2. Learning Objectives
Temperature 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.
5. 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
7. 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”
8. Conceptual Example 1 Hot Water Baseboard Heating and
Refrigerators
Hot water baseboard heating units are mounted on the wall next to
the floor. The cooling coil in a refrigerator is mounted near the top of
the refrigerator. Each location is designed to maximize the production
of convection currents. Explain how.
9. “Thermals” can be used by glider pilots to gain considerable
altitude.
11. 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.
12. 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.
14. 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.
15. 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.
16. The heat Q conducted during a time t through a bar of length
L and cross-sectional area A is
( )
L
tTkA
Q
∆
=
SI Units of Thermal Conductivity: J/(s·m·o
C)
thermal
conductivity
Conduction of Heat through a Material
17.
18. 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
19. Example 4 Layered insulation
One 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 ==
( )[ ] ( ) ( )[ ] ( )
m019.0
C0.4CmsJ080.0
m076.0
C0.25CmsJ030.0 tTAtTA
−⋅⋅
=
−⋅⋅
C8.5
=T
21. 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 metal
plate. Decide whether the plate should
be made from aluminum or stainless steel
and whether the arrangement works better
or worse when it becomes coated with
a layer of ice.
)CmJ/(s14k
)CmJ/(s240k
o
steel
o
Al
⋅⋅=
⋅⋅=
22. 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.
23. 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
24. 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.
25. 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
27. 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.
28. THE STEFAN-BOLTZMANN LAW OF RADIATION
The radiant energy Q, emitted in a time t by an object that has a
Kelvin temperature T, a surface area A, and an emissivity e, is given
by
AtTeQ 4
σ=
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 if
it were a perfect emitter.
( )428
KmsJ1067.5 ⋅⋅×= −
σ
Stefan-Boltzmann constant
Radiation
29. Example 6 A Supergiant Star
The supergiant star Betelgeuse has a surface temperature of
about 2900 K and emits a power of approximately 4x1030
W.
Assuming that Betelgeuse is a perfect emitter and spherical,
find its radius.
AtTeQ 4
σ= 2
4 rA π=
trTeQ 24
4πσ=
4
4 Te
tQ
r
σπ
=
( ) ( )[ ]( )4428
30
K2900KmsJ1067.514
W104
⋅⋅×
×
= −
π
m103 11
×=r
30. 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.
31. 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.
32. 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.
33. 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.
34. 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.
