Additional Problems

| 27 | ssm Concept Simulation 13.1 at illustrates the concepts pertinent to this problem. A person’s body is covered with 1.6 m2 of wool clothing. The thickness of the wool is . The temperature at the outside surface of the wool is 11 °C, and the skin temperature is 36 °C. How much heat per second does the person lose due to conduction?

| 28 | The temperature in an electric oven is 160 °C. The temperature at the outer surface in the kitchen is 50 °C. The oven (surface area = 1.6 m2) is insulated with material that has a thickness of 0.020 m and a thermal conductivity of . (a) How much energy is used to operate the oven for six hours? (b) At a price of $0.10 per kilowatt · hour for electrical energy, what is the cost of operating the oven?

| 29 | Multiple-Concept Example 8 reviews the approach that is used in problems such as this. A person eats a dessert that contains 260 Calories. (This “Calorie” unit, with a capital C, is the one used by nutritionists; 1 Calorie = 4186 J. See Section 12.7.) The skin temperature of a person is 36 °C and that of her environment is 21 °C. The emissivity of her skin is 0.75 and its surface area is 1.3 m2. How much time would it take for her to emit a net radiant energy from her body that is equal to the energy contained in this dessert?

| 30 | Multiple-Concept Example 8 discusses the ideas on which this problem depends. Interactive LearningWare 13.2 at reviews the concepts that are involved in this problem. Suppose the skin temperature of a naked person is 34 °C when the person is standing inside a room whose temperature is 25 °C. The skin area of the individual is 1.5 m2. (a) Assuming the emissivity is 0.80, find the net loss of radiant power from the body. (b) Determine the number of food Calories of energy (1 food Calorie = 4186 J) that are lost in one hour due to the net loss rate obtained in part (a). Metabolic conversion of food into energy replaces this loss.

| 31 | ssm A car parked in the sun absorbs energy at a rate of 560 watts per square meter of surface area. The car reaches a temperature at which it radiates energy at this same rate. Treating the car as a perfect radiator (e = 1), find the temperature.

* | 32 | A solid sphere has a temperature of 773 K. The sphere is melted down and recast into a cube that has the same emissivity and emits the same radiant power as the sphere. What is the cube’s temperature?

* | 33 | A copper rod has a length of 1.5 m and a cross-sectional area of . One end of the rod is in contact with boiling water and the other with a mixture of ice and water. What is the mass of ice per second that melts? Assume that no heat is lost through the side surface of the rod.

* | 34 | Three building materials, plasterboard [], brick [], and wood [], are sandwiched together as the drawing illustrates. The temperatures at the inside and outside surfaces are 27 °C and 0 °C, respectively. Each material has the same thickness and cross-sectional area. Find the temperature (a) at the plasterboard–brick interface and (b) at the brick–wood interface.

** | 35 | ssm www Two cylindrical rods have the same mass. One is made of silver (density = 10 500 kg/m3), and one is made of iron (density = 7860 kg/m3). Both rods conduct the same amount of heat per second when the same temperature difference is maintained across their ends. What is the ratio (silver-to-iron) of (a) the lengths and (b) the radii of these rods?

** | 36 | A 0.30-m-thick sheet of ice covers a lake. The air temperature at the ice surface is −15 °C. In five minutes, the ice thickens by a small amount. Assume that no heat flows from the ground below into the water and that the added ice is very thin compared to 0.30 m. Find the number of millimeters by which the ice thickens.

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