Chapter 13

Transfer of Heat

Learning ObjectivesTemperature and heat Mechanical equivalent of heat

Students should understand the “mechanical equivalent of heat” so they can determine how much heat can be produced by the performance of a specified quantity of mechanical work.

Heat transfer and thermal expansion

Students should understand heat transfer and thermal expansion, so they can:

Calculate how the flow of heat through a slab of material is affected by changes in the thickness or area of the slab, or the temperature difference between the two faces of the slab.

Analyze what happens to the size and shape of an object when it is heated.

Analyze qualitatively the effects of conduction, radiation, and convection in thermal processes.

Table of Contents

1. Convection

2. Conduction

3. Radiation

4. Applications

Chapter 13:Transfer of Heat

Section 1:

Convection

How can internal energy spread out? Heat is the flow of internal energy from high to low

Three options:

1. Physically move the high energy particles

2. Exchange energy with other particles through collisions

3. Exchange energy with other particles through radiation

convection currents

Convection

Convection is the process in which heat is carried from one place to another by the bulk movement of a fluid.

Usually occurs in fluids

How does convection work? Imagine taking a sample from within a fluid and only heating that

sample… What happens to the density when the sample when it gets hotter?

Volume expands density decreases What happens to the buoyant force on the sample when its density

decreases? Density of displaced fluid is now greater than sample Buoyant force increases

If the mass is unchanged, and the buoyant force is greater, what will happen to the sample? Net upward force sample rises

What happens to the unheated fluid? By similar logic, it will fall underneath the rising “sample”

Conceptual Example 1 Hot Water Baseboard Heating and Refrigerators

Hot water baseboard heating units are mounted on the wall next tothe floor. The cooling coil in a refrigerator is mounted near the top ofthe refrigerator. Each location is designed to maximize the production of convection currents. Explain how.

“Thermals” can be used by glider pilots to gain considerablealtitude.

Forced Convection

13.1.1. During the summer, sunlight warms the land beside a cool lake. This warming is followed by a breeze blowing from the direction of the lake toward the land. Which of the following provides the best explanation for this summer breeze?

a) Air naturally flows from cooler locations to warmer locations.

b) The lake must be west of the land because winds typically blow from the west.

c) The land is usually cooler near a lake, so this is a case of temperature inversion which causes air to blow from the direction of the lake.

d) Warm air rises above the land and cooler air moves downward, appearing to come from the direction of the lake, but it is really from above the land.

e) Warm air rises from above the land and is replaced by the air blowing in from the lake.

13.1.2. Randy has placed 10 thermometers at different depths and radii within a pot of water on an electric stove. He then turns on the heating element under the pot and watches the thermometers. He notices that the temperature of the water at the ten locations is approximately the same as the temperature increases from room temperature to 100 C. Which one of the flowing statements best describes the nearly uniform temperature throughout the pot?

a) Convection currents appear that evenly distribute heat throughout the pot.

b) Heat is rapidly conducted from the bottom of the pot to the top because of the temperature gradient that exists between the bottom of the pot and the top.

c) The pressure at a given depth in the water must remain constant.

d) The water is heated via radiation. The bottom of the pot is hotter than the water and all water molecules are irradiated equally.

e) The water molecules near the bottom receive energy from the pot and transfer that energy as they collide with other water molecules throughout the pot.

Chapter 13:Transfer of Heat

Section 2:

Conduction

Conduction – Think collisions Conduction is the process whereby heat is transferred

directly through a material, with any bulk motion of the material playing no role in the transfer.

One mechanism for conduction occurs when the atoms or molecules in a hotter part of the material vibrate or move with greater energy than those in a cooler part.

By means of collisions, the more energetic molecules pass on some of their energy to their less energetic neighbors.

Materials that conduct heat well are called thermal conductors, and those that conduct heat poorly are called thermal insulators.

The amount of heat Q that is conducted through the bar depends on a number of factors:

The time during which conduction takes place. The temperature difference between the ends of the

bar. The cross sectional area of the bar. The length of the bar.

The heat Q conducted during a time t through a bar of lengthL and cross-sectional area A is

L

tTkAQ

SI Units of Thermal Conductivity: J/(s·m·oC)

thermalconductivity

Conduction of Heat through a Material

Materials with dead air spaces are usually excellent thermal insulators.

Stagnant Air is an excellent thermal insulator.

Stagnant Air has low density, so particles are far apart. Fewer collisions, slower

conduction

Example 4 Layered insulationOne wall of a house consists of plywood backed by insulation. The thermal conductivities of the insulation and plywood are, respectively, 0.030 and 0.080 J/(s·m·Co), and the area of the wall is 35m2. Find the amount of heat conducted through the wall in one hour.

plywoodinsulation

L

tTkA

L

tTkA

But first we must solve for the interface temperature.

plywoodinsulation QQQ

m 019.0

C0.4CmsJ080.0

m 076.0

C0.25CmsJ030.0 tTAtTA

C8.5 T

m 076.0

s 3600C8.5C0.25m 35CmsJ030.0 2

insulation

Q

J105.9 5insulation Q

insulation

insulation

L

tTkAQQ

Conceptual Example 5 An Iced-Up Refrigerator

In a refrigerator, heat is removed by a cold refrigerant fluid that circulates within a tubular space embedded within a metalplate. Decide whether the plate shouldbe made from aluminum or stainless steeland whether the arrangement works betteror worse when it becomes coated witha layer of ice.

) CmJ/(s14 k

) CmJ/(s 240 ko

steel

oAl

13.2.1. Consider the following substances all at room temperature: (1) aluminum, (2) copper, (3) steel, and (4) wood. Which one would feel the coolest if held in your hand? Note: Your hand is at a temperature above room temperature.

a) 1

b) 2

c) 3

d) 4

e) All would seem to be the same temperature.

13.2.2. A wall is composed of four different materials as shown in the drawing. The wall on the right is maintained at 30.0 C and the other wall is at 0.5 C. The temperatures at the interfaces between the various materials are given. Rank the materials in order of largest thermal conductivity to smallest thermal conductivity.

a) A > B > C > D

b) B > C > D > A

c) C > D > A > B

d) D > A > C > B

e) C > B > A > D

13.2.3. Two bars are placed between two plates: one at temperature THOT and one at TCOLD. The thermal conductivity of bar A is three times that of bar B. The cross-sectional area of bar A is one-half that of bar B. There is no heat loss from the sides of the bars. Which one of the following statements correctly describes the heat conducted by the two bars in a time interval t?

a) The amount of heat conducted by bar A is 3 times that conducted by bar B.

b) The amount of heat conducted by bar A is 3/2 times that conducted by bar B.

c) The amount of heat conducted by bar A is the same as that conducted by bar B.

d) The amount of heat conducted by bar A is 2/3 times that conducted by bar B.

e) The amount of heat conducted by bar A is 1/3 times that conducted by bar B.

13.2.4. What thickness of concrete, with a thermal conductivity of 1.1 J/(smK) will conduct heat at the same rate as 0.25 m of air, which has a thermal conductivity of 0.0256 J/(smK), if all other conditions are the same?

a) 8.9 m

b) 4.3 m

c) 1.4 m

d) 11 m

e) 0.25 m

Chapter 13:Transfer of Heat

Section 3:

Radiation

Radiation

Radiation is the process in which energy is transferred by means of electromagnetic waves.

A material that is a good absorber is also a good emitter.

A material that absorbs completely is called a perfect blackbody.

THE STEFAN-BOLTZMANN LAW OF RADIATION

The radiant energy Q, emitted in a time t by an object that has aKelvin temperature T, a surface area A, and an emissivity e, is givenby

AtTeQ 4

The emissivity e is a dimensionless number between zero and one. It is the ratio of what an object radiates to what the object would radiate ifit were a perfect emitter.

428 KmsJ1067.5

Stefan-Boltzmann constant

Radiation

Example 6 A Supergiant Star

The supergiant star Betelgeuse has a surface temperature ofabout 2900 K and emits a power of approximately 4x1030W. Assuming that Betelgeuse is a perfect emitter and spherical,find its radius.

AtTeQ 4 24 rA

trTeQ 24 4

44 Te

tQr

4428

30

K 2900KmsJ1067.514

W104

m103 11r

13.3.1. Just before spring arrives, an airplane flies over some mountains and drops black soot on the snow and ice. This procedure is done to prevent flooding of the valley below when the warmer weather arrives with spring. How does this procedure prevent flooding?

a) The areas where the soot fails should melt earlier than those without the soot as sunlight will be absorbed. Melting the snow gradually reduces the amount that will melt as temperatures rise in spring.

b) The soot increases the temperature at which snow and ice melt causing the areas that have soot to melt later.

c) The soot lowers the temperature at which snow and ice melt causing the areas that have soot to melt earlier.

d) The soot has a higher thermal conductivity than water and ice and can transmit heat from the air more efficiently to the snow and ice underneath the soot.

e) Air convection warms the soot covered snow more efficiently than the snow without soot.

13.3.2. Metal pots used in cooking on top of a stove are usually very shiny on the top and sides. Which one of the following choices indicates why this is a good idea thermally?

a) The shiny parts of the pot have greater thermal conductivity.

b) The shiny parts of the pot have greatly reduced losses via convection.

c) The shiny parts of the pot have greatly reduced losses via radiation.

d) The shiny parts of the pot have greatly reduced losses via conduction.

e) The shiny parts of the pot do not allow any heat to be lost to the environment.

13.3.3. A heater element becomes warm when an electrical current is passed through its wires. The more current that passes through, the hotter the wires become. When looking at the wires they are glowing orange; and if you are standing in front of this heater, you will feel the warmth of it. While standing in front of this heater while it is glowing orange, someone else covers it with a glass jar and then removes the air from the jar using a vacuum pump. After the air is removed from the jar, can you still feel the warmth of the heater?

a) No, to feel the warmth there would have to be air for convection.

b) Yes, you will still feel warm because heat is transferred via electromagnetic waves that can travel through the vacuum.

c) No, the heater will not operate inside the vacuum.

d) Yes, the heat from the heater will be conducted through the glass.

e) No, there is no mechanism by which heat can be transferred out of the glass jar.

13.3.4. A device that is to be primarily used in the desert is being designed. The user would like the side facing the sun, the front, to absorb as little heat as possible and to lose as little heat on the opposite side, the back, of the device. Two materials for these sides of the device are being recommended: (1) a dull black material and (2) a shiny, metallic material. Which of these materials should be used for the front and back sides of the device?

a) The front should be material 2 and the back should be material 1.

b) The front should be material 1 and the back should be material 2.

c) Both sides should be material 1.

d) Both sides should be material 2.

e) Using either of these materials for the front and back will have the same result.

13.3.5. Two sealed containers are initially at the same temperature and have the same dimensions. The outer surfaces of container A appear to be polished aluminum. The outer surfaces of container B are roughened gray cast iron. A large, bright incandescent light bulb is brought near both containers and shines on them for equal amounts of time from the same distance. Within which container, if either, will the temperature increase at the fastest rate?

a) A

b) B

c) The temperature of both containers will increase at the same rate.

Chapter 13:Transfer of Heat

Section 4:

Applications

A thermos bottle minimizes heattransfer via conduction, convection,and radiation.

The halogen cooktop stove createselectromagnetic energy that passesthrough the ceramic top and is absorbeddirectly by the bottom of the pot.