Physics Ch 17

1) (a) Internal human body temperature is often stated to be normal at 98.6°F. What is this temperature on the Celsius and Kelvin scales? (b) Gallium boils at 2205°C. What is the corresponding temperature in the Fahrenheit and Kelvin scales? (c) The boiling point of liquid nitrogen is 77.0 K. What is the corresponding temperature in the Fahrenheit and Celsius scales?

(a) 37.0°C, 310 K (b) 4001°F, 2478 K (c) -321°F, -196°C

53) A solid metal sphere is 15.0 cm in diameter and has surface of uniform color. When its surface is at 112°C, you measure that it radiates energy at a rate of 71.3 W. What is the emissivity of the surface of this object? Any heat that enters the sphere from the outside environment is negligible. The Stefan-Boltzmann constant is 5.670 × 10-8 W/m2 · K4.

0.810

46) A spherical object 25.0 cm in diameter having an emissivity of 0.800 is held at a temperature of 275°C by an internal heater. This object is embedded in a very large vat of water at 100.0°C and atmospheric pressure. At what maximum rate (in g/min) is the water evaporating in the vat due to the radiated heat it receives from the object? You can ignore any heat radiated by the water. The latent heat of fusion for water is 33,400 J/kg, its latent heat of vaporization is 2.26 × 106 J/kg, and the Stefan-Boltzmann constant is 5.670 × 10-8 W/m2 · K4.

21.3 g/min

45) A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water 100°C and the other end in a water-ice mixture at 0.00°C. The rod has uniform cross-sectional area of 4.04 cm2 and length of 91 cm. Under steady state conditions, the heat conducted by the rod melts the ice at a rate of 1.0 g every 34 seconds. What is the thermal conductivity of the rod? (The heat of fusion of water is 3.34 × 105 J/kg.)

220 W/m ∙ K

32) A copper cylinder with a mass of 125 g and temperature of 345°C is cooled by dropping it into a glass beaker containing 565 g of water initially at 20.0°C. The mass of the beaker is 50.0 g and the specific heat of the glass is 840 J/kg∙K. What is the final equilibrium temperature of the system, assuming the cooling takes place very quickly, so that no energy is lost to the air? The specific heat of copper is 385 J/kg∙K and that of water is 4190 J/kg∙K.

26.4°C

54) A radiating body originally has a Kelvin temperature To, and its surroundings are at 500K (To > 500K). If the Kelvin temperature of the radiating body is increased to 3To, the net rate at which the body radiates increases by a factor of 333. What was the original temperature To?

536 K

34) How many grams of ice at -13°C must be added to 711 grams of water that is initially at a temperature of 87°C to produce water at a final temperature of 10.0°C? Assume that no heat is lost to the surroundings and that the container has negligible mass. The specific heat of liquid water is 4190 J/kg·C° and of ice is 2050 J/kg·C°. For water the normal melting point is 0.00°C and the heat of fusion is 334 × 103 J/kg. The normal boiling point is 100°C and the heat of vaporization is 2.26 × 106 J/kg.

570 g

10) A glass flask has a volume of 500 mL at a temperature of 20°C. The flask contains 492 mL of mercury at 20°C. The temperature of the mercury and flask is raised until the mercury reaches the 500 mL reference mark. The coefficients of volume expansion of mercury and glass are 18 × 10-5 K-1 and 2.0 × 10-5 K-1, respectively. The temperature at which this occurs is closest to A) 122°C. B) 112°C. C) 102°C. D) 110°C. E) 132°C.

A

11) The coefficient of linear expansion of aluminum is 24 × 10-6 K-1 and the coefficient of volume expansion of olive oil is 0.68 × 10-3 K-1. A novice cook, in preparation for deep-frying some potatoes, fills a 1.00-L aluminum pot to the brim and heats the oil and the pot from an initial temperature of 15°C to 190°C. To his consternation some olive oil spills over the top. How much? A) 0.11 L B) 0.12 L C) 0.13 L D) 0.14 L E) 0.15 L

A

13) A certain metal has a coefficient of linear expansion of 2.00 × 10-5 K-1. It has been kept in a laboratory oven at 325°C for a long time. It is now removed from the oven and placed in a freezer at -145°C. After it has reached freezer temperature, the percent change in its density during this process is closest to A) +2.90%. B) -2.90%. C) +2.74%. D) -2.74%. E) It is not possible to tell without knowing the mass and original volume of the metal.

A

14) It is necessary to determine the specific heat of an unknown object. The mass of the object is measured to be 199.0 g. It is determined experimentally that it takes 16.0 J to raise the temperature 10.0°C. Find the specific heat of the object. A) 8.04 J/kg ∙ K B) 1600 J/kg ∙ K C) 0.00120 J/kg ∙ K D) 3.18 × 106 J/kg ∙ K

A

15) A 648-g empty iron kettle is put on a stove. How much heat, in joules, must it absorb to raise its temperature from 15.0°C to 37.0°C? (The specific heat for iron is 113 cal/kg•C°, 1 cal = 4.190 J) A) 6740 J B) 11,300 J C) 1610 J D) 16,100 J

A

16) If we use 67 W of power to heat 148 g of water, how long will it take to raise the temperature of the water from 15°C to 25°C? The specific heat of water is 4190 J/kg•K. A) 93 s B) 5.3 s C) 22 s D) 114 h

A

17) A 905-g meteor impacts the earth at a speed of 1629 m/s. If all of its energy is entirely converted to heat in the meteor, what will be the resulting temperature rise of the meteor, assuming it does not melt? The specific heat for the meteor material is 472 J/kg∙K, which is about the same as that of iron. A) 2810°C B) 2,540,000°C C) 3.10°C D) 11,700°C

A

19) A substance has a melting point of 20°C and a heat of fusion of 3.9 x 104 J/kg. The boiling point is 150°C and the heat of vaporization is 7.8 × 104 J/kg at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg∙K), 1000 J/(kg∙K), and 400 J/(kg∙K), respectively. The quantity of heat required to raise the temperature of 3.80 kg of the substance from -6°C to 128°C at a pressure of 1.0 atm, is closest to A) 620 kJ. B) 470 kJ. C) 560 kJ. D) 210 kJ. E) 770 kJ.

A

2) A machinist needs to remove a tight fitting pin of material A from a hole in a block made of material B. The machinist heats both the pin and the block to the same high temperature and removes the pin easily. What statement relates the coefficient of thermal expansion of material A to that of material B? A) Material B has a greater coefficient of expansion than does material A. B) The situation is not possible because heating block B will shrink the hole in the material as the material expands with increasing temperature. C) Material B has the same coefficient of expansion as does material A. D) Material A has a greater coefficient of expansion than does material B.

A

20) A substance has a melting point of 20°C and a heat of fusion of 3.5 × 104 J/kg. The boiling point is 150°C and the heat of vaporization is 7.0 × 104 J/kg at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg∙K), 1000 J/(kg∙K), and 400 J/(kg∙K), respectively. The quantity of heat given up by 0.50 kg of the substance when it is cooled from 170°C to 88°C, at a pressure of 1.0 atmosphere, is closest to A) 70 kJ. B) 14 kJ. C) 21 kJ. D) 30 kJ. E) 44 kJ.

A

22) If you add 700 kJ of heat to 700 g of water at 70.0°C, how much water is left in the container? The latent heat of vaporization of water is 2.26 × 106 J/kg and its specific heat is 4190 J/(kg∙K). A) 429 g B) 258 g C) 340 g D) 600 g E) none

A

23) Heat is added to a 2.0 kg piece of ice at a rate of 793.0 kW. How long will it take for the ice to melt if it was initially at 0.00°C? (The latent heat of fusion for water is 334 kJ/kg and its latent heat of vaporization is 2260 kJ/kg.) A) 0.84 s B) 530,000 s C) 4.7 s D) 670 s

A

24) A 406.0 kg copper bar is put into a smelter for melting. The initial temperature of the copper is 300.0 K. How much heat must the smelter produce to completely melt the copper bar? (The specific heat for copper is 386 J/kg•K, the heat of fusion for copper is 205 kJ/kg, and its melting point is 1357 K.) A) 2.49 × 105 kJ B) 1.66 × 1011 kJ C) 1.66 × 108 kJ D) 2.96 × 105 kJ

A

26) A 400-g piece of metal at 120.0°C is dropped into a cup containing 450 g of water at 15.0°C. The final temperature of the system is measured to be 40.0°C. What is the specific heat of the metal, assuming no heat is exchanged with the surroundings or the cup? The specific heat of water is 4190 J/(kg∙K). A) 1470 J/(kg ∙ K) B) 2830 J/(kg ∙ K) C) 3420 J/(kg ∙ K) D) 3780 J/(kg ∙ K) E) 4280 J/(kg ∙ K)

A

27) An 80-g aluminum calorimeter contains 380 g of water at an equilibrium temperature of 20°C. A 120-g piece of metal, initially at 352°C, is added to the calorimeter. The final temperature at equilibrium is 32°C. Assume there is no external heat exchange. The specific heats of aluminum and water are 910 J/kg·K and 4190 J/kg·K, respectively. The specific heat of the metal is closest to A) 520 J/kg ∙ K. B) 480 J/kg ∙ K. C) 390 J/kg ∙ K. D) 350 J/kg ∙ K. E) 560 J/kg ∙ K.

A

3) Suppose that a steel bridge, 1000 m long, was built without any expansion joints and that only one end of the bridge was held fixed. What would the difference in the length of the bridge be between winter and summer, taking a typical winter temperature as 0.00°C, and a typical summer temperature as 40°C? The coefficient of thermal expansion of steel is 10.5 × 10-6 K-1. A) 0.42 m B) 0.11 mm C) 0.11 m D) 0.42 mm E) 0.37 cm

A

31) A block of ice at 0.000°C is added to a well-insulated 147-g aluminum calorimeter cup that holds 200 g of water at 10.0°C. The water and aluminum cup are in thermal equilibrium, and the specific heat of aluminum is 910 J/(kg∙K). If all but 2.00 g of ice melt, what was the original mass of the block of ice? The specific heat of water is 4190 J/(kg∙K), its latent heat of fusion is 334 kJ/kg, and its latent heat of vaporization is 2260 kJ/kg. A) 31.1 g B) 35.6 g C) 38.8 g D) 42.0 g E) 47.6 g

A

33) A 200-g metal container, insulated on the outside, holds 100 g of water in thermal equilibrium at 22.00°C. A 21-g ice cube, at the melting point, is dropped into the water, and when thermal equilibrium is reached the temperature is 15.00°C. Assume there is no heat exchange with the surroundings. For water, the specific heat is 4190 J/kg · K and the heat of fusion is 3.34 × 105 J/kg. The specific heat for the metal is closest to A) 3850 J/kg ∙ K. B) 2730 J/kg ∙ K. C) 4450 J/kg ∙ K. D) 4950 J/kg ∙ K. E) 5450 J/kg ∙ K.

A

37) A solid concrete wall 4.0 m by 2.4 m and 30 cm thick, with a thermal conductivity of 1.3 W/(m∙K), separates a basement at 18°C from the ground outside at 6°C. Under steady state conditions, how much heat flows through the wall in one hour? A) 1.8 MJ B) 1.8 kJ C) 500 J D) 5.0 MJ E) 5.0 kJ

A

39) A heat conducting rod, 0.90 m long, is made of an aluminum section that is 0.10 m long, and a copper section that is 0.80 m long. Both sections have cross-sectional areas of 0.00040 m2. The aluminum end is maintained at a temperature of 40°C and the copper end is at 150°C. The thermal conductivity of aluminum is 205 W/m∙K and of copper is 385 W/m∙K. Steady state has been reached, and no heat is lost through the well-insulated sides of the rod. The temperature of the aluminum-copper junction in the rod is closest to A) 61°C. B) 58°C. C) 56°C. D) 54°C. E) 52°C.

A

40) A heat conducting rod, 1.40 m long, is made of an aluminum section that is 0.50 m long and a copper section that is 0.90 m long. Both sections have cross-sectional areas of 0.00040 m2. The aluminum end and the copper end are maintained at temperatures of 40°C and 280°C, respectively. The thermal conductivity of aluminum is 205 W/m∙K of copper is 385 W/m∙K. The rate at which heat is conducted in the rod is closest to A) 20 W. B) 18 W. C) 23 W. D) 25 W. E) 28 W.

A

41) Some properties of glass are listed here. Density: 2300 kg/m3 Specific heat: 840 J/kg·C° Coefficient of linear thermal expansion: 8.5 × 10-6 (C°)-1 Thermal conductivity: 0.80 W/(m·C°) A glass window pane is 2.7 m high, 2.4 m wide, and 2.0 mm thick. The temperature at the inner surface of the glass is 22°C and at the outer surface 4.0°C. How much heat is lost each hour through the window under steady state conditions? A) 1.7 × 108 J B) 1.7 × 105 J C) 4.7 × 104 J D) 4.7 × 101 J E) 1.7 × 106 J

A

6) A brass rod is 40.1 cm long and an aluminum rod is 79.3 cm long when both rods are at an initial temperature of 0°C. The rods are placed in line with a gap of 0.60 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature of both rods is raised until the two rods are barely in contact. The coefficients of linear expansion of brass and aluminum are 2.0 × 10-5 K-1 and 2.4 × 10-5 K-1, respectively. The temperature at which contact of the rods barely occurs is closest to A) 220°C. B) 210°C. C) 200°C. D) 230°C. E) 240°C.

A

8) The hole for a bolt in a brass plate has a diameter of 1.200 cm at 20°C. What is the diameter of the hole when the plate is heated to 220°C? The coefficient of linear thermal expansion for brass is 19 × 10-6/C°. (Express your answer to 4 significant figures.) A) 1.205 cm B) 1.125 cm C) 1.195 cm D) 1.200 cm E) 1.210 cm

A

12) The coefficient of volume expansion of olive oil is 0.68 × 10-3 K-1. A 1.00-L glass beaker is filled to the brim with olive oil at room temperature. The beaker is placed on a range and the temperature of the oil and beaker increases by 25 C°. As a result, 0.0167 L of olive oil spill over the top of the beaker. What is the coefficient of linear expansion of the glass? A) 1.0 × 10-6 K-1 B) 4.0 × 10-6 K-1 C) 1.0 × 10-5 K-1 D) 2.0 × 10-5 K-1 E) 3.0 × 10-5 K-1

B

25) A person pours 330 g of water at 45°C into an 855-g aluminum container with an initial temperature of 10°C. The specific heat of aluminum is 900 J/(kg∙K) and that of water is 4190 J/(kg∙K). What is the final temperature of the system, assuming no heat is exchanged with the surroundings? A) 28°C B) 32°C C) 31°C D) 33°C E) 35°C

B

28) Two experimental runs are performed to determine the calorimetric properties of an alcohol that has a melting point of -10°C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20°C and the temperature at thermal equilibrium is 10°C. The specific heat of water is 4190 J/kg·K. Assume that no heat is exchanged with the styrofoam container and with the surroundings. The heat of fusion of the alcohol is closest to A) 5.5 × 104 J/kg B) 6.3 × 104 J/kg C) 7.1 × 104 J/kg D) 7.9 × 104 J/kg E) 8.7 × 104 J/kg

B

38) Two metal rods, one silver and the other copper, are both attached to a steam chamber as shown in the figure, with a temperature of 100°C, at one end, and an ice water bath, with a temperature of 0°C, at the other. The rods are 5.0 cm long and have a square cross-section, 2.0 cm on a side. When steady state has been reached, how much heat flows through the two rods in 1.0 min? The thermal conductivity of silver is 417 W/(m∙K), and that of copper is 395 W/(m∙K). No heat is exchanged between the rods and the surroundings, except at their ends. A) 20 kJ B) 39 kJ C) 47 kJ D) 49 kJ E) 11 kJ

B

4) It is a well-known fact that water has a higher specific heat than iron. Now, consider equal masses of water and iron that are initially in thermal equilibrium. The same amount of heat, 30 calories, is added to each one. Which statement is true? A) They remain in thermal equilibrium. B) They are no longer in thermal equilibrium; the iron is warmer. C) They are no longer in thermal equilibrium; the water is warmer. D) It is impossible to say without knowing the exact mass involved. E) It is impossible to say without knowing the exact specific heats.

B

51) A cube at 100°C radiates heat at a rate of 80.0 J/s. If its surface temperature is increased to 200°C, the rate at which it will now radiate is closest to A) 160 J/s. B) 207 J/s. C) 320 J/s. D) 640 J/s. E) 1280 J/s.

B

52) What is the net power that a person loses through radiation if her surface area is 1.20 m2, if her emissivity is 0.895, if her skin temperature is 300 K, and if she is in a room that is at a temperature of 17°C? The Stefan-Boltzmann constant is 5.670 × 10-8 W/m2 · K4. A) 60.3 W B) 62.6 W C) 65.7 W D) 68.4 W E) 64.8 W

B

1) If the temperature of an iron sphere is increased A) its density will increase. B) its volume will decrease. C) its density will decrease. D) its mass will decrease. E) its density will remain unchanged.

C

2) A rod has a length 2.00000 m at 10.0°C. The length of the rod increases to 2.00060 m when the temperature increases to 30.0°C. What is the coefficient of linear expansion of the material from which the rod is made? A) 2.0 × 10-5/K B) 2.5 × 10-5/K C) 1.5 × 10-5/K D) 1.0 × 10-3/K E) 1.0 × 10-5/K

C

29) Two experimental runs are performed to determine the calorimetric properties of an alcohol that has a melting point of -10°C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20°C and the temperature at thermal equilibrium is 10°C. The specific heat of water is 4190 J/kg·K. Assume that no heat is exchanged with the styrofoam container and with the surroundings. The specific heat of the alcohol is closest to A) 1700 J/kg·K. B) 1900 J/kg·K. C) 2100 J/kg·K. D) 2300 J/kg·K. E) 2500 J/kg·K.

C

3) Two steel spheres are made of the same material and have the same diameter, but one is solid and the other is hollow. If their temperature is increased by the same amount A) the solid sphere becomes bigger than the hollow one. B) the hollow sphere becomes bigger than the solid one. C) the two spheres remain of equal size. D) the solid sphere becomes heavier and the hollow one becomes lighter. E) the solid sphere becomes lighter and the hollow one becomes heavier.

C

30) A person makes ice tea by adding ice to 1.8 kg of hot tea, initially at 80°C. How many kilograms of ice, initially at 0.00°C, are required to bring the mixture to 10°C? The heat of fusion of ice is 334 kJ/kg, and we can assume that tea has essentially the same thermal properties as water, so its specific heat is 4190 J/(kg∙K). A) 1.0 kg B) 1.2 kg C) 1.4 kg D) 1.5 kg E) 1.7 kg

C

4) The exterior of a supersonic airplane is made of aluminum, which has a coefficient of linear expansion of 24 × 10-6 K-1. At 15°C, the plane measures 62.1 m in length. When the plane is in flight, friction with the air increases the temperature of the exterior skin to 200°C. What is the change in the length of the outer skin of the plane? A) 20 cm B) 24 cm C) 28 cm D) 32 cm E) 36 cm

C

42) A cylindrical bar that us well insulated around its sides connects hot and cold reservoirs and conducts heat at a rate of 10.0 J/s under steady state conditions. If all of its linear dimensions (diameter and length) are reduced by half, the rate at which it will now conduct heat between the same reservoirs is closest to A) 80.0 J/s. B) 20.0 J/s. C) 5.00 J/s. D) 2.50 J/s. E) 1.25 J/s.

C

7) When a vapor condenses A) the temperature of the substance increases. B) the temperature of the substance decreases. C) heat energy leaves the substance. D) heat energy enters the substance.

C

8) A chunk of ice (T = -20°C) is added to a thermally insulated container of cold water (T = 0°C). What happens in the container? A) The ice melts until thermal equilibrium is established. B) The water cools down until thermal equilibrium is established. C) Some of the water freezes and the chunk of ice gets larger. D) None of the above things happen.

C

9) 1.000 L of water at 20.00°C will occupy what volume if it is heated to 80.00°C? Water has a volume expansion coefficient of 210 × 10-6/C°. (Express your answer to 4 significant figures.) A) 1.600 L B) 1.326 L C) 1.013 L D) 0.9870 L E) 0.9987 L

C

9) An architect is interested in estimating the heat loss (in kcal/s) through a sheet of insulating material as a function of the thickness of the sheet. Assuming fixed temperatures on the two faces of the sheet, which one of the graphs in the figure best represents the rate of heat transfer as a function of the thickness of the insulating sheet? A) A B) B C) C D) D E) E

C

18) Heat is added to a pure substance in a closed container at a constant rate. The figure shows a graph of the temperature of the substance as a function of time. If Lf = latent heat of fusion and Lv = latent heat of vaporization, what is the value of the ratio Lv / Lf for this substance? A) 5.0 B) 4.5 C) 7.2 D) 3.5 E) 1.5

D

21) If 2.0 g of water at 0.00°C is to be vaporized, how much heat must be added to it? The specific heat of water is 1.0 cal/g∙K, its heat of fusion is 80 cal/g, and its heat of vaporization is 539 cal/g. A) 1100 cal B) 1100 kcal C) 1200 cal D) 1300 cal E) 1500 cal

D

36) Under steady state conditions, a piece of wood 350 mm by 350 mm and 15 mm thick conducts heat through its thickness and loses no appreciable heat through its well-insulated sides. The rate of heat flow is measured to be 14.0 W when the temperature difference across its thickness is 28 C°. Determine the thermal conductivity of this wood. A) 9.2 × 10-4 W/(m∙C°) B) 270 W/(m∙C°) C) 16 W/(m∙C°) D) 0.061 W/(m∙C°) E) 33 W/(m∙C°)

D

43) A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick. The room temperature is maintained at -10°C and the outside temperature is 20°C The inside wall is to be covered by a layer of wood in order to reduce the rate of heat loss through the wall BY 90 percent. The thermal conductivities of concrete and wood are 0.80 W/m·K and 0.040 W/m·K, respectively. Under steady state conditions, the thickness of the layer of wood required is closest to A) 60 mm. B) 70 mm. C) 80 mm. D) 90 mm. E) 100 mm.

D

48) A blacksmith is flattening a steel plate that measures 10 cm × 15 cm × 1 mm. He has heated the plate to 900 K. If the emissivity of the plate is 0.75, what is the total rate at which it radiates energy? The Stefan-Boltzmann constant is 5.670 × 10-8 W/m2 · K4. Ignore any heat it receives from the surroundings. A) 360 W B) 760 W C) 790 W D) 850 W E) 880 W

D

5) A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper; the aluminum and the copper are in thermal contact. The specific heat of aluminum is more than double that of copper. Which object experiences the greater temperature change during the time the system takes to reach thermal equilibrium? A) The copper experiences a greater temperature change. B) The aluminum experiences a greater temperature change. C) Neither; both objects experience the same magnitude temperature change. D) It is impossible to tell without knowing the masses. E) It is impossible to tell without knowing the volumes.

D

5) Two identical concrete slabs lie flat and in contact with each other as shown in the figure. If the temperature increases by 40°C, the lower edges opposite the contact edges remained fixed in position, and the lower edges of the contact side remain in contact, at what angle will the slabs be tilted? The coefficient of thermal expansion of the concrete is 10 × 10-6/K. A) 19° B) 0.028° C) 15° D) 1.6° E) The answer depends on the length of the slabs.

D

50) A cube at 100.0°C radiates heat at a rate of 80.0 J/s. If the length of each side is cut in half, the rate at which it will now radiate is closest to A) 56.6 J/s. B) 40.0 J/s. C) 28.3 J/s. D) 20.0 J/s. E) 10.0 J/s.

D

6) When a solid melts A) the temperature of the substance increases. B) the temperature of the substance decreases. C) heat energy leaves the substance. D) heat energy enters the substance.

D

35) What is the steady state rate of heat flow through a pane of glass that is 40.0 cm by 30.0 cm with a thickness of 4.00 mm when the outside temperature of the glass is -10.0°C and its inside temperature is 25.0°C? The thermal conductivity of glass is 0.105 W/(m∙K), the specific heat of glass is 0.180 cal/(g∙°C), and 1 cal = 4.190 J. A) 24.2 W B) 3.81 W C) 18.6 W D) 47.3 W E) 110 W

E

44) The walls of an ice chest are made of 2.00-mm-thick insulation having a thermal conductivity 0.00300 W/m∙K. The total surface area of the ice chest is 1.20 m2. If 4.00 kg of ice at 0.00°C are placed in the chest and the temperature of the outside surface of the chest is 20.0°C, how long does it take the ice to melt under steady state conditions? The latent heat of fusion of water is 79.6 cal/g = 334 kJ/kg. A) 4.22 h B) 22.1 h C) 17.6 h D) 1.33 d E) 10.3 h

E

47) The filament in a light bulb has a diameter of 0.050 mm and an emissivity of 1.0. The temperature of the filament is 3000°C. What should be the length of the filament so it will radiate 60 W of power? The Stefan-Boltzmann constant is 5.670 × 10-8 W/m2 · K4. A) 11 cm B) 9.4 cm C) 8.6 cm D) 7.2 cm E) 5.9 cm

E

49) Betelgeuse is a red supergiant star in the constellation Orion. It radiates heat at the rate of 2.70 × 1030 W and has a surface temperature of 3000 K. Assuming that it is a perfect emitter, what is the radius of Betelgeuse? The Stefan-Boltzmann constant is 5.670 × 10-8 W/m2 · K4. A) 7.80 × 1010 m B) 8.70 × 1010 m C) 1.40 × 1011 m D) 1.90 × 1011 m E) 2.16 × 1011 m

E

7) You want to insert an aluminum rod, which at 20°C has a radius of 1.000200 cm into a copper tube which has a radius of 1.000100 cm at the same temperature. You decide to put both of them in the refrigerator. At what temperature will the rod just fit if both are cooled to the same temperature? The coefficient of thermal expansion for aluminum is 2.4 × 10-5 K-1, and that of copper is 1.7 × 10-5 K-1. A) 7.8°C B) 6.3°C C) 9.2°C D) 15°C E) 5.7°C

E