Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 37 | Concept Questions A pot of water is boiling on a stove under one atmosphere of pressure. Assume that heat enters the pot only through its bottom, which is copper and rests on a heating element. In a certain time, a mass m of water boils away. (a) What is the temperature of the boiling water and does it change during this time? (b) What determines the amount of heat needed to boil the water? (c) Is the temperature of the heating element in contact with the pot greater than, smaller than, or equal to 100 °C? Explain.
Problem In two minutes, the mass of water boiled away is m = 0.45 kg. The radius of the pot bottom is R = 6.5 cm and the thickness is L = 2.0 mm. What is the temperature TE of the heating element in contact with the pot? Verify that your answer is consistent with your answers to the Concept Questions.

| 38 | Concept Questions A wall in a house contains a single window, the area and thickness of which are small relative to the area and thickness of the wall. The window consists of a single pane of glass. Treat the wall as a slab of the insulating material Styrofoam. The temperature difference between the inside and outside is the same for the wall and the window. Heat is lost via conduction through the window and the wall. Decide, for a given time period, whether each of the following factors, by itself, causes the window to lose more than, less than, or the same amount of heat as the wall: (a) the area, other things being equal, (b) the thickness, other things being equal, and (c) the thermal conductivity (see Table 13-1), other things being equal. Give your reasoning.
Problem The glass window pane has an area of 0.16 m2 and a thickness of 2.0 mm. The Styrofoam area and thickness are 18 m2 and 0.10 m, respectively. Of the total heat lost by the wall and the window, what is the percentage lost by the window?

| 39 | Concept Questions Two objects are maintained at constant temperatures, one hot and one cold. Two identical bars can be attached end to end, as in part a of the drawing, or one on top of the other, as in part b. When either of these arrangements is placed between the hot and the cold objects for the same amount of time, heat Q flows from left to right. (a) Is the area through which the heat flows greater for arrangement a or arrangement b? (b) Is the thickness of the material through which the heat flows greater for arrangement a or arrangement b? (c) Is Qa less than, greater than, or equal to Qb ? Account for your answers.
Problem Find the ratio Qa/Qb. Be sure that your answer is consistent with your answers to the Concept Questions.

| 40 | Concept Questions Light bulb 1 operates with a higher filament temperature than light bulb 2, but both filaments have the same emissivity. (a) How is the power P expressed in terms of the energy Q radiated by a bulb and the time t during which the energy is radiated? (b) Does a higher filament temperature generate more radiated power or less radiated power? (c) Does a smaller area for radiation promote more radiated power or less radiated power? (d) Suppose that both bulbs radiate the same power. Is the filament area of bulb 1 greater than, less than, or the same as the filament area of bulb 2? Give your reasoning.
Problem Bulb 1 has a filament temperature of 2700 K, whereas bulb 2 has a filament temperature of 2100 K. Both bulbs radiate the same power. Find the ratio A1/A2 of the filament areas of the bulbs. Verify that your answer is consistent with your answers to the Concept Questions.

| 41 | Concept Questions Via radiation, an object emits more power than it absorbs from the room in which it is located. (a) The object has a temperature T (in kelvins). According to the Stefan–Boltzmann law, the power radiated by the object is , where A is the area from which the radiation is emitted. What is the expression for the power absorbed from the room, which has a temperature T0 (in kelvins)? (b) Is the temperature of the object greater than, less than, or equal to the temperature of the room? Explain, assuming the temperatures are constant.
Problem The temperature of the room is 293 K. The object emits three times as much power as it absorbs from the room. What is the temperature of the object? Check to see that your answer is consistent with your answers to the Concept Questions.

| 42 | Concept Questions Sirius B is a white star that has a much greater surface temperature than our sun does. Assume that both Sirius B and our sun are spherical and have the same emissivity. (a) Other things being equal, would the greater surface temperature imply that the power radiated by Sirius B is greater than, less than, or equal to the power radiated by our sun? (b) The fact is that Sirius B radiates much less power than our sun does. Considering this fact, is the surface area of Sirius B greater than, less than, or equal to the surface area of our sun? (c) Is the radius of Sirius B greater than, less than, or equal to the radius of our sun? Explain your answers.
Problem Our sun has a radius of . Sirius B radiates only 0.04 times the power radiated by our sun. Its surface temperature is four times that of our sun. Find the radius of Sirius B. Be sure that your answer is consistent with your answers to the Concept Questions.

| 43 | Concept Questions The block shown in the drawing has dimensions . In drawings A, B, and C, heat is conducted through the block in three different directions. In each case, the same temperature difference exists between the opposite surfaces through which the heat passes, and the time during which the heat flows is the same. (a) The cross-sectional area of the opposite surfaces in C is greater than that in A. Does this fact alone mean that the heat conducted in C is greater than that conducted in A? Provide a reason for your answer. (b) The length of material through which heat is conducted is greater in A than in B. Does this fact alone imply that the heat conducted in A is smaller than that conducted in B? Why? (c) Rank the heat conducted in each of the three cases, largest first.
Problem The block in the drawing has a thermal conductivity of , and the length L0 is 0.30 m. For each case—A, B, and C—the temperature of the warmer surface is 35 °C while that of the cooler surface is 19 °C. Determine the heat that flows in 5.0 s for each case. Be sure your answers are consistent with that in part (c) of the Concept Questions.

| 44 | Concept Questions Part (a) of the drawing shows a rectangular bar whose dimensions are . The bar is at the same temperature as the room (not shown) in which it is located. (a) Is the net radiant power emitted by the bar greater than zero, equal to zero, or less than zero? Provide a reason for your answer. (b) The bar is then cut, lengthwise, into two equal pieces, as shown in part (b) of the drawing. The temperature of the bars does not change. Which situation, if either, emits more power into the room, the single bar in part (a) or the two bars in part (b) of the drawing? Why? (c) Which situation, if either, absorbs more power from the room, the single bar in part (a) or the two bars in part (b) of the drawing? Justify your reasoning.
Problem (a) What is the ratio of the power absorbed by the two bars in part (b) of the drawing to the single bar in part (a)? (b) Suppose the temperature of the single bar in part (a) is 450 K. What would the temperature (in kelvins) of the room and the two bars in part (b) have to be such that the two bars absorb the same power as the single bar in part (a)?

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