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 for thermal conductivities given in Table 13-1 unlesse stated otherwise.
ssm Solution is in the Student Solutions Manual.
This icon represents a biomedical application.
Section 13.2 Conduction

| 1 | ssm One end of an iron poker is placed in a fire where the temperature is 502 °C, and the other end is kept at a temperature of 26 °C. The poker is 1.2 m long and has a radius of . Ignoring the heat lost along the length of the poker, find the amount of heat conducted from one end of the poker to the other in 5.0 s.

| 2 | Concept Simulation 13.1 at illustrates the concepts pertinent to this problem. A refrigerator has a surface area of 5.3 m2. It is lined with 0.075-m-thick insulation whose thermal conductivity is . The interior temperature is kept at 5 °C, while the temperature at the outside surface is 25 °C. How much heat per second is being removed from the unit?

| 3 | The amount of heat per second conducted from the blood capillaries beneath the skin to the surface is 240 J/s. The energy is transferred a distance of through a body whose surface area is 1.6 m2. Assuming that the thermal conductivity is that of body fat, determine the temperature difference between the capillaries and the surface of the skin.

| 4 | A skier wears a jacket filled with goose down that is 15 mm thick. Another skier wears a wool sweater that is 5.0 mm thick. Both have the same surface area. Assuming that the temperature difference between the inner and outer surfaces of each garment is the same, calculate the ratio (wool/goose down) of the heat lost due to conduction during the same time interval.

| 5 | ssm Due to a temperature difference , heat is conducted through an aluminum plate that is 0.035 m thick. The plate is then replaced by a stainless steel plate that has the same temperature difference and cross-sectional area. How thick should the steel plate be so that the same amount of heat per second is conducted through it?

| 6 | Consult Interactive Solution 13.6 at to explore a model for solving this problem. One end of a brass bar is maintained at 306 °C, while the other end is kept at a constant, but lower, temperature. The cross-sectional area of the bar is . Because of insulation, there is negligible heat loss through the sides of the bar. Heat flows through the bar, however, at the rate of 3.6 J/s. What is the temperature of the bar at a point 0.15 m from the hot end?

| 7 | ssm www In the conduction equation , the combination of factors kA/L is called the conductance. The human body has the ability to vary the conductance of the tissue beneath the skin by means of vasoconstriction and vasodilation, in which the flow of blood to the veins and capillaries underlying the skin is decreased and increased, respectively. The conductance can be adjusted over a range such that the tissue beneath the skin is equivalent to a thickness of 0.080 mm of Styrofoam or 3.5 mm of air. By what factor can the body adjust the conductance?

| 8 | Interactive LearningWare 13.1 at explores the approach taken in problems such as this one. A composite rod is made from stainless steel and iron and has a length of 0.50 m. The cross section of this composite rod is shown in the drawing and consists of a square within a circle. The square cross section of the steel is 1.0 cm on a side. The temperature at one end of the rod is 78 °C, while it is 18 °C at the other end. Assuming that no heat exits through the cylindrical outer surface, find the total amount of heat conducted through the rod in two minutes.

* | 9 | Review Conceptual Example 5 before attempting this problem. To illustrate the effect of ice on the aluminum cooling plate, consider the drawing shown here and the data contained therein. Ignore any limitations due to significant figures. (a) Calculate the heat per second per square meter that is conducted through the ice–aluminum combination. (b) Calculate the heat per second per square meter that would be conducted through the aluminum if the ice were not present. Notice how much larger the answer is in (b) as compared to (a).

* | 10 | Two pots are identical except that the flat bottom of one is aluminum, whereas that of the other is copper. Water in these pots is boiling away at 100.0 °C at the same rate. The temperature of the heating element on which the aluminum bottom is sitting is 155.0 °C. Assume that heat enters the water only through the bottoms of the pots and find the temperature of the heating element on which the copper bottom rests.

* | 11 | ssm In a house the temperature at the surface of a window is 25 °C. The temperature outside at the window surface is 5.0 °C. Heat is lost through the window via conduction, and the heat lost per second has a certain value. The temperature outside begins to fall, while the conditions inside the house remain the same. As a result, the heat lost per second increases. What is the temperature at the outside window surface when the heat lost per second doubles?

* | 12 | Multiple-Concept Example 3 discusses an approach to problems such as this. The ends of a thin bar are maintained at different temperatures. The temperature of the cooler end is 11 °C, while the temperature at a point 0.13 m from the cooler end is 23 °C and the temperature of the warmer end is 48 °C. Assuming that heat flows only along the length of the bar (the sides are insulated), find the length of the bar.

* | 13 | Refer to Interactive Solution 13.13 at for help in solving this problem. In an aluminum pot, 0.15 kg of water at 100 °C boils away in four minutes. The bottom of the pot is thick and has a surface area of 0.015 m2. To prevent the water from boiling too rapidly, a stainless steel plate has been placed between the pot and the heating element. The plate is thick, and its area matches that of the pot. Assuming that heat is conducted into the water only through the bottom of the pot, find the temperature at (a) the aluminum–steel interface and (b) the steel surface in contact with the heating element.

** | 14 | Two cylindrical rods are identical, except that one has a thermal conductivity k1 and the other has a thermal conductivity k2. As the drawing shows, they are placed between two walls that are maintained at different temperatures TW (warmer) and TC (cooler). When the rods are arranged as in part a of the drawing, a total heat flows from the warmer to the cooler wall, but when the rods are arranged as in part b, the total heat flow is Q. Assuming that the conductivity k2 is twice as great as k1 and that heat flows only along the lengths of the rods, determine the ratio .

** | 15 | ssm www The drawing shows a solid cylindrical rod made from a center cylinder of lead and an outer concentric jacket of copper. Except for its ends, the rod is insulated (not shown), so that the loss of heat from the curved surface is negligible. When a temperature difference is maintained between its ends, this rod conducts one-half the amount of heat that it would conduct if it were solid copper. Determine the ratio of the radii r1/r2.
Section 13.3 Radiation

| 16 | A person is standing outdoors in the shade where the temperature is 28 °C. (a) What is the radiant energy absorbed per second by his head when it is covered with hair? The surface area of the hair (assumed to be flat) is 160 cm2 and its emissivity is 0.85. (b) What would be the radiant energy absorbed per second by the same person if he were bald and the emissivity of his head were 0.65?

| 17 | ssm www How many days does it take for a perfect blackbody cube (0.0100 m on a side, 30.0 °C) to radiate the same amount of energy that a one-hundred-watt light bulb uses in one hour?

| 18 | In an old house, the heating system uses radiators, which are hollow metal devices through which hot water or steam circulates. In one room the radiator has a dark color (emissivity = 0.75). it has a temperature of 62 °C. The new owner of the house paints the radiator a lighter color (emissivity = 0.50). Assuming that it emits the same radiant power as it did before being painted, what is the temperature (in degrees Celsius) of the newly painted radiator?

| 19 | The filament of a light bulb has a temperature of and radiates sixty watts of power. The emissivity of the filament is 0.36. Find the surface area of the filament.

| 20 | The amount of radiant power produced by the sun is approximately . Assuming the sun to be a perfect blackbody sphere with a radius of , find its surface temperature (in kelvins).

| 21 | ssm Review Multiple-Concept Example 8 before attempting this problem. Suppose the stove in that example had a surface area of only 2.00 m2. What would its temperature (in kelvins) have to be so that it still generated a net power of 7300 W?

| 22 | Consult Multiple-Concept Example 8 to see the concepts that are pertinent here. A person’s body is producing energy internally due to metabolic processes. If the body loses more energy than metabolic processes are generating, its temperature will drop. If the drop is severe, it can be life-threatening. Suppose a person is unclothed and energy is being lost via radiation from a body surface area of 1.40 m2, which has a temperature of 34 °C and an emissivity of 0.700. Suppose that metabolic processes are producing energy at a rate of 115 J/s. What is the temperature of the coldest room in which this person could stand and not experience a drop in body temperature?

| 23 | The concrete wall of a building is 0.10 m thick. The temperature inside the building is 20.0 °C, while the temperature outside is 0.0 °C. Heat is conducted through the wall. When the building is unheated, the inside temperature falls to 0.0 °C, and heat conduction ceases. However, the wall does emit radiant energy when its temperature is 0.0 °C. The radiant energy emitted per second per square meter is the same as the heat lost per second per square meter due to conduction. What is the emissivity of the wall?

* | 24 | Liquid helium is stored at its boiling-point temperature of 4.2 K in a spherical container (r = 0.30 m). The container is a perfect blackbody radiator. The container is surrounded by a spherical shield whose temperature is 77 K. A vacuum exists in the space between the container and the shield. The latent heat of vaporization for helium is . What mass of liquid helium boils away through a venting valve in one hour?

** | 25 | ssm A solid cylinder is radiating power. It has a length that is ten times its radius. It is cut into a number of smaller cylinders, each of which has the same length. Each small cylinder has the same temperature as the original cylinder. The total radiant power emitted by the pieces is twice that emitted by the original cylinder. How many smaller cylinders are there?

** | 26 | A small sphere (emissivity = 0.90, radius = r1) is located at the center of a spherical asbestos shell (thickness = 1.0 cm, outer radius = r2). The thickness of the shell is small compared to the inner and outer radii of the shell. The temperature of the small sphere is 800.0 °C, while the temperature of the inner surface of the shell is 600.0 °C, both temperatures remaining constant. Assuming that and ignoring any air inside the shell, find the temperature of the outer surface of the shell.

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