Solved: Consider a 40,000-km steel pipe that forms a ring

Problem 1E 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?

Problem 1P What would be the final temperature of a mixture of 50 g of 20°C water and 50 g of 40°C water?

Why does a penny become warmer when it is struck by a hammer?

Problem 2E Which is greater—an increase in temperature of 1 Celsius degree or an increase of 1 Fahrenheit degree?

Problem 2P Suppose that a brass rod 1.0 m long expands 0.5 cm when its temperature is increased a certain amount. By how much will a brass rod 100 m long expand with the same change of temperature?

Problem 2RQ What are the temperatures for freezing water on the Celsius and Fahrenheit scales? For boiling water?

Problem 3E In a glass of water at room temperature, do all the molecules have the same speed?

Problem 3RQ What are the temperatures for freezing water and boiling water on the Kelvin temperature scale?

Problem 4E Why wouldn’t you expect all the molecules in a gas to have the same speed?

Problem 4P Consider a 40,000-km steel pipe that forms a ring to fit snugly all around the circumference of the Earth. Suppose people along its length breathe on it so as to raise its temperature 1°C. The pipe gets longer. It also is no longer snug. How high does it stand above ground level? (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?r. The result is surprising!)

Problem 4RQ What is meant by “translational” kinetic energy?

Problem 5E Why can’t you establish whether you are running a high temperature by touching your own forehead?

Problem 5RQ Which defines temperature—translational kinetic energy, rotational kinetic energy, vibrational kinetic energy, or all of these?

Problem 6E Which has more kinetic energy—a molecule in a gram of ice water or a molecule in a gram of steam? Defend your answer.

Problem 6RQ What is meant by the statement that a thermometer measures its own temperature?

Problem 7E Which has the greater amount of internal energy—an iceberg or a cup of hot coffee? Defend your answer.

Problem 7RQ When you touch a cold surface, does cold travel from the surface to your hand or does energy travel from your hand to the cold surface? Explain.

Problem 8E 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?

Problem 8RQ Distinguish between temperature and heat.

Problem 9E Which is the largest unit of heat transfer—Calorie, calorie, or joule?

Problem 9RQ Distinguish between heat and internal energy.

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? Explain.

Problem 10RQ What determines the direction of heat flow?

Problem 11E 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°C?

Problem 11RQ How is the energy value of foods determined?

Problem 12E Would you expect the temperature of water at the bottom of Niagara Falls to be slightly higher than the temperature at the top of the falls? Why?

Problem 12RQ Distinguish between a calorie and a Calorie.

Problem 13E 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?

Problem 13RQ Distinguish between a calorie and a joule.

Problem 14E Why does the pressure of gas enclosed in a rigid container increase as the temperature increases?

Problem 14RQ Which warms up faster when heat is applied—iron or silver?

Problem 15E Adding the same amount of heat to two different objects does not necessarily produce the same increase in temperature. Why not?

Problem 15RQ Does a substance that heats up quickly have a high or a low specific heat capacity?

Problem 16E A certain quantity of heat is supplied to both a kilogram of water and to a kilogram of iron. Which undergoes the greater change in temperature? Defend your answer.

Problem 16RQ Does a substance that cools off quickly have a high or a low specific heat capacity?

Problem 17E Which has the greater specific heat capacity—an object that cools quickly, or an object of the same mass that cools more slowly?

Problem 17RQ How does the specific heat capacity of water compare with the specific heat capacities of other common materials?

Problem 18E If the specific heat capacity of water were less, would a nice hot bath be a longer or a shorter experience?

Problem 18RQ 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?

Problem 19RQ According to the law of conservation of energy, if ocean water cools, something else should warm. What is it that warms?

Problem 20E 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?

Problem 20RQ Why is the temperature fairly constant for land masses surrounded by large bodies of water?

Problem 21E 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?

Problem 21RQ Why do substances expand when temperature is increased?

Problem 22E 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?

Problem 22RQ Why does a bimetallic strip bend with changes in temperature?

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.

Problem 23RQ Which generally expands more for an equal increase in temperature—solids or liquids?

Problem 24E 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?

Problem 24RQ When the temperature of ice-cold water is increased slightly, does it undergo a net expansion or a net contraction?

Problem 26E 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?

Problem 25E 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?

Problem 26RQ Does “microscopic slush” in water tend to make it more dense or less dense?

Problem 27E If the winds at the latitude of San Francisco and Washington, D.C., were from the east rather than from the west, why might San Francisco be able to grow only cherry trees and Washington, D.C., both cherry trees and palm trees?

Problem 27RQ What happens to the amount of “microscopic slush” in cold water when its temperature is increased?

Problem 28E Desert sand is very hot in the day and very cool at night. What does this indicate about its specific heat capacity?

Problem 28RQ At what temperature do the combined effects of contraction and expansion produce the smallest volume for water?

Problem 29E Cite an exception to the claim that all substances expand when heated.

Problem 29RQ Why does all the water in a lake have to be cooled to 4°C before surface water can be cooled below 4°C?

Problem 30E Would a bimetallic strip function if the two different metals have the same rates of expansion? Is it important that they expand at different rates? Explain.

Problem 30RQ Why does ice form at the surface of a body of water instead of at the bottom?

Problem 31E 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?

Problem 32E 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?

Problem 33E After you have driven a car for some distance, why does the air pressure in the tires increase?

Problem 34E Structural groaning noises are sometimes heard in the attic of old buildings on cold nights. Give an explanation in terms of thermal expansion.

Problem 35E An old remedy for 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?

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

Problem 37E In terms of thermal expansion, why is it important that a key and its lock be made of the same or similar materials?

Problem 38E Any architect will tell you that chimneys are never used as a weight-bearing part of a wall. Why?

Problem 39E Looking at the expansion joint in the photo of Figure 15.13, would you say it was taken on a warm day or a cold day? Why?

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

Problem 41E After filling your gas tank to the top and parking your car in direct hot sunlight, why does the gasoline overflow?

Problem 42E 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? Will the size of the hole increase, stay the same, or decrease?

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

Problem 44E After a machinist very quickly slips a hot, snugly fitting iron ring over a very cold brass cylinder, there is no way that the two can be separated intact. Can you explain why this is so?

Problem 45E Suppose that you cut a small gap in a metal ring. If you were to heat the ring, would the gap become wider or narrower?

Problem 46E When a mercury thermometer is warmed, the mercury level momentarily goes down before it rises. Can you give an explanation for this?

Problem 47E Why do long steam pipes often have one or more relatively large U-shaped sections of pipe?

Problem 48E Why are incandescent bulbs typically made of very thin glass?

Problem 49E One of the reasons the first lightbulbs were expensive was due to the platinum electrical lead wires into the bulb, necessary because they expanded at about the same rate as glass when heated. Why is it important that the metal leads and the glass have the same coefficient of expansion?

Problem 50E 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?

Problem 51E What was the precise temperature at the bottom of Lake Superior at 12:01 am on October 31, 2000?

Problem 52E Suppose that water is used in a thermometer instead of mercury. If the temperature is at 4°C and then changes, why can’t the thermometer indicate whether the temperature is rising or falling?

Problem 53E 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 does a piece of solid water (ice) not sink in a container of “molten” (liquid) water? Explain, using molecular terms.

Problem 54E How would the shape of the 0°C–18°C curve in Figure 15.20 differ if density rather than volume were plotted against temperature? Make a rough sketch.

Problem 55E What happens to the volume of water as it is cooled from 3°C to 1°C?

Problem 56E How does the combined volume of the billions and billions of hexagonal open spaces in the structures of ice crystals in a piece of ice compare with the portion of ice that floats above the waterline?

Problem 57E State whether water at the following temperatures will expand or contract when warmed a little: 0°C; 4°C; 6°C.

Problem 58E Why is it important to protect water pipes in the winter so that they don’t freeze?

Problem 59E If water had a lower specific heat capacity, would ponds be more likely to freeze or less likely to freeze?

Problem 60E If cooling occurred at the bottom of a pond instead of at the surface, would the pond freeze from the bottom up? Explain.