Three kinds of metal wires, A, $\mathrm{B}$ , and $\mathrm{C}$ , are stretched between distant telephone poles. From greatest to least, rank the wires in how much they'll sag on a hot summer day.
a. Copper, $\alpha=17 \times 10^{-6 /^{\circ} \mathrm{C}} \mathrm{C}$
b. Aluminum, $\alpha=24 \times 10^{-6} /^{\circ} \mathrm{C}$
c. Steel, $\alpha=11 \times 10^{-6 / 9} \mathrm{C}$

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Problem 45

The precise volume of water in a beaker depends on the temperature of the water. Rank from greatest to least the volumes of water at these temperatures:
a. $0^{\circ} \mathrm{C}$
b. $4^{\circ} \mathrm{C}$
c. $10^{\circ} \mathrm{C}$

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Problem 46

In a meeting room, there are chairs, a table, and people. Which of these things has a temperature (a) lower than, (b) greater than, or (c) equal to the temperature of the air?

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Problem 47

Which is greater: an increase in temperature of 1 Celsius degree or an increase of 1 Fahrenheit degree?

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Problem 48

Are the oscillating molecules of water responsible for food getting cooked in a microwave oven?

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Problem 49

Why wouldn’t you expect all the molecules in a gas to have the same speed?

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Problem 50

Why can’t you establish whether you are running a high temperature by touching your own forehead?

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Problem 51

Which has more kinetic energy: a molecule in a gram of ice water or a molecule in a gram of steam? Defend your answer.

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Problem 52

Which has the greater amount of internal energy: an ice-berg or a cup of hot coffee? Defend your answer.

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Problem 53

When a mercury thermometer is heated, the mercury expands and rises in the thin tube of glass. What does this indicate about the relative rates of expansion for mercury and glass? What would happen if their expansion rates were the same?

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Problem 54

Which is the largest unit of heat transfer: Calorie, calorie, or joule?

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Problem 55

Consider two glasses, one filled with water and the other half-full, with the water in the two glasses being at the same temperature. In which glass are the water molecules moving faster? In which is there greater internal energy? In which will more heat be required to increase the temperature by $1^{\circ} \mathrm{C} ?$

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Problem 56

Thermometers in a physics lab often use gas rather than mercury. Whereas changes in volume indicate temperature in a mercury thermometer, what changes in a gas do you think indicate temperature in a gas thermometer?

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Problem 57

Why does the pressure of gas enclosed in a rigid container increase as the temperature increases?

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Problem 58

Adding the same amount of heat to two different objects of the same mass does not necessarily produce the same increase in temperature. Why not?

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Problem 59

A certain quantity of heat is supplied to both a kilogram of water and a kilogram of iron. Which undergoes the greater change in temperature? Defend your answer.

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Problem 60

Which likely has the greater specific heat capacity: an object that cools quickly, or an object of the same mass that cools more slowly?

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Problem 61

If the specific heat capacity of water were less, would a nice hot bath be a longer or a shorter experience?

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Problem 62

Why does a piece of watermelon stay cool for a longer time than sandwiches do when both are removed from a picnic cooler on a hot day?

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Problem 63

Ethyl alcohol has about one-half the specific heat capacity of water. If equal masses of each at the same temperature are supplied with equal quantities of heat, which will undergo the greater change in temperature?

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Problem 64

When a 1-kg metal pan containing 1 kg of cold water is removed from the refrigerator and set on a table, which absorbs more heat from the room: the pan or the water?

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Problem 65

In times past, on a cold winter night, it was common to bring a hot object to bed with you. Which would keep you warmer through the cold night: a 10-kg iron brick or a 10-kg jug of hot water at the same temperature? Explain.

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Problem 66

Bermuda is about as far north of the equator as North Carolina, but, unlike North Carolina, it has a subtropical climate year-round. Why is this so?

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Problem 67

Iceland, so named to discourage conquest by expanding empires, is not at all ice covered, like Greenland and parts of Siberia, even though it is not far from the Arctic Circle. The average winter temperature of Iceland is considerably higher than it is in regions at the same latitude in eastern Greenland and central Siberia. Why is this so?

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Problem 68

Why does the presence of large bodies of water tend to moderate the climate of nearby land—to make it warmer in cold weather and cooler in hot weather?

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Problem 69

If the winds at the latitude of San Francisco and Washington, DC, were from the east rather than from the west, why might San Francisco be able to grow only cherry trees and Washington, DC, both cherry trees
and palm trees?

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Problem 70

Desert sand is very hot in the day and very cool at night. What does this indicate about its specific heat capacity?

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Problem 71

Cite an exception to the claim that all substances expand when heated.

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Problem 72

Would a bimetallic strip function if the two different metals had the same rates of expansion? Is it important that they expand at different rates? Explain.

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Problem 73

Steel plates are commonly attached to each other with rivets, which are slipped into holes in the plates and rounded over with hammers. The hotness of the rivets makes them easier to round over, but their hotness has another important advantage in providing a tight fit. What is it?

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Problem 74

An old method for breaking boulders was to put them in a hot fire and then to douse them with cold water. Why would this fracture the boulders?

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Problem 75

After you have driven a car for some distance, why does the air pressure in the tires increase?

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Problem 76

Structural groaning noises are sometimes heard in the attics of old buildings on cold nights. Give an explanation in terms of thermal expansion.

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Problem 77

An old technique for separating a pair of nested drinking glasses that stick together is to run water at different temperatures into the inner glass and over the surface of the outer glass. Which water should be hot, and which cold?

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Problem 78

Why is it important that glass mirrors used in astronomical observatories be made of glass with a low “coefficient of expansion”?

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Problem 79

In terms of thermal expansion, why is it important that a key and its lock be made of the same or similar
materials?

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Problem 80

Any architect will tell you that chimneys are never used as a weight-bearing part of a wall. Why?

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Problem 81

Look at the expansion joint in the photo of Figure 15.13. Would you say the photo was taken on a warm day or a cold day? Why?

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Problem 82

Would you or the gas company gain by having gas warmed before it passes through your gas meter?

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Problem 83

After filling your gas tank to the top and parking your car in direct hot sunlight, why does the gasoline
overflow?

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Problem 84

When a mercury thermometer is warmed, the mercury level momentarily goes down before it rises. Can you give an explanation for this?

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Problem 85

Why do long steam pipes often have one or more relatively large U-shaped sections of pipe?

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Problem 86

Why are incandescent bulbs typically made of very thin glass?

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Problem 87

One reason the first lightbulbs were expensive was due to the platinum lead wires into the bulb, necessary because their expansion matched that of glass when heated. Why is it important that the metal leads and the glass have the same coefficient of expansion?

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Problem 88

What was the precise temperature at the bottom of Lake Superior at 12:01 am on December 31, 2013?

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Problem 89

Suppose that water is used in a thermometer instead of mercury. If the temperature is at $4^{\circ} \mathrm{C}$ and then changes, why can’t the thermometer indicate whether the temperature is rising or falling?

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Problem 90

A piece of solid iron sinks in a container of molten iron. A piece of solid aluminum sinks in a container of molten aluminum. Why doesn’t a piece of solid water (ice) sink in a container of “molten” (liquid) water? Explain, using molecular terms.

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Problem 91

What happens to the volume of water as it is cooled from $3^{\circ} \mathrm{C}$ to $1^{\circ} \mathrm{C} ?$

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Problem 92

State whether water at the following temperatures will expand or contract when warmed a little: $0^{\circ} \mathrm{C}, 4^{\circ} \mathrm{C}, 6^{\circ} \mathrm{C}$ .

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Problem 93

Why is it important to protect water pipes in the winter so that they don’t freeze?

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Problem 94

If water had a lower specific heat capacity, would ponds be more likely to freeze or less likely to freeze?

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Problem 95

If cooling occurred at the bottom of a pond instead of at the surface, would the pond freeze from the bottom up? Explain.

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Problem 96

If you drop a hot rock into a pail of water, the temperature of the rock and the water will change until both are equal. The rock will cool and the water will warm. Does this hold true if the hot rock is dropped into the Atlantic Ocean? Discuss.

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Problem 97

Would you expect the temperature of the water at the bottom of Niagara Falls to be slightly higher than the temperature at the top of the falls? Discuss.

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Problem 98

Heat added to a substance goes partly into the translational kinetic energy of its molecules, which directly elevates temperature. For some substances, large proportions of heat also go into vibrations and rotations of the molecules. Discuss whether you’d expect materials in which a lot of energy goes into nontranslational molecular motions to have a high or a low specific heat capacity.

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Problem 99

A metal ball is just able to pass through a metal ring. When Anette increases the temperature of the ball, however, it will not pass through the ring. What would happen if she instead increased the temperature of the ring rather than the ball? Discuss whether the size of the hole increases, stays the same, or decreases.

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Problem 100

Consider a pair of brass balls of the same diameter, one hollow and the other solid. Both are heated with equal increases in temperature. Discuss and compare the diameters of the heated balls.

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Problem 101

After a machinist very quickly slips a hot, snugly fitting iron ring over a very cold brass cylinder, the two cannot be separated intact. Discuss why this is so.

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Problem 102

Suppose that you cut a small gap in a metal ring. If you were to heat the ring, discuss whether the gap would become wider or narrower.

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Problem 103

After you measure the dimensions of a plot of land with a steel tape on a hot day, you return and remeasure the same plot on a cold day. On which day do you determine the larger area for the land?

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Problem 104

How would the shape of the $0^{\circ} \mathrm{C}-18^{\circ} \mathrm{C}$ curve in Figure 15.21 differ if density rather than volume were plotted against temperature? Make a rough sketch.

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Problem 105

Discuss how the combined volume of the billions and billions of hexagonal open spaces in the structures of ice crystals in a piece of ice compares with the portion of the ice that floats above the waterline.

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