Deck 13: The Transfer of Heat

Question 1

Which of the following materials is the poorest thermal conductor?

A)gold
B)ice
C)copper
D)wood
E)air

Answer 1

air

Question 2

Suppose you are sitting next to a fire burning in a fireplace. One end of a metal poker has been left in the fire. Which one of the following statements concerning this situation is true?

A)You can feel the heat of the fire primarily because of convection.
B)The end of the poker that is not in the fire is warmed through conduction.
C)Heat escapes through the chimney primarily through conduction.
D)You can feel the heat of the fire primarily because of conduction.
E)The end of the poker that is not in the fire is warmed through convection.

Answer 2

The end of the poker that is not in the fire is warmed through conduction.

Question 3

Which of the following materials is the best thermal conductor?

A)diamond
B)Styrofoam
C)nitrogen gas
D)concrete
E)goose down

Answer 3

diamond

Question 4

At what rate is heat lost through a 1.5 m × 3.0 m rectangular glass windowpane that is 0.4 cm thick when the inside temperature is 22 °C and the outside temperature is 6.0 °C? The thermal conductivity for the glass is 0.75 W/(m · C°).

A)560 W
B)1800 W
C)7200 W
D)3600 W
E)13 500 W

Question 5

Complete the following statement: The space between the inner walls of a thermos bottle is evacuated to minimize heat transfer by

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

Question 6

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)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

Question 7

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 %

Question 8

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.

Question 9

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. The thermal conductivities of the bars are
k_A = 439 J/(s . m . K) and k_B = 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

Question 10

Which one of the following processes does not occur during the convective transfer of heat within a container of air?

A)The volume of a warmed part of the air is reduced and its density increases.
B)A continuous flow of warmer and cooler parts of air is established.
C)The flow of air molecules results in a flow of heat.
D)The cooler portion of the air surrounding a warmer part exerts a buoyant force on it.
E)As the warmer part of the air moves, it is replaced by cooler air that is subsequently warmed.

Question 11

The ends of a cylindrical steel rod are maintained at two different temperatures. The rod conducts heat from one end to the other at a rate of 10 cal/s. At what rate would a steel rod twice as long and twice the diameter conduct heat between the same two temperatures?

A)5 cal/s
B)10 cal/s
C)20 cal/s
D)40 cal/s
E)80 cal/s

Question 12

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. The thermal conductivities of the bars are
k_A = 439 J/(s . m . K) and k_B = 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.

-Which one of the following statements is true concerning the above situation?

A)For a given time t, the amount of heat transferred through bar A is the same as that through B.
B)For a given time t, the amount of heat transferred through bar A is smaller than that through B.
C)For a given time t, the amount of heat transferred through bar A is less than that through B.
D)The time for a quantity of heat Q to pass through bar A is less than that for B.
E)Time is not a factor in determining the quantity of heat conducted through these bars.

Question 13

Complete the following statement: The transfer of heat by convection will occur

A)only in metals.
B)only in a vacuum.
C)only in non-metallic solids.
D)with or without the presence of matter.
E)only in the presence of a liquid or a gas.

Question 14

In an experiment to determine the thermal conductivity of a bar of a new alloy, one end of the bar is maintained at 0.0 °C and the other end at 100.0 °C. The bar has a cross-sectional area of 1.0 cm² and a length of 15 cm. If the rate of heat conduction through the bar is 34 W, what is the thermal conductivity of the bar?

A)34 W/(m · C°)
B)360 W/(m · C°)
C)160 W/(m · C°)
D)510 W/(m · C°)
E)0.029 W/(m · C°)

Question 15

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

Question 16

Which one of the following statements best explains why convection does not occur in solids?

A)Molecules in a solid are more closely spaced than in a gas.
B)The molecules in a solid are not free to move throughout the volume of the solid.
C)Molecules in a solid vibrate at a lower frequency than those in a liquid.
D)Solids are more compressible than liquids.
E)Solids are less compressible than gases.

Question 17

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.

Question 18

A granite wall has a thickness of 0.50 m and a thermal conductivity of 2.1 W/(m · C°). The temperature on one face of the wall is 5.2 °C and 20.0 °C on the opposite face. How much heat is transferred in one hour through each square meter of the granite wall?

A)2.2 × 10⁵ J/m²
B)1.7 × 10⁵ J/m²
C)7.4 × 10⁴ J/m²
D)1.1 × 10⁶ J/m²
E)62 J/m²

Question 19

A cabin has a 0.159-m thick wooden floor [k = 0.141 W/(m · C°)] with an area of 13.4 m². A roaring fire keeps the interior of the cabin at a comfortable 18.0 °C while the air temperature in the crawl space below the cabin is -16.4 °C. What is the rate of heat conduction through the wooden floor?

A)19 J/s
B)138 J/s
C)264 J/s
D)408 J/s
E)459 J/s

Question 20

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, L_A/L_B?

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

Question 21

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

Question 22

If a beaker of water is placed under a broiler so that the heating coil is above the beaker. It is observed that only the surface layer boils. The water at the bottom of the beaker remains close to the initial temperature of the water. Which of the following statements is the most reasonable conclusion to be drawn from these observations?

A)Water is a poor conductor of heat.
B)The sample must contain impurities.
C)Water is easily heated by radiation.
D)Water exhibits anomalous thermal behavior.
E)The molecular motion in the sample is not random.

Question 23

Object A has an emissivity of 0.95; and its temperature is 25 °C. At what temperature (in degrees Celsius) does object B, whose emissivity is 0.50, emit radiation at the same rate as object A if both objects have the same surface area?

A)29 °C
B)40 °C
C)61 °C
D)77 °C
E)93 °C

Question 24

The power radiated by a distant star is 6.2 × 10²⁷ W. The radius of the star, which may be considered a perfect radiator, is 1.06 × 10¹⁰ m. Determine the surface temperature of the star.

A)2970 K
B)4630 K
C)7440 K
D)8710 K
E)9970 K

Question 25

Complete the following statement: The interior of a thermos bottle is silvered to minimize heat transfer due to

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

Question 26

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.

Question 27

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

Question 28

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

Question 29

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.

Question 30

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. The thermal conductivities of the bars are
k_A = 439 J/(s . m . K) and k_B = 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

Question 31

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

Question 32

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. The thermal conductivities of the bars are
k_A = 439 J/(s . m . K) and k_B = 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 rate of heat transfer through this combination?

A)3.7 × 10³ J/s
B)6.4 × 10³ J/s
C)8.8 × 10³ J/s
D)1.5 × 10⁴ J/s
E)2.2 × 10⁴ J/s

Question 33

A beaker of water is placed on a Bunsen burner. As the lower layers of water are heated, they become less dense and rise. This permits cooler layers to move downward and be heated. Eventually, the water boils. Which method(s) of heat transfer is (are) primarily responsible for boiling the sample?

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

Question 34

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.

Question 35

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

Question 36

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)

Question 37

Which object will emit more electromagnetic radiation than it absorbs from its surroundings?

A)a 600 °C copper sphere in a 700 °C oven
B)a girl scout sitting close to a campfire
C)an ice cube in beaker of water at 50 °C
D)a 200 °C copper coin in a beaker of water at 98 °C
E)an ice cube in thermal equilibrium with the interior of a freezer

Question 38

A person steps out of the shower and dries off. The person's skin with an emissivity of 0.70 has a total area of 1.2 m² and a temperature of 33 °C. What is the net rate at which energy is lost to the room through radiation by the naked person if the room temperature is 24 °C?

A)0.041 W
B)25 W
C)81 W
D)67 W
E)47 W

Question 39

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.

Question 40

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

Question 41

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

Question 42

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.
Approximately, how long does it take all of the ice to melt?

A)4.7 min
B)7.8 min
C)18 min
D)36 min
E)2.7 h