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Module 9
Temperature and Heat
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Temperature We associate the concept of temperature with
how hot or cold an object feels
Our senses provide us with a qualitativeindication of temperature
Our senses are unreliable for this purpose
We need a reliable and reproducible method
for measuring the relative hotness orcoldness of objects We need a technical definition of temperature
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Thermal Contact Two objects are in thermal contact
with each other if energy can be
exchanged between them The exchanges we will focus on will be in
the form of heat or electromagnetic
radiation The energy is exchanged due to a
temperature difference
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Thermal Equilibrium Thermal equilibrium is a situation in
which two objects would not exchange
energy by heat or electromagneticradiation if they were placed in thermalcontact
The thermal contact does not have to alsobe physical contact
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Zeroth Law of
Thermodynamics If objects A and B are separately in
thermal equilibrium with a third object
C, then A and B are in thermalequilibrium with each other
Let object C be the thermometer
Since they are in thermal equilibrium witheach other, there is no energy exchangedamong them
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Temperature – Definition Temperature can be thought of as the
property that determines whether an
object is in thermal equilibrium withother objects
Two objects in thermal equilibrium witheach other are at the same temperature If two objects have different temperatures,
they are not in thermal equilibrium witheach other
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Thermometers A thermometer is a device that is
used to measure the temperature of a
system
Thermometers are based on theprinciple that some physical property of
a system changes as the system’stemperature changes
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Thermometers, cont These properties include:
The volume of a liquid
The dimensions of a solid The pressure of a gas at a constant volume
The volume of a gas at a constant pressure
The electric resistance of a conductor
The color of an object
A temperature scale can be established onthe basis of any of these physical properties
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Mercury-in glassthermometer
alcohol thermometer
digital thermometer
infrared thermometer
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Celsius Scale Proposed by Swedish astronomer Anders
Celsius in 1742
The ice point of water is defined to be 0o C The steam point of water is defined to be
100o C
The length of the column between these twopoints is divided into 100 increments, calleddegrees
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Fahrenheit Scale A common scale in everyday use in the
US
Named for Daniel Fahrenheit (1724) Temperature of the ice point is 32oF
Temperature of the steam point is
212oF There are 180 divisions (degrees)
between the two reference points
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Absolute Temperature Scale/
Kelvin Scale Proposed by mathematical physicist and engineer
William Thomson, 1st Baron Kelvin in 1848
Absolute zero is used as the basis of the absolutetemperature scale
The size of the degree on the absolute scale isthe same as the size of the degree on the Celsius
scale To convert:
TC = T – 273.15
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Absolute Temperature Scale, 2 The absolute temperature scale is now based
on two new fixed points
Adopted by in 1954 by the InternationalCommittee on Weights and Measures
One point is absolute zero
The other point is the triple point of water
This is the combination of temperature and pressurewhere ice, water, and steam can all coexist
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Absolute Temperature Scale, 3 The triple point of water occurs at
0.01o C and 4.58 mm of mercury
This temperature was set to be 273.16on the absolute temperature scale
This made the old absolute scale agree
closely with the new one
The units of the absolute scale are kelvins
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Absolute Temperature Scale, 4 The absolute scale is also called the Kelvin
scale
The triple point temperature is 273.16 K No degree symbol is used with kelvins
The kelvin is defined as 1/273.16 of thedifference between absolute zero and thetemperature of the triple point of water
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Some Examples of Absolute
Temperatures The figure at right gives
some absolutetemperatures at which
various physicalprocesses occur
The scale is logarithmic
The temperature of absolute zero cannot beachieved Experiments have come
close
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Comparison of Scales Celsius and Kelvin have the same size
degrees, but different starting points
TC = T – 273.15
Celsius and Fahrenheit have differentsized degrees and different starting
points
F C
932
5T T F
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Comparison of Scales, cont To compare changes in temperature
Ice point temperatures 0oC = 273.15 K = 32o F
Steam point temperatures 100oC = 373.15 K = 212o F
C F
5
9T T T
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Thermal Expansion Thermal expansion is the increase in the size of an
object with an increase in its temperature
Thermal expansion is a consequence of the change in
the average separation between the atoms in anobject
If the expansion is small relative to the originaldimensions of the object, the change in anydimension is, to a good approximation, proportionalto the first power of the change in temperature
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Linear Expansion Assume an object has an initial length L
That length increases by L as the
temperature changes by T We define the coefficient of linear
expansion as
A convenient form is L = a L 0 T
a
0/L LT
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Linear Expansion, cont This equation can also be written in
terms of the initial and final conditions
of the object: L f – L i = a L 0 (T f – T i )
The coefficient of linear expansion, a ,
has units of (oC)-1
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Some Coefficients
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Linear Expansion, final Some materials expand along one dimension,
but contract along another as the
temperature increases Since the linear dimensions change, it follows
that the surface area and volume also changewith a change in temperature
A cavity in a piece of material expands in thesame way as if the cavity were filled with thematerial
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Volume Expansion The change in volume is proportional to
the original volume and to the change
in temperature V = b V 0 T
b is the coefficient of volume expansion
For a solid, b 3a This assumes the material is isotropic, the
same in all directions
For a liquid or gas, b is given in the table
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Area Expansion The change in area is proportional to
the original area and to the change in
temperature: A = 2a A i T
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Bimetallic Strip Each substance has its
own characteristicaverage coefficient of
expansion
This can be made useof in the device shown,called a bimetallic strip
It can be used in athermostat
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Water’s Unusual Behavior As the temperature
increases from 0oC to4oC, water contracts Its density increases
Above 4oC, waterexpands with increasingtemperature Its density decreases
The maximum densityof water (1.000 g/cm3)occurs at 4oC
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Heat Heat is defined as the transfer of
energy across the boundary of a system
due to a temperature differencebetween the system and itssurroundings
The term heat will also be used torepresent the amount of energytransferred by this method
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Units of Heat Historically, the calorie was the unit used for heat
One calorie is the amount of energy transfer necessary toraise the temperature of 1 g of water from 14.5oC to 15.5oC
The “Calorie” used for food is actually 1 kilocalorie
In the US Customary system, the unit is a BTU(British Thermal Unit)
One BTU is the amount of energy transfer necessary to raise
the temperature of 1 lb of water from 63o
F to 64o
F The standard in the text is to use Joules
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James Prescott Joule 1818 – 1889
British physicist
Largely self-educated
Some formal education fromJohn Dalton
Research led toestablishment of theprinciple of Conservation of
Energy Determined the amount of
work needed to produce oneunit of energy
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Mechanical Equivalent of Heat Joule established the
equivalence betweenmechanical energy and
internal energy His experimental setup
is shown at right
The loss in potentialenergy associated withthe blocks equals thework done by thepaddle wheel on thewater
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Mechanical Equivalent of Heat,
cont Joule found that it took approximately 4.18 J
of mechanical energy to raise the water 1oC
Later, more precise, measurementsdetermined the amount of mechanical energyneeded to raise the temperature of waterfrom 14.5oC to 15.5oC
1 cal = 4.186 J
This is known as the mechanical equivalent of heat
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Heat Capacity The heat capacity, C, of a particular
sample is defined as the amount of
energy needed to raise the temperatureof that sample by 1oC
If energy Q produces a change of
temperature of T , thenQ = C T
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Specific Heat Specific heat, c, is the heat capacity
per unit mass
If energy Q transfers to a sample of asubstance of mass m and thetemperature changes by T , then the
specific heat is
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Specific Heat, cont The specific heat is essentially a measure of
how thermally insensitive a substance is to
the addition of energy The greater the substance’s specific heat, the
more energy that must be added to cause aparticular temperature change
The equation is often written in terms of Q :
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Some Specific Heat Values
NOTE – Lead andGold have smallest
specific heats
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More Specific Heat Values
NOTE – ice andsteam (different forms of H2O) have ~ ½ x thespecific heat of liquid
water.
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Sign Conventions If the temperature increases:
Q and T are positive
Energy transfers into the system
If the temperature decreases:
Q and T are negative
Energy transfers out of the system
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Specific Heat Varies With
Temperature Technically, the specific heat varies with
temperature
The corrected equation is However, if the temperature intervals are not
too large, the variation can be ignored and ccan be treated as a constant For example, for water there is only about a 1%
variation between 0o and 100oC
These variations will be neglected unlessotherwise stated
f
i
T
T Q m c dT
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Specific Heat of Water Water has the highest specific heat of
common materials
This is in part responsible for manyweather phenomena
Moderate temperatures near large bodies
of water Global wind systems
Land and sea breezes
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CAUTION: The definition of heat. Remember that dQ does not represent a change in the amount of heatcontained in a body; this is a meaningless
concept. Heat is always energy in transit as aresult of a temperature difference. There is no suchthing as “the amount of heat in a body” .
CAUTION: The meaning of “heat capacity” . The term “heat capacity” is unfortunate because it gives theerroneous impression that a body contains certainamount of heat. Remember, heat is energy intransit to or from a body, not the energy residing inthe body.
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Why does a metal rod at 200C feelscolder than a piece of wood at200C?
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Why do you feel cold whenyou first step out of a
swimming pool?
Evaporative cooling!
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Calorimetry One technique for measuring specific
heat involves heating a material, adding
it to a sample of water, and recordingthe final temperature
This technique is known as
calorimetry A calorimeter is a device in which this
energy transfer takes place
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Calorimetry, cont The system of the sample and the water is
isolated
Conservation of energy requires that theamount of energy that leaves the sampleequals the amount of energy that enters thewater
Conservation of Energy gives amathematical expression of this:
Q cold= -Q hot
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Example, Calorimetry
Answer =
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STEEL INGOT
ALUMINUM INGOT
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Phase Changes A phase change is when a substance changes from
one form to another
Two common phase changes are
Solid to liquid (melting)
Liquid to gas (boiling)
During a phase change, there is no change intemperature of the substance
For example, in boiling the increase in internal energy isrepresented by the breaking of the bonds betweenmolecules, giving the molecules of the gas a higherintermolecular potential energy
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Latent Heat Different substances react differently to the
energy added or removed during a phasechange Due to their different internal molecular
arrangements
The amount of energy also depends on themass of the sample
If an amount of energy Q is required tochange the phase of a sample of mass m ,
L ≡ Q /m
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Latent Heat, cont The quantity L is called the latent heat
of the material
Latent means “hidden” The value of L depends on the substance
as well as the actual phase change
The energy required to change thephase is Q = mL
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Latent Heat, final The latent heat of fusion is used when the
phase change is from solid to liquid
The latent heat of vaporization is used whenthe phase change is from liquid to gas
The positive sign is used when the energy istransferred into the system
This will result in melting or boiling The negative sign is used when energy is
transferred out of the system This will result in freezing or condensation
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Sample Latent Heat Values
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Mechanisms of EnergyTransfer by Heat
We want to know the rate at whichenergy is transferred
There are various mechanismsresponsible for the transfer:
Conduction
Convection Radiation
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Conduction
The transfer can be viewed on an atomicscale It is an exchange of kinetic energy between
microscopic particles by collisions The microscopic particles can be atoms, molecules or
free electrons
Less energetic particles gain energy duringcollisions with more energetic particles
Rate of conduction depends upon thecharacteristics of the substance
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Conduction, cont.
In general, metals are good thermalconductors They contain large numbers of electrons that are
relatively free to move through the metal They can transport energy from one region to
another
Poor conductors include asbestos, paper, and
gases Conduction can occur only if there is a
difference in temperature between two partsof the conducting medium
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Conduction, equation
The slab at right allowsenergy to transfer fromthe region of higher
temperature to theregion of lowertemperature
The rate of transfer is
given by:
Q dT H kA
t dx
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Conduction, equationexplanation
A is the cross-sectional area
Δx is the thickness of the slab
Or the length of a rod is in Watts when Q is in Joules and t is in
seconds
k is the thermal conductivity of the material
Good conductors have high k values and goodinsulators have low k values
H
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Temperature Gradient
The quantity |dT / dx | iscalled the temperaturegradient of the material
It measures the rate atwhich temperature varieswith position
For a rod, the temperaturegradient can be expressedas:
h cdT T T
dx L
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Rate of Energy Transfer in a Rod
Using the temperature gradient for therod, the rate of energy transfer
becomes:
h c T T
H kAL
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Compound Slab
For a compound slab containing severalmaterials of various thicknesses (L 1, L 2,
…) and various thermal conductivities(k 1, k 2, …) the rate of energy transferdepends on the materials and the
temperatures at the outer edges:
h c
i i
i
A T T H
L k
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Some Thermal Conductivities
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More Thermal Conductivities
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Home Insulation
Substances are rated by their R values
R = L / k and the rate becomes
For multiple layers, the total R value is the sum of
the R values of each layer
Wind increases the energy loss by conductionin a home
h c
i
i
A T T H R
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Convection
Energy transferred by the movement of a substance
When the movement results fromdifferences in density, it is called natural convection
When the movement is forced by a fan ora pump, it is called forced convection
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Convection example
Air directly abovethe radiator iswarmed and
expands The density of the
air decreases, and itrises
A continuous aircurrent isestablished
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Radiation
Radiation does not require physicalcontact
All objects radiate energy continuouslyin the form of electromagnetic wavesdue to thermal vibrations of theirmolecules
Rate of radiation is given by Stefan’s
law
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Stefan’s Law
P = σ AeT4
P is the rate of energy transfer, in Watts
σ = 5.6696 x 10-8 W/m2 . K 4 A is the surface area of the object
e is a constant called the emissivity e varies from 0 to 1
The emissivity is also equal to the absorptivity
T is the temperature in Kelvins
E Ab ti d
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Energy Absorption andEmission by Radiation
With its surroundings, the rate at whichthe object at temperature T with
surroundings at T o radiates is P net = σAe (T 4 –T o
4)
When an object is in equilibrium with its
surroundings, it radiates and absorbs atthe same rate
Its temperature will not change
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Ideal Absorbers
An ideal absorber is defined as anobject that absorbs all of the energy
incident on it e = 1
This type of object is called a black body
An ideal absorber is also an idealradiator of energy
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Ideal Reflector
An ideal reflector absorbs none of theenergy incident on it
e = 0
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The Dewar Flask
A Dewar flask is a container designed tominimize the energy losses by
conduction, convection, and radiation Invented by Sir James Dewar (1842 –
1923)
It is used to store either cold or hot
liquids for long periods of time A Thermos bottle is a common household
equivalent of a Dewar flask
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Dewar Flask, Details
The space between the wallsis a vacuum to minimizeenergy transfer byconduction and convection
The silvered surfaceminimizes energy transfersby radiation
Silver is a good reflector
The size of the neck isreduced to further minimizeenergy losses