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Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m2, are placed end to end as shown in the figure. Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m<sup>2</sup>, are placed end to end as shown in the figure.   The thermal conductivities of the bars are k<sub>A</sub> = 439 J/(s . m . K)  and k<sub>B</sub> = 887 J/(s . m . K) , respectively. The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K. -What is the temperature at the interface between A and B? A) 296 K B) 306 K C) 313 K D) 323 K E) 332 K The thermal conductivities of the bars are kA = 439 J/(s . m . K) and kB = 887 J/(s . m . K) , respectively. The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K. -What is the temperature at the interface between A and B?


A) 296 K
B) 306 K
C) 313 K
D) 323 K
E) 332 K

F) A) and B)
G) A) and C)

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The sun continuously radiates energy into space in all directions. Some of the sun's energy is intercepted by the earth. The average temperature of the surface of the earth remains a little above 300 K. Why doesn't the earth's temperature rise as it intercepts the sun's energy?


A) The earth reflects the sun's light.
B) The earth radiates an amount of energy into space equal to the amount it receives.
C) The energy only raises the temperature of the upper atmosphere and never reaches the surface.
D) The thermal conductivity of the earth is low.
E) The heat is carried away from the earth by convection currents.

F) B) and C)
G) All of the above

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Two identical solid spheres have the same temperature. One of the spheres is cut into two identical pieces. These two hemispheres are then separated. The intact sphere radiates an energy Q during a given time interval. During the same interval, the two hemispheres radiate a total energy Q'. What is the ratio Q'/Q?


A) 2.0
B) 0.50
C) 4.0
D) 1.5
E) 0.25

F) D) and E)
G) B) and D)

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Assuming a filament in a 100 W light bulb acts like a perfect blackbody, what is the temperature of the hottest portion of the filament if it has a surface area of 6.3 × 10-5 m2? The Stefan-Boltzmann constant is 5.67 × 10-8 W/(m2 · K2) .


A) 130 K
B) 1100 K
C) 2300 K
D) 5800 K
E) 30 000 K

F) B) and E)
G) A) and B)

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The two ends of an iron rod are maintained at different temperatures. The amount of heat that flows through the rod by conduction during a given time interval does not depend upon


A) the length of the iron rod.
B) the thermal conductivity of iron.
C) the temperature difference between the ends of the rod.
D) the mass of the iron rod.
E) the duration of the time interval.

F) B) and E)
G) A) and B)

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Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m2, are placed end to end as shown in the figure. Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 m<sup>2</sup>, are placed end to end as shown in the figure.   The thermal conductivities of the bars are k<sub>A</sub> = 439 J/(s . m . K)  and k<sub>B</sub> = 887 J/(s . m . K) , respectively. The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K. -How much heat passes the interface between A and B in 6.0 s? A) 6.0 × 10<sup>4</sup> J B) 1.5 × 10<sup>3</sup> J C) 1.2 × 10<sup>5</sup> J D) 8.8 × 10<sup>4</sup> J E) 3.0 × 10<sup>4</sup> J The thermal conductivities of the bars are kA = 439 J/(s . m . K) and kB = 887 J/(s . m . K) , respectively. The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K. -How much heat passes the interface between A and B in 6.0 s?


A) 6.0 × 104 J
B) 1.5 × 103 J
C) 1.2 × 105 J
D) 8.8 × 104 J
E) 3.0 × 104 J

F) None of the above
G) C) and D)

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Complete the following statement: Most of the heat that is lost to space from the earth occurs by


A) conduction.
B) convection.
C) radiation.
D) both conduction and radiation.
E) both conduction and convection.

F) A) and E)
G) A) and B)

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On a cold winter day, the outside temperature is -5.0 °C while the interior of a well-insulated garage is maintained at 20.0 °C by an electric heater. Assume the walls have a total area of 75 m2, a thickness of 0.15 m, and a thermal conductivity of 0.042 W/(m · C°) . What is the cost to heat the garage for six hours at these temperatures if the cost of electricity is $ 0.11/kWh? Note: 1 kWh = 3.6 × 106 J.


A) $ 0.18
B) $ 0.44
C) $ 0.61
D) $ 0.35
E) $ 1.09

F) A) and B)
G) B) and E)

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Heat is conducted by two cylindrical rods, one carbon and one aluminum, with identical cross-sectional area and length. The temperature difference between the ends of each rod is the same. Carbon has a thermal conductivity of 1100 J/(s . m . C°) and that of aluminum is 240 J/(s . m . C°) . What percentage of the total energy transferred by the two rods each second is conducted by the silver rod?


A) 64 %
B) 18 %
C) 30 %
D) 46 %
E) 82 %

F) None of the above
G) A) and B)

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A slab of insulation is made of three layers, as Drawing I indicates. Each of the layers A, B, and C has the same thickness, but a different thermal conductivity. Heat flows through the slab, and the temperatures are as shown. What are the temperatures T1 and T2 in Drawing II where the layers are arranged in a different order? A slab of insulation is made of three layers, as Drawing I indicates. Each of the layers A, B, and C has the same thickness, but a different thermal conductivity. Heat flows through the slab, and the temperatures are as shown. What are the temperatures T<sub>1</sub> and T<sub>2</sub> in Drawing II where the layers are arranged in a different order?   A) T<sub>1</sub> = 230 °C and T<sub>2</sub> = 170 °C B) T<sub>1</sub> = 200 °C and T<sub>2</sub> = 180 °C C) T<sub>1</sub> = 220 °C and T<sub>2</sub> = 160 °C D) T<sub>1</sub> = 180 °C and T<sub>2</sub> = 160 °C E) T<sub>1</sub> = 210 °C and T<sub>2</sub> = 190 °C


A) T1 = 230 °C and T2 = 170 °C
B) T1 = 200 °C and T2 = 180 °C
C) T1 = 220 °C and T2 = 160 °C
D) T1 = 180 °C and T2 = 160 °C
E) T1 = 210 °C and T2 = 190 °C

F) A) and E)
G) A) and D)

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Which one of the following statements concerning the Stefan-Boltzmann equation is true?


A) This equation applies only to perfect radiators.
B) This equation applies only to perfect absorbers.
C) This equation is valid with any temperature units.
D) This equation describes the transport of thermal energy by conduction.
E) The equation can be used to calculate the power absorbed by any surface.

F) C) and D)
G) B) and C)

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A blue supergiant star has a radius of 7.4 × 1010 m. The spherical surface behaves as a blackbody radiator. If the surface temperature is 2.4 × 104 K, what is the rate at which energy is radiated from the star?


A) 1.2 × 103 J/s
B) 9.4 × 1019 J/s
C) 2.0 × 1023 J/s
D) 8.2 × 1032 J/s
E) 1.3 × 1033 J/s

F) B) and E)
G) All of the above

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Which one of the following is not an example of convection?


A) Smoke rises above a fire.
B) An eagle soars on an updraft of wind.
C) A person gets a suntan on a beach.
D) Spaghetti is cooked in water.
E) An electric heater warms a room.

F) D) and E)
G) A) and C)

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Which one of the following statements concerning emissivity is false?


A) The emissivity is 1.0 for a perfect radiator.
B) The emissivity is 1.0 for a perfect absorber.
C) Emissivity depends on the condition of the surface.
D) Emissivity is a dimensionless quantity.
E) Emissivity depends on the surface area of the object.

F) A) and C)
G) C) and D)

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Two cylindrical steel rods A and B have radii of 0.02 m and 0.04 m, respectively. The two steel rods conduct the same amount of heat per unit time for the same temperature differences between their two ends. What is the ratio of the lengths of the rods, LA/LB?


A) 0.25
B) 0.50
C) 1.00
D) 2.00
E) 4.00

F) A) and D)
G) D) and E)

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Which one of the following graphs shows the rate at which heat is emitted from a hot body as a function of its Kelvin temperature T? Which one of the following graphs shows the rate at which heat is emitted from a hot body as a function of its Kelvin temperature T?   A) (a)  B) (b)  C) (c)  D) (d)  E) (e)


A) (a)
B) (b)
C) (c)
D) (d)
E) (e)

F) B) and C)
G) None of the above

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Assume that the sun is a sphere of radius 6.96 × 108 m and that its surface temperature is 5.8 × 103 K. If the sun radiates at a rate of 3.90 × 1026 W and is a perfect emitter, at what rate is energy emitted per square meter at the sun's surface?


A) 5.6 × 107 W/m2
B) 6.4 × 107 W/m2
C) 5.6 × 1017 W/m2
D) 12.8 × 107 W/m2
E) 25.6 × 107 W/m2

F) B) and E)
G) None of the above

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A hot metal ball is hung in an oven that is maintained at 700 K; and it cools. When the temperature of the ball is 950 K, it is losing heat at a rate of 0.15 J/min. At what rate will the ball lose heat when the ball reaches 820 K? Assume that the emissivity of the ball and its surface area do not change appreciably with temperature.


A) 0.1 J/min
B) 0.007 J/min
C) 0.08 J/min
D) 0.06 J/min
E) 0.04 J/min

F) C) and D)
G) B) and D)

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Two kilograms of ice at 0.0 °C are placed in a sealed glass container [k = 0.80 W/(m · C°) ]. The container is then placed in a room that is maintained at 30.0 °C. The top cover is a thermal insulator and all other sides of the container are exposed to room air. The surface area of the container is 6.53 × 10-2 m2; and its glass walls are 0.0050 m thick. -How much heat is required to melt the ice?


A) 16 J
B) 1080 J
C) 1.6 × 105 J
D) 6.7 × 105 J
E) 4.5 × 106 J

F) B) and D)
G) D) and E)

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Which one of the following objects, all initially at the same temperature, will be most efficient in losing heat?


A) a dull black box in vacuum
B) a dull black box in air
C) a box with an emissivity of 0.1
D) a polished silver box in air
E) a polished silver box in vacuum

F) A) and E)
G) B) and C)

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