Ch12. Temperature and Heat Common Temperature Scales

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Ch12. Temperature and Heat Common Temperature
Scales
A number of different temperature scales have
been devised, two popular choices being the
Celsius (formerly, centigrade) and Fahrenheit
scales.
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On the Celsius scale, an ice point of 0 C (0
degrees Celsius) and a steam point of 100 C were
selected. On the Fahrenheit scale, an ice point
of 32 F (32 degrees Fahrenheit) and a steam
point of 212 F were chosen. The Celsius scale is
used worldwide, while the Fahrenheit scale is
used mostly in the United States.
The temperature of the human body is about 37 C,
where the symbol C stands for degrees Celsius.
However, the change between two temperatures is
specified in Celsius degrees (C)not in
degrees Celsius.
The separation between the ice and steam points
on the Celsius scale is divided into 100 Celsius
degrees, while on the Fahrenheit scale the
separation is divided into 180 Fahrenheit
degrees. Therefore, the size of the Celsius
degree is larger than that of the Fahrenheit
degree by a factor of , or .
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Example 1.  Converting from a Fahrenheit to a
Celsius Temperature
A healthy person has an oral temperature of 98.6
F. What would this reading be on the Celsius
scale?
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Example 2.  Converting from a Celsius to a
Fahrenheit Temperature
A time and temperature sign on a bank indicates
that the outdoor temperature is 20.0 C. Find
the corresponding temperature on the Fahrenheit
scale .
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Reasoning Strategy
Converting Between Different Temperature Scales
  1. Determine the magnitude of the difference
between the stated temperature and the ice point
on the initial scale.    2. Convert this number
of degrees from one scale to the other scale by
using the fact that.    3.Add or subtract the
number of degrees on the new scale to or from the
ice point on the new scale.
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Check Your Understanding 1
On a new temperature scale the steam point is 348
X, and the ice point is 112 X. What is the
temperature on this scale that corresponds to
28.0 C?
178 X
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The Kelvin Temperature Scale
Kelvin temperature scale was introduced by the
Scottish physicist William Thompson (Lord Kelvin,
18241907), and in his honor each degree on the
scale is called a kelvin (K). By international
agreement, the symbol K is not written with a
degree sign (), nor is the word degrees used
when quoting temperatures. For example, a
temperature of 300 K (not 300 K) is read as
three hundred kelvins, not three hundred
degrees kelvin. The kelvin is the SI base unit
for temperature.
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The ice point (0 C) occurs at 273.15 K on the
Kelvin scale.
When a gas confined to a fixed volume is heated,
its pressure increases. Conversely, when the gas
is cooled, its pressure decreases. The change in
gas pressure with temperature is the basis for
the constant-volume gas thermometer.
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A constant-volume gas thermometer.
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A plot of absolute pressure versus temperature
for a low-density gas at constant volume. The
graph is a straight line and, when extrapolated
(dashed line), crosses the temperature axis at
273.15 C.
Absolute zero means that temperatures lower
than 273.15 C cannot be reached by continually
cooling a gas or any other substance.
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Thermometers
A property that changes with temperature is
called a thermometric property.
The thermocouple is a thermometer used
extensively in scientific laboratories. It
consists of thin wires of different metals,
welded together at the ends to form two junctions.
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One of the junctions, called the hot junction,
is placed in thermal contact with the object
whose temperature is being measured. The other
junction, termed the reference junction, is
kept at a known constant temperature (usually an
icewater mixture at 0 C). The thermocouple
generates a voltage that depends on the
difference in temperature between the two
junctions. This voltage is the thermometric
property and is measured by a voltmeter.
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Because this electrical resistance changes with
temperature, electrical resistance is another
thermometric property. Electrical resistance
thermometers are often made from platinum wire,
because platinum has excellent mechanical and
electrical properties in the temperature range
from 270 C to 700 C. The electrical
resistance of platinum wire is known as a
function of temperature. Thus, the temperature of
a substance can be determined by placing the
resistance thermometer in thermal contact with
the substance and measuring the resistance of the
platinum wire.
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Radiation emitted by an object can also be used
to indicate temperature. At low to moderate
temperatures, the predominant radiation emitted
is infrared. As the temperature is raised, the
intensity of the radiation increases
substantially.
Thermal painting is called a thermograph or
thermogram. Thermography is an important
diagnostic tool in medicine.
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Linear Thermal Expansion
NORMAL SOLIDS
The increase in any one dimension of a solid is
called linear expansion .
When the temperature of a rod is raised by T,
the length of the rod increases by L .
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For modest temperature changes, experiments show
that the change in length is directly
proportional to the change in temperature
In addition, the change in length is
proportional to the initial length of the rod.
L is proportional to both L0 and T (
) by using a proportionality constant
, which is called the coefficient of linear
expansion.
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LINEAR THERMAL EXPANSION OF A SOLID The length L0
of an object changes by an amount L when its
temperature changes by an amount T
where is the coefficient of linear
expansion. Common Unit for the Coefficient of
Linear Expansion
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    Coefficient of Thermal Expansion (C)1   Coefficient of Thermal Expansion (C)1 
 Substance   Linear (a)  Volumetric (b) 
 Solids       
Aluminium   23 106   69 106 
   Brass   19 106   57 106 
   Concrete   12 106   36 106 
   Copper   17 106   51 106 
   Glass (common)   8.5 106   26 106 
Glass (Pyrex)   3.3 106   9.9 106 
   Gold   14 106   42 106 
   Iron or steel   12 106   36 106 
   Lead   29 106   87 106 
   Nickel   13 106   39 106 
   Quartz (fused)   0.50 106   1.5 106 
   Silver   19 106   57 106
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Liquidsb        
   Benzene      1240 106 
   Carbon tetrachloride      1240 106 
   Ethyl alcohol      1120 106 
   Gasoline      950 106 
   Mercury      182 106 
   Methyl alcohol      1200 106 
   Water      207 106 
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Example 3.   Buckling of a Sidewalk
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A concrete sidewalk is constructed between two
buildings on a day when the temperature is 25 C.
The sidewalk consists of two slabs, each three
meters in length and of negligible thickness . As
the temperature rises to 38 C, the slabs expand,
but no space is provided for thermal expansion.
The buildings do not move, so the slabs buckle
upward. Determine the vertical distance y in part
b of the drawing.
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Antiscalding device screws onto the end of a
faucet and quickly shuts off the flow of water
when it becomes too hot. As the water temperature
rises, the actuator spring expands and pushes the
plunger forward, shutting off the flow. When the
water cools, the spring contracts and the water
flow resumes.
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THERMAL STRESS Example 4.  The Stress on a
Steel Beam
A steel beam is used in the roadbed of a bridge.
The beam is mounted between two concrete supports
when the temperature is 23 C, with no room
provided for thermal expansion. What
compressional stress must the concrete supports
apply to each end of the beam, if they are to
keep the beam from expanding when the temperature
rises to 42 C?
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Y 2.0 1011 N/m2
12 106 (C) 1
DT 19 C
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THE BIMETALLIC STRIP
A bimetallic strip is made from two thin strips
of metal that have different coefficients of
linear expansion.
Bass
Steel
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Bimetallic strips are frequently used as
adjustable automatic switches in electrical
appliances.
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THE EXPANSION OF HOLES Conceptual
Example 5.  Do Holes Expand or Contract When the
Temperature Increases?
Eight square tiles that are arranged to form a
square pattern with a hole in the center. If the
tiles are heated, what happens to the size of the
hole?
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The hole expands just as if it were made of the
material of the surrounding tiles.
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Example 6.  A Heated Engagement Ring
A gold engagement ring has an inner diameter of
1.5 102 m and a temperature of 27 C. The ring
falls into a sink of hot water whose temperature
is 49 C. What is the change in the diameter of
the hole in the ring?
a 14 106 (C)1
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Conceptual Example 7.  Expanding Cylinders
In a cross-sectional view of three cylinders, A,
B, and C, each is made from a different material
one is lead, one is brass, and one is steel. 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?
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A brass, B steel, and C lead
A lead, B steel, and C brass
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Check Your Understanding 2

• A metal ball has a diameter that is slightly
  greater than the diameter of a hole that has been
  cut into a metal plate. The coefficient of linear
  thermal expansion for the metal from which the
  ball is made is greater than that for the metal
  of the plate. Which one or more of the following
  procedures can be used to make the ball pass
  through the hole?
• Raise the temperatures of the ball and the plate
  by the same amount.
• Lower the temperatures of the ball and the plate
  by the same amount.
• Heat the ball and cool the plate.
• Cool the ball and heat the plate.

b d
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Volume Thermal Expansion
VOLUME THERMAL EXPANSION The volume V0 of an
object changes by an amount V when its
temperature changes by an amount T
where is the coefficient of volume
expansion.
Common Unit for the Coefficient of Volume
Expansion (C) 1
b 3a.
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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 a coefficient of volume expansion of . If
the radiator is filled to its 15-quart capacity
when the engine is cold (6.0 C), how much
overflow from the radiator will spill into the
reservoir when the coolant reaches its operating
temperature of 92 C?
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The overflow volume is 0.53 quarts 0.066 quarts
0.46 quarts.
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The fact that water has its greatest density at 4
C, rather than at 0 C, has important
consequences for the way in which a lake freezes.
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The fact that the density of ice is smaller than
the density of water has an important consequence
for home owners, who have to contend with the
possibility of bursting water pipes during severe
winters.
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Heat and Internal Energy

• Heat is energy in transit from hot to cold.
• Heat flows from the hotter coffee cup to the
  colder hand.
• Heat flows from the warmer hand to the colder
  glass of ice water.

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DEFINITION OF HEAT Heat is energy that flows from
a higher-temperature object to a
lower-temperature object because of the
difference in temperatures. SI Unit of Heat
joule (J)
The internal energy of a substance is the sum of
the molecular kinetic energy (due to the random
motion of the molecules), the molecular potential
energy (due to forces that act between the atoms
of a molecule and between molecules), and other
kinds of molecular energy. When heat flows in
circumstances where the work done is negligible,
the internal energy of the hot substance
decreases and the internal energy of the cold
substance increases.
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Heat and Temperature Change Specific Heat
Capacity
SOLIDS AND LIQUIDS
HEAT SUPPLIED OR REMOVED IN CHANGING THE
TEMPERATURE OF A SUBSTANCE The heat Q that must
be supplied or removed to change the temperature
of a substance of mass m by an amount T is
where c is the specific heat capacity of the
substance. Common Unit for Specific Heat
Capacity J/(kgC)
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 Substance   Specific Heat Capacity, c J/(kgC) 
 Solids 
   Aluminum   9.00 102 
   Copper   387 
   Glass   840 
   Human body (37 C, average)   3500 
   Ice (15 C)   2.00 103 
   Iron or steel   452 
   Lead   128 
   Silver   235
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Liquids 
   Benzene   1740 
   Ethyl alcohol   2450 
   Glycerin   2410 
   Mercury   139 
   Water (15 C)   4186 
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Example 9.  A Hot Jogger
In a half hour, a 65-kg jogger can generate 8.0
105 J of heat. This heat is removed from the
joggers body by a variety of means, including
the bodys own temperature-regulating mechanisms.
If the heat were not removed, how much would the
body temperature increase?
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Example 10.  Taking a Hot Shower
Cold water at a temperature of 15 C enters a
heater, and the resulting hot water has a
temperature of 61 C. A person uses 120 kg of hot
water in taking a shower. (a) Find the energy
needed to heat the water. (b) Assuming that the
utility company charges 0.10 per kilowatthour
for electrical energy, determine the cost of
heating the water.
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(b)
At a cost of 0.10 per kWh, the bill for the heat
is 0.64 or 64 cents.
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GASES
The value of the specific heat capacity depends
on whether the pressure or volume is held
constant while energy in the form of heat is
added to or removed from a substance. The
distinction between constant pressure and
constant volume is usually not important for
solids and liquids but is significant for gases.
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HEAT UNITS OTHER THAN THE JOULE
There are three heat units other than the joule
in common use.
One kilocalorie (1 kcal) was defined historically
as the amount of heat needed to raise the
temperature of one kilogram of water by one
Celsius degree. one calorie (1 cal) was defined
as the amount of heat needed to raise the
temperature of one gram of water by one Celsius
degree The British thermal unit (Btu) is the
other commonly used heat unit and was defined
historically as the amount of heat needed to
raise the temperature of one pound of water by
one Fahrenheit degree.
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Joules experiments revealed that the performance
of mechanical work, like rubbing your hands
together, can make the temperature of a substance
rise, just as the absorption of heat can.
This conversion factor is known as the mechanical
equivalent of heat.
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CALORIMETRY
The kind of heat transfer that occurs within a
thermos of iced tea also occurs within a
calorimeter, which is the experimental apparatus
used in a technique known as calorimetry.
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Example 11.  Measuring the Specific Heat Capacity
A calorimeter cup is made from 0.15 kg of
aluminum and contains 0.20 kg of water.
Initially, the water and the cup have a common
temperature of 18.0 C. A 0.040-kg mass of
unknown material is heated to a temperature of
97.0 C and then added to the water. The
temperature of the water, the cup, and the
unknown material is 22.0 C after thermal
equilibrium is reestablished. Ignoring the small
amount of heat gained by the thermometer, find
the specific heat capacity of the unknown
material.
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Heat lost by unknown material
Heat gained by aluminum and water
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DTAl DTwater 22.0 C 18.0 C 4.0
C
DTunknown 97.0 C 22.0 C 75.0 C.
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Check Your Understanding 3
Consider a mass m of a material and a change
T in its temperature. Various possibilities for
these variables are listed in the table below.
Rank these possibilities in descending order
(largest first), according to how much heat is
needed to bring about the change in temperature.
    m (kg)    T (C) 
(a)  2.0   15 
 (b)   1.5   40 
 (c)   3.0   25 
 (d)   2.5   20 
c, b, d, a
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Heat and Phase Change Latent Heat
Three familiar phases of mattersolid, liquid,
and gasand the phase changes that can occur
between any two of them.
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The graph shows the way the temperature of water
changes as heat is added, starting with ice at
30 C. The pressure is atmospheric pressure.
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Conceptual Example 12.  Saving Energy
Suppose you are cooking spaghetti for dinner,
and the instructions say boil the pasta in water
for ten 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?
Turn down the heat, because the least amount of
energy is expended when the water barely boils.
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HEAT SUPPLIED OR REMOVED IN CHANGING THE PHASE OF
A SUBSTANCE The heat Q that must be supplied or
removed to change the phase of a mass m of a
substance is
where L is the latent heat of the substance. SI
Unit of Latent Heat J/kg
The latent heat of fusion Lf refers to the change
between solid and liquid phases, the latent heat
of vaporization Lv applies to the change between
liquid and gas phases, and the latent heat of
sublimation Ls refers to the change between solid
and gas phases.
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Substance   Melting Point (C)   Latent Heat of Fusion, Lf (J/kg)   Boiling Point (C)   Latent Heat of Vaporization, Lv (J/kg) 
 Ammonia   77.8   33.2 104   33.4   13.7 105 
 Benzene   5.5   12.6 104   80.1   3.94 105 
 Copper   1083   20.7 104   2566   47.3 105 
 Ethyl alcohol   114.4   10.8 104   78.3   8.55 105 
 Gold   1063   6.28 104   2808   17.2 105 
 Lead   327.3   2.32 104   1750   8.59 105 
 Mercury   38.9   1.14 104   356.6   2.96 105 
 Nitrogen   210.0   2.57 104   195.8   2.00 105 
 Oxygen   218.8   1.39 104   183.0   2.13 105 
 Water   0.0   33.5 104   100.0   22.6 105 
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Example 13.  Ice-cold Lemonade
Ice at 0 C is placed in a Styrofoam cup
containing 0.32 kg of lemonade at 27 C. The
specific heat capacity of lemonade is virtually
the same as that of water that is, c 4186
J/(kgC). After the ice and lemonade reach an
equilibrium temperature, some ice still remains.
The latent heat of fusion for water is Lf 3.35
105 J/kg. Assume that the mass of the cup is so
small that it absorbs a negligible amount of
heat, and ignore any heat lost to the
surroundings. Determine the mass of ice that has
melted.
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Q mLf
Q cm DT
Heat gained by ice
Heat lost by lemonade
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Example 14.  Getting Ready for a Party
A 7.00-kg glass bowl c 840 J/(kgC) contains
16.0 kg of punch at 25.0 C. Two-and-a-half
kilograms of ice c 2.00 103 J/(kgC) are
added to the punch. The ice has an initial
temperature of 20.0 C, having been kept in a
very cold freezer. The punch may be treated as if
it were water c 4186 J/(kgC), and it may be
assumed that there is no heat flow between the
punch bowl and the external environment. The
latent heat of fusion for water is 3.35 105
J/kg. When thermal equilibrium is reached, all
the ice has melted, and the final temperature of
the mixture is above 0 C. Determine this
temperature.
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(a)
(b)
(c)
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(d)
(e)
           .
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A dye-sublimation printer. As the plastic film
passes in front of the print head, the heat from
a given heating element causes one of three
pigments or dyes on the film to sublime from a
solid to a gas. The gaseous dye is absorbed onto
the coated paper as a dot of color. The size of
the dots on the paper has been exaggerated for
clarity.
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Check Your Understanding 4
When ice cubes are used to cool a drink, both
their mass and temperature are important in how
effective they are. The table below lists several
possibilities for the mass and temperature of the
ice cubes used to cool a particular drink. Rank
the possibilities in descending order (best
first), according to their cooling effectiveness.
    Mass of ice cubes   Temperature of ice cubes 
 (a)   m   6.0 C 
 (b)   ½m   12 C 
 (c)   2m   3.0 C 
c, a, b
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Equilibrium Between Phases of Matter
The pressure of the vapor that coexists in
equilibrium with the liquid is called the
equilibrium vapor pressure of the liquid.
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The equilibrium vapor pressure does not depend on
the volume of space above the liquid. Only when
the temperature and vapor pressure correspond to
a point on the curved line, which is called the
vapor pressure curve or the vaporization curve,
do liquid and vapor phases coexist in
equilibrium.
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Conceptual Example 15.  How to Boil Water That
Is Cooling Down
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Water is boiling in an open flask. 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 (but not boiling) water or cold
water over the neck of the flask, as in part b of
the drawing?
It is possible to restart the boiling by pouring
cold water over the neck of the flask.
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The operation of spray cans is based on the
equilibrium between a liquid and its vapor.
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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. For each temperature, there is a single
pressure at which the two phases can coexist in
equilibrium. A plot of the equilibrium pressure
versus equilibrium temperature is referred to as
the fusion curve.
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Humidity
The partial pressure of a gas is the pressure it
would exert if it alone occupied the entire
volume at the same temperature as the mixture.
When the partial pressure of the water vapor
equals the equilibrium vapor pressure of water at
a given temperature, the relative humidity is
100. In such a situation, the vapor is said to
be saturated because it is present in the maximum
amount, as it would be above a pool of liquid at
equilibrium in a closed container.
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Example 16.  Relative Humidities
One day, the partial pressure of water vapor in
the air is 2.0 103 Pa. Using the vaporization
curve for water, determine the relative humidity
if the temperature is (a) 32 C and (b) 21 C.
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(a)
(b)
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When air containing a given amount of water vapor
is cooled, a temperature is reached in which the
partial pressure of the vapor equals the
equilibrium vapor pressure. This temperature is
known as the dew point.
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Concepts Calculations Example 17.  Linear and
Volume Thermal Expansion
Three rectangular blocks are made from the same
material. The initial dimensions of each are
expressed as multiples of D, where D 2.00 cm.
They are heated and their temperatures increase
by 35.0 C.
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The coefficients of linear and volume expansion
are
and
respectively. Determine the change in their (a)
vertical heights and (b) volumes.
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(b)
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Concepts Calculations Example 18.  Heat and
Temperature Changes
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Objects A and B are made from copper, but the
mass of B is three times that of A. Object C is
made from glass and has the same mass as B. The
same amount of heat Q is supplied to each one Q
14 J. Determine the rise in temperature for
each.
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Conceptual Question 3
REASONING AND SOLUTION The plate is made of
aluminum the spherical ball is made of
brass. The coefficient of linear expansion of
aluminum is greater than the coefficient of
linear expansion of brass. Therefore, if the
plate and the ball are heated, both will expand
however, the diameter of the hole in the aluminum
plate will expand more than the diameter of the
brass ball. In order to prevent the ball from
falling through the hole, the plate and the ball
must be cooled. Both the diameter of the hole in
the plate and the diameter of the ball will
contract. The diameter of the hole will decrease
more than the diameter of the ball, thereby
preventing the ball from falling through the
hole.
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Problem 12
REASONING AND SOLUTION a. The radius of the
hole will be larger when the plate is heated,
because the hole expands as if it were made of
copper.
b. The expansion of the radius is
. Using the value for the coefficient
of thermal expansion of copper given in Table
12.1, we find that the fractional change in the
radius is
Dr/r0 aDT (17 106 C1)(110 C - 11 C)
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Problem 18
REASONING AND SOLUTION The initial diameter of
the sphere, ds, is
ds (5.0 104)dr dr
where dr is the initial diameter of the ring.
Applying to
the diameter of the sphere gives
and to the ring gives
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If the sphere is just to fit inside the ring, we
must have
Substituting Equation (1) in this result and
taking values for the coefficients of thermal
expansion of steel and lead from Table 10.1 yield
Tf 70.0 C - 29 C
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Problem 30
REASONING AND SOLUTION Both the water and pipe
expand as the temperature increases.
The initial volume of the pipe and water is
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Problem 32
REASONING AND SOLUTION Both the coffee and
beaker expand as the temperature increases.
Taking the coefficients of volumetric expansion
w and c for coffee (water) and glass (Pyrex)
from Table 12.1, we find
7.310-6m3
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Problem 46
REASONING AND SOLUTION We wish to convert 2.0
of the heat Q into gravitational potential
energy, i.e., (0.020)Q mgh. Thus