Ch 12 Temperature and Heat

Chapter 12
Temperature and Heat

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.

Table of Contents
1. Common Temperature Scales
2. The Kelvin Temperature Scale
3. Thermometers
4. Linear Thermal Expansion
5. Volume Thermal Expansion
6. Heat & Internal Energy
7. Heat & Temperature Change: Specific Heat
Capacity
8. Heat and Phase Change: Latent Heat
9. Equilibrium between Phases of Matter (AP?)
10. Humidity (AP?)

Chapter 12:
Section 1:
Common Temperature Scales

Temperature
 A measure of the physical quantity of the thermal
energy held by an object
 A measure of the average internal kinetic energy of
the particles
 As the particles move faster, they have stronger
collisions.
 That energy exchanges rapidly
 Think of a bunch of kids in a “bounce house”

Temperature Scales
 First “Modern” Thermometer is thought to have been
created in 1654
 Simply an unmarked tube of liquid that rose and fell
with different temperatures
 Late 1600’s Newton first put a scale on it
 0 was the freezing point of water
 12 was the human body temperature
 The English were fascinated with 12 when it
comes to measurement
 12 inches=1 ft, 12 oz = 1 lb*, 12 pence = shilling,
12 units = 1 dozen, 12 dozen = 1 gross

Fahrenheit Scale
 Why 32o
and 212o
?
 1701 Ole Rømer used a brine solution for freezing point (0)
 Wanted 0o
to be the coldest temperature at which water could
be a liquid
 set boiling point of water as 60 on his scale
 Daniel Fahrenheit modified Rømer’s scale in 1724
 Used Mercury as liquid in device which increased range of
measurements
 Used the temperature of the human body as 100 on scale
 Adjusted the scale so the melting point and boiling point of
water were whole numbers, and difference was 180.

Celsius Scale
 First proposed by the Swedish Astronomer Anders Celsius in
1742
 He set it up as 100o
as the freezing point and 0o
as boiling
point of distilled water at normal atmospheric pressure
 Swedish Botanist Carolus Linnaeus is among many scientist who
switched the direction of the scale around 1744
 From 1744 until 1948, called the Centigrade scale
 Name changed to Celsius due to conflicts in translations with
measures of angles. (1 centigrade = 1/10,000 of a right angle)
 1954 reformatted to directly match Kelvin Scale
 Scale based on absolute zero and triple point of pure water
 Correctly written as degrees Celsius (capitalization is correct!)
 Zero is freezing, 10 is not. 20 is pleasant, 30 is hot.

Temperatures are reported in degrees
Celsius or degrees Fahrenheit.
Temperatures changed, on the
other hand, are reported in Celsius
degrees or Fahrenheit degrees:

F
5
9
C1 =
Note: I haven’t seen this convention anywhere
other than this textbook.
I don’t think AP recognizes it!

“English” vs. SI
 Most scientist agree the SI system (yes that’s redundant) is a
superior system of measure
 Especially when is comes to conversions due to size
 How many inches are in 2.67 miles?
 Some still argue about the Temperature scales.
 Blame the French on this one
 Fahrenheit had ties to England, Celsius to France
 Lord Kelvin sealed the debate by “using” Celsius scale as
basis for his absolute scale
 But is it better?
 Habitable Earth fluctuates from 0 to 100 o
F wouldn’t that fit
the SI’s power of 10 thing?

Example 1 Converting from a Fahrenheit to a Celsius Temperature
A healthy person has an oral temperature of 98.6o
F. What would this
reading be on the Celsius scale?

F6.66F32F98.6 =−
degrees above ice point
( ) 



C0.37
F
C1
F6.66
5
9
=







C0.37C0.37C0 
=+
ice point

Example 2 Converting from a Celsius to a Fahrenheit Temperature
A time and temperature sign on a bank indicates that the outdoor
temperature is -20.0o
C. Find the corresponding temperature on
the Fahrenheit scale.
( ) 



F0.36
C1
F
C0.20 5
9
=





degrees below ice point
F0.4F0.36F0.32 
−=−
ice point

12.1.1. Three thermometers are used to measure the temperature inside a closed,
insulated box. Thermometer A is calibrated in degrees Fahrenheit,
thermometer B in degrees Celsius, and thermometer C in kelvin. When the
thermometers reach thermal equilibrium with the interior of the box, B reads
−40 °C and C reads 233 K. Which one of the following statements is
necessarily true?
a) Thermometer C should read −233 K.
b) Thermometer A must read –40 °F.
c) If the temperature of the interior of the box is increased until A reads −20 °F,
thermometer B will read −10 °C.
d) Thermometer B should read −77 °C.
e) If the temperature of the interior of the box is increased until C reads 293 K,
thermometer A will read 36 °F.

12.1.2. Unsatisfied with the Celsius and Fahrenheit temperature
scales, you decide to create your own. On your temperature
scale, the ice point is 77 °M and the steam point is at 437 °M,
where “M” stands for “my scale.” What temperature on your
scale corresponds to 68 °F?
a) 154 °M
b) 168 °M
c) 140 °M
d) 136 °M
e) 149 °M

Chapter 12:
Section 2:
The Kelvin Scale

An Absolute Scale
 Proposed by William Thomson, 1st Baron Kelvin in
1848
 Does not use a “o
” as it is an absolute scale
 Double the number, double the energy
 The zero point is absolute zero
 Temperature of zero internal energy
 Second point is now defined as triple point of water
 Celsius scale was slightly modified so that a change
of 1 o
C is a change of 1 K.
 Similar scale developed by William Rankine in 1859
that was based on the Fahrenheit scale.

The Kelvin Temperature Scale
15.273+= cTT
Kelvin temperature

A constant-volume gas
thermometer.

absolute zero point = -273.15o
C

12.2.1. Unsatisfied with the Celsius and Kelvin temperature scales,
you decide to create your own. On your temperature scale, the
ice point is 0.0 °M and the steam point is at 366.1 °M, where
“M” stands for “my scale.” What temperature on your scale
corresponds to 0 K?
a) −273.1 °M
b) −500.0 °M
c) −1000.0 °M
d) −732.4 °M
e) −633.9 °M

Chapter 12:
Section 3:
Thermometers

Thermometers make use of the change in some physical property with temperature.
A property that changes with temperature is called a thermometric property.
Thermometers

Thermometers
 Early thermometers used water, mercury and alcohol due to their
thermal expansion
 “Modern” devices often use other substances/properties
 Bimetallic Coil thermometers (old A/C thermostats)
 Coiled metal expands and rotates a dial
 Infrared Thermometers
 Measure the colors of light being produced
 Thermocouples
 Joined metals produce an electric potential
 Thermisters
 Electric Resistance depends on temperature

12.3.1. Which one of the following properties is not likely to be used
as a temperature-sensitive property to construct a thermometer?
a) The volume of a liquid increases with increasing temperature.
b) A gas held within a constant volume container exhibits pressure
changes with corresponding temperature changes.
c) The length of a metal rod changes linearly with temperature.
d) The mass of a solid decreases with increasing temperature.
e) The electrical resistance of a wire increases with increasing
temperature.

Chapter 12:
Section 4:
Linear Thermal Expansion

 Most objects expand as they rise in temperature
 The particles are moving faster
 The collisions have more energy
 Net force of collisions is outward
 Objects therefore tend to expand

oLL ∝∆
T
L
L
o
∆∝
∆
Tk
L
L
o
∆=
∆

The length of an object changes when its temperature
changes:
TLL o∆=∆ α
coefficient of
linear expansion
Common Unit for the Coefficient of Linear Expansion: ( ) 1
C
C
1 −
= 

LINEAR THERMAL EXPANSION OF A SOLID

Example 3 The Buckling of a Sidewalk
A concrete sidewalk is constructed between
two buildings on a day when the temperature
is 25 o
C. As the temperature rises to 38 o
C,
the slabs expand, but no space is provided for
thermal expansion. Determine the distance y
in part (b) of the drawing.
TLL o∆=∆ α
( ) ( )22
m00000.3m00047.3 −=y
( )[ ]( )( )
C13m0.3C1012
16 −−
×=∆L m00047.0=
LLLL o ∆+=
mmL 47000.000000.3 +=∆ m47000.3=
m053.0=

Conceptual Example 5 The Expansion of Holes
The figure shows eight square tiles that are arranged to form a square pattern
with a hold in the center. If the tiled are heated, what happens to the size of the
hole?
The Expansion of Holes

A hole in a piece of solid material expands when heated and contracts when
cooled, just as if it were filled with the material that surrounds it.
The Expansion of Holes

Conceptual Example 7 Expanding Cylinders
Each cylinder is made from a different material.
All three have the same temperature and they
barely fit inside each other.
As the cylinders are heated to the same,
but higher, temperature, cylinder C falls
off, while cylinder A becomes tightly wedged
to cylinder B.
Which cylinder is made from which material?
( )
( )
( ) 16
16
16
1029
1012
1019
−−
−−
−−
×=
×=
×=
C
C
C
o
Lead
o
Steel
o
Brass
α
α
α

12.4.1. An artist wishes to insert a gold pin into a hole in an iron sculpture and
have it held permanently. The pin is slightly larger than the hole. The
coefficient of linear thermal expansion of gold is slightly larger than that of
iron. Consider the following options: (1) increase the temperature of the pin
and the sculpture by the same amount, (2) decrease the temperature of the pin
and the sculpture by the same amount, (3) increase the temperature of the pin
and decrease the temperature of the sculpture, and (4) decrease the
temperature of the pin and increase the temperature of the sculpture. Which
of the choices would most likely accomplish the artist’s task?
a) 1
b) 2
c) 3
d) 4
e) 2 and 4

12.4.2. The length of an aluminum pendulum in a certain clock is
0.2480 m on a day when the temperature is 23.30 °C. This length
was chosen so that the period of the pendulum is exactly 1.000 s.
The clock is then hung on a wall where the temperature is −5.00 °C
and set to the correct local time. Assuming the acceleration due to
gravity is the same at both locations, by how much time is the clock
incorrect after one day at this temperature?
a) 69.3 s
b) 115 s
c) 87.2 s
d) 31.0 s
e) 11.5 s

12.4.3. A rod of length L is heated so that its temperature
increases by ∆T. As a result, the length of the rod increases
by ∆L. The rod is then cut into two pieces, one of length L/3
and one of length 2L/3. What is the ratio of the change in
length of the rod of length 2L/3 to ∆L of the original rod
when its temperature is increased by ∆T?
a) 1/3
b) 2/3
c) 1
d) 3/2
e) 3

12.4.4. A square piece of metal has a hole drilled through its center.
If the metal piece is uniformly heated, what is the effect on the
hole?
a) The diameter of the hole will decrease, but remain open, as the
temperature increases.
b) The diameter of the hole will increase as the temperature
increases.
c) The diameter of the hole will not change, but the area of the
square will increase as the temperature increases.
d) The diameter of the hole may either increase or decrease
depending on the type of metal.

Chapter 12:
Section 5:
Volume Thermal Expansion

If the length expands, and Volume is L3,
Then the volume must also expand
TVV o∆=∆ β
coefficient of
volume expansion
Common Unit for the Coefficient of Volume Expansion: ( ) 1
C
C
1 −
= 

Volume Thermal Expansion

Example 8 An Automobile Radiator
A small plastic container, called the coolant reservoir, catches
the radiator fluid that overflows when an automobile engine
becomes hot. The radiator is made of
copper and the coolant has an
expansion coefficient of
4.0x10-4
(Co
)-1
. If the radiator
is filled to its 15-quart capacity
when the engine is cold (6o
C),
how much overflow will spill into the
reservoir when the coolant reaches its
operating temperature (92o
C)?
( )( )( )( ) quarts53.0C86quarts15C1010.4
14
coolant =×=∆
−− 
V
( )( )( )( ) quarts066.0C86quarts15C1051
16
radiator =×=∆
−− 
V
quarts0.46quarts066.0quarts53.0spill =−=∆V
TVV o∆=∆ β

Thermal Volume Expansion of Water

12.5.1. Which one of the following statements is the best explanation for
the fact that metal pipes that carry water often burst during cold
winter months?
a) Both the metal and the water expand, but the water expands to a
greater extent.
b) Water contracts upon freezing while the metal expands at lower
temperatures.
c) The metal contracts to a greater extent than the water.
d) The interior of the pipe contracts less than the outside of the pipe.
e) Water expands upon freezing while the metal contracts at lower
temperatures.

12.5.2. Consider the four blocks made from the same material that are
shown in the drawing. The sides have lengths of L, 2L, or 3L.
Rank these blocks according to their expected increase, largest to
smallest, in their volumes when their temperatures are increased
by the same amount.
a) B > C > A > D
b) C > B > A > D
c) D > C > A > B
d) C > D > B > A
e) All would have the same increase in volume.

Chapter 12:
Section 6:
Heat & Internal Energy

Heat is energy that flows from a higher-
temperature object to a lower-temperature
object because of a difference in temperatures.
SI Unit of Heat: joule (J)
Definition of Heat
Think diffusion – If a bunch of particles
are randomly moving, their concentration
will tend to spread out until it is even.
The heat that flows from hot to cold
originates in the internal energy of
the hot substance.
It is not correct to say that a substance
contains heat. It contains internal energy.

Chapter 12:
Section 7:
Heat & Temperature Change: Specific Heat
Capacity

Since Solids and Liquids tend to incompressible with a fixed volume,
the ambient pressure is usually insignificant.
The heat that must be supplied or removed to change the temperature of
a substance is
TmCQ ∆=
specific heat
capacity
Common Unit for Specific Heat Capacity: J/(kg·o
C)
Heat Changes in Solids and Liquids
Common Units for Heat 1 Cal = 1 kcal = 4186 joules

Example 9 A Hot Jogger
In a half-hour, a 65-kg jogger can generate 8.0x105
J of heat. This heat
is removed from the body by a variety of means, including the body’s own
temperature-regulating mechanisms. If the heat were not removed, how
much would the body temperature increase?
TmCQ ∆=
mC
Q
T =∆
( ) ( )[ ]
CkgJ3500kg65
J100.8 5
⋅
×
= 
C5.3=

Heat Changes in Gases
 The value of the specific heat of a gas depends on
whether the pressure or volume is held constant.
 This distinction is not important for solids.
 This will be discussed in greater detail later in the
unit

If there is no heat loss to the surroundings,
the heat lost by the hotter object equals the
heat gained by the cooler ones.
Calorimetry

Example 12 Measuring the Specific Heat Capacity
The calorimeter is made of 0.15 kg of aluminum
and contains 0.20 kg of water. Initially, the
water and cup have the same temperature
of 18.0o
C. A 0.040 kg mass of unknown
material is heated to a temperature of
97.0o
C and then added to the water.
After thermal equilibrium is reached, the
temperature of the water, the cup, and the
material is 22.0o
C. Ignoring the small amount
of heat gained by the thermometer, find
the specific heat capacity of the
unknown material.

( ) ( ) ( )unknownwaterAl TmCTmCTmC ∆=∆+∆
( )
CkgJ1300unknown ⋅=C
( ) ( )
( )unknown
waterAl
unknown
Tm
TmcTmc
C
∆
∆+∆
=
( )[ ]( )( ) ( )[ ]( )( )
( )( )

C0.75kg040.0
C0.4kg20.0CkgJ4186C0.4kg15.0CkgJ1000.9 2
unknown
⋅+⋅×
=C

12.7.1. A certain amount of heat Q is added to materials A, B, and
C. The masses of these three materials are 0.04 kg, 0.01 kg,
and 0.02 kg, respectively. The temperature of material A
increases by 4.0 C° while the temperature of the other two
materials increases by only 3.0 C°. Rank these three materials
from the largest specific heat capacity to the smallest value.
a) A > B > C
b) C > B > A
c) B > A > C
d) B = C > A
e) A > B = C

12.7.2. A swimming pool has a width of 9.0 m and a length of
12.0 m. The depth of the water is 1.83 m. One morning, the
temperature of the pool water was 15.0 °C. The water then
absorbed 2.00 × 109
J of heat from the Sun. What is the
final temperature of the water? Assume no heat loss to the
surroundings.
a) 16.9 °C
b) 18.1 °C
c) 17.4 °C
d) 19.6 °C
e) 20.2 °C

12.7.3. Which of the following substances would be the most
effective in cooling 0.300 kg of water at 98 °C?
a) 0.100 kg of lead at 22 °C
b) 0.100 kg of water at 22 °C
c) 0.100 kg of glass at 22 °C
d) 0.100 kg of aluminum at 22 °C
e) 0.100 kg of copper at 22 °C

12.7.4. Elena’s normal body temperature is 36.5 °C. When she
recently became ill, her body temperature increased to 38.0 °C.
What was the minimum amount of heat required for this
increase in body temperature if her weight is 561 N?
a) 2.96 × 106
J
b) 3.50 × 103
J
c) 4.98 × 104
J
d) 3.00 × 105
J
e) 7.60 × 105
J

12.7.5. Four 1-kg cylinders are heated to 100 °C and placed on top of a
block of paraffin wax, which melts at 63 °C. There is one cylinder
made from lead, one of copper, one of aluminum, and one of iron.
After a few minutes, it is observed that the cylinders have sunk into the
paraffin to differing depths. Rank the depths of the cylinders from
deepest to shallowest.
a) lead > iron > copper > aluminum
b) aluminum > copper > lead > iron
c) aluminum > iron > copper > lead
d) copper > aluminum > iron > lead
e) iron > copper > lead > aluminum

12.7.6. Why is water often used as a coolant in automobiles, other
than the fact that it is abundant?
a) Water expands very little as it is heated.
b) The freezing temperature of water has a relatively large value.
c) The specific heat of water is relatively small and its temperature
can be rapidly decreased.
d) The specific heat of water is relatively large and it can store a
great deal of thermal energy.
e) Water does not easily change into a gas.

Chapter 12:
Section 8:
Heat & Phase Change: Latent Heat

During a phase change, the temperature of the mixture does not
change (provided the system is in thermal equilibrium).
Heating Curve

Conceptual Example 13 Saving Energy
Suppose you are cooking spaghetti for dinner, and the instructions
say “boil pasta in water for 10 minutes.” To cook spaghetti in an open
pot with the least amount of energy, should you turn up the burner
to its fullest so the water vigorously boils, or should you turn down
the burner so the water barely boils?

The heat that must be supplied or removed to change the phase
of a mass, m, of a substance is
mLQ =
latent heat
SI Units of Latent Heat: J/kg
HEAT SUPPLIED OR REMOVED IN CHANGING
THE PHASE OF A SUBSTANCE

Example 14 Ice-cold Lemonade
Ice at 0o
C is placed in a Styrofoam cup containing 0.32 kg of lemonade
at 27o
C. The specific heat capacity of lemonade is virtually the same as
that of water. After the ice and lemonade reach and equilibrium
temperature, some ice still remains. Assume that mass of the cup is
so small that it absorbs a negligible amount of heat.
( ) ( )   
lemonade
bylostHeat
lemonade
iceby
gainedHeat
ice
TCmmLf ∆=
( )[ ]( )( )
kgJ103.35
C0C27kg32.0CkgJ4186
5
×
−⋅
=

icem
( )
f
lemonade
ice
L
TCm
m
∆
=
kg11.0=

12.8.1. Heat is added to a substance, but its temperature does not
increase. Which one of the following statements provides the
best explanation for this observation?
a) The substance has unusual thermal properties.
b) The substance must be cooler than its environment.
c) The substance must be a gas.
d) The substance must be an imperfect solid.
e) The substance undergoes a change of phase.

12.8.2. What is the final temperature when 2.50 × 105
J are
added to 0.950 kg of ice at 0.0 °C?
a) 0.0 °C
b) 4.2 °C
c) 15.7 °C
d) 36.3 °C
e) 62.8 °C

12.8.3. By adding 25 kJ to solid material A, 4.0 kg will melt. By
adding 50 kJ to solid material B, 6.0 kg will melt. Solid material
C requires 30 kJ to melt 3.0 kg. Which of these materials, if any,
has the largest value for the heat of fusion?
a) A
b) B
c) C
d) A = B

12.8.4. Consider the system shown in the drawing. A test tube containing
water is inserted into boiling water. Will the water in the test tube
eventually boil?
a) Yes, heat is continually transferred to the
water inside the test tube and eventually it
will boil?
b) Yes, the pressure above the water in the test
tube will be reduced to less than atmospheric
pressure and cause the water to boil.
c) No, heat will only be transferred until the water in the test tube is 100 °C.
d) No, the temperature of the water in the test tube will never reach 100 °C.

Chapter 12:
Section 9:
Equilibrium Between Phases of Matter

The pressure of vapor that coexists in equilibrium with the liquid is
called the equilibrium vapor pressure of the liquid.
Equilibrium Between Phases

Only when the temperature and vapor pressure correspond to a point
on the curved line do the liquid and vapor phases coexist in equilibrium.

Conceptual Example 16 How to Boil Water That is
Cooling Down
Shortly after the flask is removed from the burner,
the boiling stops. A cork is then placed in the neck
of the flask to seal it. To restart the boiling, should
you pour hot or cold water over the neck of the
flask?

As is the case for liquid/vapor
equilibrium, a solid can be in
equilibrium with its liquid phase
only at specific conditions of
temperature and pressure.

All 3 Phases can be combined
Critical Point
TC
Most Substances
Water

Chapter 12:
Section 10:
Humidity

Air is a mixture of gases.
The total pressure is the sum of the partial pressures of the component
gases.
The partial pressure of water vapor depends on weather conditions. It
can be as low as zero or as high as the vapor pressure of water at the
given temperature.
( ) ( )
( )
100
retemperatuexistingatwaterofpressurevapormEquilibriu
orwater vapofpressurePartial
humidityrelativePercent ×=
To provide an indication of how much water vapor is in the air, weather
forecasters usually give the relative humidity:

Example 17 Relative Humidities
One day, the partial pressure of water vapor is 2.0x103
Pa. Using the
vaporization curve, determine the relative humidity if the temperature
is 32o
C.

( ) ( )
( )
100
retemperatuexistingatwaterofpressurevapormEquilibriu
orwater vapofpressurePartial
humidityrelativePercent ×=
%42100
Pa108.4
Pa100.2
humidityRelative 3
3
=×
×
×
=

The temperature at which the relative humidity is 100% is called the dew
point.

Ch 12 Temperature and Heat

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Ch 12 Temperature and Heat