Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an on-line homework management program such as WileyPLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
Note: For problems in this set, use the values of and in Table 12-1, and the values of c, Lf, and Lv in Tables 12-2 and 12-3, unless stated otherwise.
ssm Solution is in the Student Solutions Manual.
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Section 12.1 Common Temperature Scales,
Section 12.2 The Kelvin Temperature Scale,
Section 12.3 Thermometers

| 1 | ssm A temperature of absolute zero occurs at −273.15 °C. What is this temperature on the Fahrenheit scale?

| 2 | Suppose you are hiking down the Grand Canyon. At the top, the temperature early in the morning is a cool 3 °C. By late afternoon, the temperature at the bottom of the canyon has warmed to a sweltering 34 °C. What is the difference between the higher and lower temperatures in (a) Fahrenheit degrees and (b) kelvins?

| 3 | On the moon the surface temperature ranges from 375 K during the day to at night. What are these temperatures on the (a) Celsius and (b) Fahrenheit scales?

| 4 | Dermatologists often remove small precancerous skin lesions by freezing them quickly with liquid nitrogen, which has a temperature of 77 K. What is this temperature on the (a) Celsius and (b) Fahrenheit scales?

| 5 | ssm What’s your normal body temperature? It may not be 98.6 °F, the oft-quoted average that was determined in the nineteenth century. A more recent study has reported an average temperature of 98.2 °F. What is the difference between these averages, expressed in Celsius degrees?

* | 6 | Space invaders land on earth. On the invaders’ temperature scale, the ice point is at 25 °I (I = invader), and the steam point is at 156 °I. The invaders’ thermometer shows the temperature on earth to be 58 °I. Using logic similar to that in Example 1 in the text, what would this temperature be on the Celsius scale?

* | 7 | ssm A constant-volume gas thermometer (see Figures 12-3 and 12-4) has a pressure of when the gas temperature is 0.00 °C. What is the temperature (in °C) when the pressure is ?

* | 8 | On the Rankine temperature scale, which is sometimes used in engineering applications, the ice point is at 491.67 °R and the steam point is at 671.67 °R. Determine a relationship (analogous to Equation 12.1) between the Rankine and Fahrenheit temperature scales.
Section 12.4 Linear Thermal Expansion

| 9 | A steel section of the Alaskan pipeline had a length of 65 m and a temperature of 18 °C when it was installed. What is its change in length when the temperature drops to a frigid −45 °C?

| 10 | An aluminum baseball bat has a length of 0.86 m at a temperature of 17 °C. When the temperature of the bat is raised, the bat lengthens by 0.000 16 m. Determine the final temperature of the bat.

| 11 | ssm www Find the approximate length of the Golden Gate bridge if it is known that the steel in the roadbed expands by 0.53 m when the temperature changes from +2 to +32 °C.

| 12 | Conceptual Example 5 provides background for this problem. A hole is drilled through a copper plate whose temperature is 11 °C. (a) When the temperature of the plate is increased, will the radius of the hole be larger or smaller than the radius at 11 °C? Why? (b) When the plate is heated to 110 °C, by what fraction will the radius of the hole change?

| 13 | A steel beam is used in the construction of a skyscraper. By what fraction does the length of the beam increase when the temperature changes from that on a cold winter day (−15 °F) to that on a summer day (+105 °F)?

| 14 | When the temperature of a coin is raised by 75 C°, the coin’s diameter increases by . If the original diameter of the coin is , find the coefficient of linear expansion.

| 15 | ssm A rod made from a particular alloy is heated from 25.0 °C to the boiling point of water. Its length increases by . The rod is then cooled from 25.0 °C to the freezing point of water. By how much does the rod shrink?

* | 16 | Concrete sidewalks are always laid in sections, with gaps between each section. For example, the drawing shows three identical 2.4-m sections, the outer two of which are against immovable walls. The two identical gaps between the sections are provided so that thermal expansion will not create the thermal stress that could lead to cracks. What is the minimum gap width necessary to account for an increase in temperature of 32 C°?

* | 17 | The brass bar and the aluminum bar in the drawing are each attached to an immovable wall. At 28 °C the air gap between the rods is . At what temperature will the gap be closed?

* | 18 | Multiple-Concept Example 4 reviews the concepts that are involved in this problem. A ruler is accurate when the temperature is 25 °C. When the temperature drops to −14 °C, the ruler shrinks and no longer measures distances accurately. However, the ruler can be made to read correctly if a force of magnitude is applied to each end so as to stretch it back to its original length. The ruler has a cross-sectional area of , and it is made from a material whose coefficient of linear expansion is . What is Young’s modulus for the material from which the ruler is made?

* | 19 | ssm www A simple pendulum consists of a ball connected to one end of a thin brass wire. The period of the pendulum is 2.0000 s. The temperature rises by 140 C°, and the length of the wire increases. Determine the period of the heated pendulum.

* | 20 | As the drawing shows, two thin strips of metal are bolted together at one end and have the same temperature. One is steel, and the other is aluminum. The steel strip is 0.10% longer than the aluminum strip. By how much should the temperature of the strips be increased, so that the strips have the same length?

* | 21 | Consult Conceptual Example 5 for background pertinent to this problem. A lead sphere has a diameter that is 0.050% larger than the inner diameter of a steel ring when each has a temperature of 70.0 °C. Thus, the ring will not slip over the sphere. At what common temperature will the ring just slip over the sphere?

** | 22 | A steel bicycle wheel (without the rubber tire) is rotating freely with an angular speed of 18.00 rad/s. The temperature of the wheel changes from −100.0 to +300.0 °C. No net external torque acts on the wheel, and the mass of the spokes is negligible. (a) Does the angular speed increase or decrease as the wheel heats up? Why? (b) What is the angular speed at the higher temperature?

** | 23 | ssm A wire is made by attaching two segments together, end to end. One segment is made of aluminum and the other is steel. The effective coefficient of linear expansion of the two-segment wire is . What fraction of the length is aluminum?

** | 24 | Consult Multiple-Concept Example 4 for insight into solving this problem. An aluminum wire of radius is stretched between the ends of a concrete block, as the drawing illustrates. When the system (wire and concrete) is at 35 °C, the tension in the wire is 50.0 N. What is the tension in the wire when the system is heated to 185 °C?
Section 12.5 Volume Thermal Expansion

| 25 | A copper kettle contains water at 24 °C. When the water is heated to its boiling point, the volume of the kettle expands by . Determine the volume of the kettle at 24 °C.

| 26 | A flask is filled with 1.500 L (L = liter) of a liquid at 97.1 °C. When the liquid is cooled to 15.0 °C, its volume is only 1.383 L, however. Neglect the contraction of the flask and use Table 12-1 to identify the liquid.

| 27 | Interactive Solution 12.27 at presents a model for solving problems of this type. A thin spherical shell of silver has an inner radius of when the temperature is 18 °C. The shell is heated to 147 °C. Find the change in the interior volume of the shell.

| 28 | At a temperature of 0 °C, the mass and volume of a fluid are 825 kg and 1.17 m3. The coefficient of volume expansion is . (a) What is the density of the fluid at this temperature? (b) What is the density of the fluid when the temperature has risen to 20.0 °C?

| 29 | ssm A lead object and a quartz object each have the same initial volume. The volume of each increases by the same amount, because the temperature increases. If the temperature of the lead object increases by 4.0 C°, by how much does the temperature of the quartz object increase?

| 30 | Consult Interactive LearningWare 12.1 at for help in solving this problem. During an all-night cram session, a student heats up a one-half liter () glass (Pyrex) beaker of cold coffee. Initially, the temperature is 18 °C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 92 °C. The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beaker?

| 31 | ssm Suppose that the steel gas tank in your car is completely filled when the temperature is 17 °C. How many gallons will spill out of the twenty-gallon tank when the temperature rises to 35 °C?

| 32 | Interactive LearningWare 12.1 at provides some useful background for this problem. Many hot-water heating systems have a reservoir tank connected directly to the pipeline, so as to allow for expansion when the water becomes hot. The heating system of a house has 76 m of copper pipe whose inside radius is . When the water and pipe are heated from 24 to 78 °C, what must be the minimum volume of the reservoir tank to hold the overflow of water?

* | 33 | At the bottom of an old mercury-in-glass thermometer is a 45-mm3 reservoir filled with mercury. When the thermometer was placed under your tongue, the warmed mercury would expand into a very narrow cylindrical channel, called a capillary, whose radius was . Marks were placed along the capillary that indicated the temperature. Ignore the thermal expansion of the glass and determine how far (in mm) the mercury would expand into the capillary when the temperature changed by 1.0 C°.

* | 34 | A solid aluminum sphere has a radius of 0.50 m and a temperature of 75 °C. The sphere is then completely immersed in a pool of water whose temperature is 25 °C. The sphere cools, while the water temperature remains nearly at 25 °C, because the pool is very large. The sphere is weighed in the water immediately after being submerged (before it begins to cool) and then again after cooling to 25 °C. (a) Which weight is larger? Why? (b) Use Archimedes’ principle to find the magnitude of the difference between the weights.

* | 35 | ssm The bulk modulus of water is . What change in pressure (in atmospheres) is required to keep water from expanding when it is heated from 15 to 25 °C?

* | 36 | A spherical brass shell has an interior volume of . Within this interior volume is a solid steel ball that has a volume of . The space between the steel ball and the inner surface of the brass shell is filled completely with mercury. A small hole is drilled through the brass, and the temperature of the arrangement is increased by 12 C°. What is the volume of the mercury that spills out of the hole?

** | 37 | ssm www Two identical thermometers made of Pyrex glass contain, respectively, identical volumes of mercury and methyl alcohol. If the expansion of the glass is taken into account, how many times greater is the distance between the degree marks on the methyl alcohol thermometer than that on the mercury thermometer?

** | 38 | The column of mercury in a barometer (see Figure 12-12) has a height of 0.760 m when the pressure is one atmosphere and the temperature is 0.0 °C. Ignoring any change in the glass containing the mercury, what will be the height of the mercury column for the same one atmosphere of pressure when the temperature rises to 38.0 °C on a hot day? (Hint: The pressure in the barometer is given by Pressure = ρgh, and the density of the mercury changes when the temperature changes.)
Section 12.6 Heat and Internal Energy,
Section 12.7 Heat and Temperature Change:
Specific Heat Capacity

| 39 | ssm If the price of electrical energy is $0.10 per kilowatt ċ hour, what is the cost of using electrical energy to heat the water in a swimming pool () from 15 to 27 °C?

| 40 | When you take a bath, how many kilograms of hot water (49.0 °C) must you mix with cold water (13.0 °C) so that the temperature of the bath is 36.0 °C? The total mass of water (hot plus cold) is 191 kg. Ignore any heat flow between the water and its external surroundings.

| 41 | Blood can carry excess energy from the interior to the surface of the body, where the energy is dispersed in a number of ways. While a person is exercising, 0.6 kg of blood flows to the surface of the body and releases 2000 J of energy. The blood arriving at the surface has the temperature of the body interior, 37.0 °C. Assuming that blood has the same specific heat capacity as water, determine the temperature of the blood that leaves the surface and returns to the interior.

| 42 | An ice chest at a beach party contains 12 cans of soda at 5.0 °C. Each can of soda has a mass of 0.35 kg and a specific heat capacity of 3800 J/(kg·C°). Someone adds a 6.5-kg watermelon at 27 °C to the chest. The specific heat capacity of watermelon is nearly the same as that of water. Ignore the specific heat capacity of the chest and determine the final temperature T of the soda and watermelon.

| 43 | Review Interactive Solution 12.43 at for help in approaching this problem. When resting, a person has a metabolic rate of about joules per hour. The person is submerged neck-deep into a tub containing of water at 21.00 °C. If the heat from the person goes only into the water, find the water temperature after half an hour.

| 44 | A piece of glass has a temperature of 83.0 °C. Liquid that has a temperature of 43.0 °C is poured over the glass, completely covering it, and the temperature at equilibrium is 53.0 °C. The mass of the glass and the liquid is the same. Ignoring the container that holds the glass and liquid and assuming that the heat lost to or gained from the surroundings is negligible, determine the specific heat capacity of the liquid.

| 45 | ssm At a fabrication plant, a hot metal forging has a mass of 75 kg and a specific heat capacity of 430 J/(kg·C°). To harden it, the forging is immersed in 710 kg of oil that has a temperature of 32 °C and a specific heat capacity of 2700 J/(kg ċ C°). The final temperature of the oil and forging at thermal equilibrium is 47 °C. Assuming that heat flows only between the forging and the oil, determine the initial temperature of the forging.

* | 46 | Multiple-Concept Example 11 deals with a situation that is similar, but not identical, to that here. When 4200 J of heat are added to a 0.15-m-long silver bar, its length increases by . What is the mass of the bar?

* | 47 | Interactive Solution 12.47 at deals with one approach to solving problems such as this. A 0.35-kg coffee mug is made from a material that has a specific heat capacity of 920 J/(kg·C°) and contains 0.25 kg of water. The cup and water are at 15 °C. To make a cup of coffeee, a small electric heater is immersed in the water and brings it to a boil in three minutes. Assume that the cup and water always have the same temperature and determine the minimum power rating of this heater.

* | 48 | Multiple-Concept Example 11 uses the same physics principles as those employed in this problem. A block of material has a mass of 130 kg and a volume of . The material has a specific heat capacity and coefficient of volume expansion, respectively, of 750 J/(kg·C°) and . How much heat must be added to the block in order to increase its volume by ?

* | 49 | ssm An electric hot water heater takes in cold water at 13.0 °C and delivers hot water. The hot water has a constant temperature of 45.0 °C when the “hot” faucet is left open all the time, and the volume flow rate is /s. What is the minimum power rating of the hot water heater?

** | 50 | A 1.5-kg steel sphere will not fit through a circular hole in a 0.85-kg aluminum plate, because the radius of the sphere is 0.10% larger than the radius of the hole. If both the sphere and the plate are always kept at the same temperature, how much heat must be put into the two so the ball just passes through the hole?
Section 12.8 Heat and Phase Change: Latent Heat

* | 51 | ssm How much heat must be added to 0.45 kg of aluminum to change it from a solid at 130 °C to a liquid at 660 °C (its melting point)? The latent heat of fusion for aluminum is .

| 52 | To help prevent frost damage, fruit growers sometimes protect their crop by spraying it with water when overnight temperatures are expected to go below the freezing mark. When the water turns to ice during the night, heat is released into the plants, thereby giving them a measure of protection against the falling temperature. Suppose a grower sprays 7.2 kg of water at 0 °C onto a fruit tree. (a) How much heat is released by the water when it freezes? (b) How much would the temperature of a 180-kg tree rise if it absorbed the heat released in part (a)? Assume that the specific heat capacity of the tree is and that no phase change occurs within the tree itself.

| 53 | Assume that the pressure is one atmosphere and determine the heat required to produce 2.00 kg of water vapor at 100.0 °C, starting with (a) 2.00 kg of water at 100.0 °C and (b) 2.00 kg of liquid water at 0.0 °C.

| 54 | A person eats a container of strawberry yogurt. The Nutritional Facts label states that it contains 240 Calories (1 Calorie = 4186 J). What mass of perspiration would one have to lose to get rid of this energy? At body temperature, the latent heat of vaporization of water is .

| 55 | ssm Liquid nitrogen boils at a chilly −195.8 °C when the pressure is one atmosphere. A silver coin of mass and temperature 25 °C is dropped into the boiling liquid. What mass of nitrogen boils off as the coin cools to −195.8 °C?

| 56 | A 10.0-kg block of ice has a temperature of −10.0 °C. The pressure is one atmosphere. The block absorbs of heat. What is the final temperature of the liquid water?

| 57 | A woman finds the front windshield of her car covered with ice at −12.0 °C. The ice has a thickness of , and the windshield has an area of 1.25 m2. The density of ice is 917 kg/m3. How much heat is required to melt the ice?

| 58 | A thermos contains 150 cm3 of coffee at 85 °C. To cool the coffee, you drop two 11-g ice cubes into the thermos. The ice cubes are initially at 0 °C and melt completely. What is the final temperature of the coffee? Treat the coffee as if it were water.

* | 59 | ssm Ice at −10.0 °C and steam at 130 °C are brought together at atmospheric pressure in a perfectly insulated container. After thermal equilibrium is reached, the liquid phase at 50.0 °C is present. Ignoring the container and the equilibrium vapor pressure of the liquid at 50.0 °C, find the ratio of the mass of steam to the mass of ice. The specific heat capacity of steam is 2020 J/(kg·C°).

* | 60 | Equal masses of two different liquids have the same temperature of 25.0 °C. Liquid A has a freezing point of −68.0 °C and a specific heat capacity of 1850 J/(kg·C°). Liquid B has a freezing point of −96.0 °C and a specific heat capacity of 2670 J/(kg·C°). The same amount of heat must be removed from each liquid in order to freeze it into a solid at its respective freezing point. Determine the difference Lf, A − Lf, B between the latent heats of fusion for these liquids.

* | 61 | Interactive Solution 12.61 12.61 at provides a model for solving problems such as this. A 42-kg block of ice at 0 °C is sliding on a horizontal surface. The initial speed of the ice is 7.3 m/s and the final speed is 3.5 m/s. Assume that the part of the block that melts has a very small mass and that all the heat generated by kinetic friction goes into the block of ice, and determine the mass of ice that melts into water at 0 °C.

* | 62 | Water at 23.0 °C is sprayed onto 0.180 kg of molten gold at 1063 °C (its melting point). The water boils away, forming steam at 100.0 °C and leaving solid gold at 1063 °C. What is the minimum mass of water that must be used?

* | 63 | ssm www An unknown material has a normal melting/ freezing point of −25.0 °C, and the liquid phase has a specific heat capacity of 160 J/(kg·C°). One-tenth of a kilogram of the solid at −25.0 °C is put into a 0.150-kg aluminum calorimeter cup that contains 0.100 kg of glycerin. The temperature of the cup and the glycerin is initially 27.0 °C. All the unknown material melts, and the final temperature at equilibrium is 20.0 °C. The calorimeter neither loses energy to nor gains energy from the external environment. What is the latent heat of fusion of the unknown material?

* | 64 | To help keep his barn warm on cold days, a farmer stores 840 kg of solar-heated water () in barrels. For how many hours would a 2.0-kW electric space heater have to operate to provide the same amount of heat as the water does when it cools from 10.0 to 0.0 °C and completely freezes?

* | 65 | ssm It is claimed that if a lead bullet goes fast enough, it can melt completely when it comes to a halt suddenly, and all its kinetic energy is converted into heat via friction. Find the minimum speed of a lead bullet (initial temperature = 30.0 °C) for such an event to happen.

** | 66 | A locomotive wheel is 1.00 m in diameter. A 25.0-kg steel band has a temperature of 20.0 °C and a diameter that is less than that of the wheel. What is the smallest mass of water vapor at 100 °C that can be condensed on the steel band to heat it, so that it will fit onto the wheel? Do not ignore the water that results from the condensation.
Section 12.9 Equilibrium Between Phases of Matter, Section 12.10 Humidity

| 67 | ssm Use the vapor pressure curve that accompanies this problem to determine the temperature at which liquid carbon dioxide exists in equilibrium with its vapor phase when the vapor pressure is .

| 68 | At a temperature of 10 °C the percent relative humidity is R10, and at 40 °C it is R40. At each of these temperatures the partial pressure of water vapor in the air is the same. Using the vapor pressure curve for water that accompanies this problem, determine the ratio R10/R40 of the two humidity values.

| 69 | The relative humidity is 35% when the temperature is 27 °C. Using the vapor pressure curve for water that accompanies problem 68. determine the dew point.

| 70 | Suppose that air in the human lungs has a temperature of 37 °C, and the partial pressure of water vapor has a value of . What is the relative humidity in the lungs? Consult the vapor pressure curve for water that accompanies problem 68.

| 71 | The temperature of 2.0 kg of water is 100.0 °C, but the water is not boiling, because the external pressure acting on the water surface is . Using the vapor pressure curve for water given in Figure 12-33, determine the amount of heat that must be added to the water to bring it to the point where it just begins to boil.

* | 72 | The temperature of the air in a room is 36 °C. A person turns on a dehumidifier and notices that when the cooling coils reach 30 °C, water begins to condense on them. What is the relative humidity in the room? Use the vapor pressure curve that accompanies problem 68.

* | 73 | A woman has been outdoors where the temperature is 10 °C. She walks into a 25 °C house, and her glasses “steam up.” Using the vapor pressure curve for water that accompanies problem 68, find the smallest possible value for the relative humidity of the room.

* | 74 | A container is fitted with a movable piston of negligible mass and radius r = 0.061 m. Inside the container is liquid water in equilibrium with its vapor, as the drawing shows. The piston remains stationary with a 120-kg block on top of it. The air pressure acting on the top of the piston is one atmosphere. By using the vaporization curve for water in Figure 12-33, find the temperature of the water.

* | 75 | ssm At a picnic, a glass contains 0.300 kg of tea at 30.0 °C, which is the air temperature. To make iced tea, someone adds 0.0670 kg of ice at 0.0 °C and stirs the mixture. When all the ice melts and the final temperature is reached, the glass begins to fog up, because water vapor condenses on the outer glass surface. Using the vapor pressure curve for water that accompanies problem 68, ignoring the specific heat capacity of the glass, and treating the tea as if it were water, estimate the relative humidity.

** | 76 | A tall column of water is open to the atmosphere. At a depth of 10.3 m below the surface, the water is boiling. What is the temperature at this depth? Use the vaporization curve for water in Figure 12-33, as needed.

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