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    Lecture 13 Chapter 18Temperature, Heat, and the First Law of Thermodynamics

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    Lecture 13 Chapter 18Temperature, Heat, and the First Law of

    Thermodynamics

    Temperature and Thermal EquilibriumLinear ExpansionHeat and Energy Transfer and Specific HeatThermal Conductivity

    Work and the First Law of Thermodynamics ( E int = Q -W

    Conduction, Convection and Radiation

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    P ressure reduction due to cooling inside coke can crushingthe coke can as it is placed in water.Thermal expansion cracking the nut.Thermal expansion Ring and ballThermal effects using liquid nitrogenThermal ConductivityLight The Match

    Leslie CubeJug O' AirBoiling by CoolingBoiling by Reducing P ressureRadiometerDipping Duck Toy

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    Temperature and Thermal Equilibrium

    If two thermal systems are in thermal equilibriumwith one another, then they have the sametemperature .

    If two systems are each in thermal equilibrium witha third, then they are in thermal equilibrium withone another.

    The zeroth law of thermodynamics:

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    If the third body is a thermometer, we can

    measure the temperature of each body andthen say they are in thermal equilibriumwithout actually doing it.

    What is temperature? A measure of themotion of the atoms in a body. http://www.colorado.edu/physics/2000/bec

    /

    How do we measure it? For example,by measuring the volume expansion of mercury in a glass tube, which issensitive to temperature .

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    Temperature and Thermal Equilibrium

    Thermal reservoir: system so large that itstemperature doesnt change when interacting with

    other systems

    Thermal contact can occur through conduction,convection, and radiation

    The zeroth law of thermodynamics (cont):

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    How do you calibrate your thermometer?

    By international agreement the triple point of water has been assigned the value of 273.16 K.

    This is called the Kelvin scale or absolute scale. Celsius scale Fahrenheit scale

    T C ! T 273.15 K ! 0 .0 1oC

    T

    F !

    9

    5T

    C 32 ! 32. 0 2o F

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    Coefficient of Linear expansionSubstance E (10 -6/C)

    Ice at 0 deg C 51

    Aluminum 23

    Brass 1 9

    Copper 17

    Steel 11

    Glass (pyrex) 3. 2

    ( L ! LE( T

    L

    L+ ( L

    Heat up rod fromT1 to T 2. ( T=T 1- T2

    All dimensions increase bythe fraction below:( L L

    ! E( T

    Bimetalic metal strip :Use to measure temperature.( V

    V ! 3E( T

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    9) A circular hole in an aluminum plate is 2.725 cmin diameter (D) at 1 0 .0 C. What is the change in its

    diameter when the temperature of the plate is raisedto 11 0 .0 C?

    D

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    Linear Expansion demos

    Thermal expansion Ring and ballThermal expansion cracking the nut.Thermal effects using liquid nitrogen

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    What is heat? What is heat? Heat is energy transferred from one object to

    another due to a temperature difference. This thermalenergy is internal energy consisting of kinetic and potentialenergy of the atoms and molecules that make up the object.

    The symbol for heat is Q. It is positive when it istransferred to the system of interest. Heat is energy that istransferred between systems

    A system or object does not contain heat. You can not sayan object has 1 00 Joules of heat or 1 00 Joules of work.Heat is not a property of the system like temperature,

    pressure or volume.

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    The property that measures a substance abilityto transfer heat is called specific heat c.

    The sp ecific heat determine d f or a sol id o r liquid d e pen dssl ight ly on the tem perature, an d us ua lly a ss ume s it is mea s ure dat cons tant pre ss ure (us ua lly atm osp heric), an d cons tant volume. It turn s o ut the sp ecific heat f or sol ids an d liquids do e snot ver y much. Only a few per cent. Fo r ga s e s , howe ver, it can var y a lot with pre ss ure an d vol ume a s yo u will see.

    The unit s o f sp ecific heat are Jo ule s p er kg per K

    c ! Qm( T

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    Specific Heat = c

    Heat up paper cup of water.

    Specific Heats c at RoomTemperature

    Substance Joules/kg/K lead 128

    copper 386

    aluminum 900

    glass 84 0

    water 41 90

    Example: What is the amount of heat Q absorbed to raise the temperature of 1 00 gramsof water from 2 0 C to 1 00 C (and not evaporate it)?Q = 41 90 J/kg/K x (8 0 K)x 0 .1 kg = 3352 0 J = 33.52 0 KJ

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    When a solid or liquid absorbs energy as heat, a phasechange may occur such as a solid to liquid (melting)or liquidto vapor (boiling)or vice versa. The required heat is calledHeat of Fusion and Heat of Vaporization, respectively.

    Heat of Fusion

    Ice to water at the same T and vice versa.System absorbs/releases energy.

    Heat of Vaporization Liquid water to water vapor at same T and vice versa.

    System absorbs/releases energy.

    L F ! 333 kJ / kg

    LV ! 2256 kJ / kg

    To evaporate 1 00 grams of water at 1 00 C would require

    Q = mL v=0 .100 kg x 2256 kJ/kg = 225.6 kJ

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    Specific heat for water =1 cal/g .C

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    Heat Transfer Mechanism: Conduction, Convection,and Radiation

    Conduction Through solid slabs

    (poker to handle)- Carried by conduction

    electrons Pcond = Q / t (energy/time)

    k is called the thermal conductivity

    Substance k (W/m . K)

    Stainless steel 14

    aluminum 235

    copper 4 0 1

    Polyurethane foam 0 .0 24

    air 0 .0 26

    Demo: heat up rods. What order willthe wads of putty fall off?

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    Conduction thru one slab in a steady state

    51) Consider the slab shown above. Suppose that L = 26. 0 cm, A =9 1.0 cm2, and the material is copper. If T H = 1 0 4 C, T C = 12. 0 C,and a steady state is reached, find the conduction rate through theslab.

    Q

    t !

    kA(T H T C ) L

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    Conduction thru two slabs in a steady state

    We want to know the conduction rate from T H to T C during steady state

    Rate through each slab are equal in steady state.

    P cond

    ! k 1 A (T x T C ) L1

    ! k 2 A (T H T x ) L2

    P cond

    !A (T H T C )

    L1k 1

    L2k 2

    P cond

    !A (T H T C )

    L1k 1

    L2k 2

    L3k 3

    Three slabs

    Two slabs

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    Heat Conduction

    Copper rod k = 4 0 1 W/m . K Aluminum rod k = 235 W/m . K Steel rod k = 14 W/m . K

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    Convection Convection and Buoyancy

    Works because when a fluid such as air or water is

    heated its density decreases. The unheated fluid belowit pushes it up through a buoyant force because thelower colder air, for example is more dense. The heatedair from a candle flame or hot stove rises because of this.

    Requires a medium

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    B lackbody Radiation

    Objects that become sufficiently hot will glowvisibly; as they get hotter they go from red, toyellow, to a bluish white.

    This is electromagnetic radiation; objects at anytemperature will emit it at various frequencies,from radio waves all the way to gamma rays.

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    B lackbody Radiation

    This radiation from a body in thermal equilibriumis called blackbody radiation, as it is purelythermal and doesnt depend on any properties of the body other than its temperature and area.

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    RadiationN o medium is needed for E/M waves. Called thermalradiation or blackbody radiation

    Wis the Stefan Boltzman constant = 5.603 x 10 -8 W/m 2 .K 4

    e is the emissivity between 0 and 1, e=1 means perfectemitter

    Units are WattsA good emitter is a good absorber

    P ra d ! W I A T 4

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    B lackbody RadiationDeriving the energy density as a function of

    frequency and temperature required introducingsome new concepts:

    Here, c is the speed of light:

    And h is Plancks constant:

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    B lackbody RadiationThe Discovery and Measurement of the B ackground

    Radiation of the Universe

    In 1964, background radiation was discovered, comingfrom no particular source but having a blackbodyfrequency distribution corresponding to a temperature

    of about 3K.This radiation is left over from the early days of theuniverse.

    At first, matter and radiation were in thermal equilibrium;

    as the universe cooled this was no longer true.The blackbody radiation is the remnant of the frozen-outradiation, cooled to near absolute zero by the expansion

    of the universe.

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    B lackbody Radiation

    This is the observed

    blackbody radiation dataas well as the distributionfor T = 2.735K. The error bars on the data points are

    smaller than the pointsthemselves.

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    Electromagnetic spectrum of a

    black body

    Note curve peaksat Infrared at 25 00 C

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    Radiation related demos Light The Match

    light from a filament focused on a match

    Leslie Cubes compare IR radiation emitted for black surface,

    white, gray, shiny

    Radiometer Works in reverse. Really demonstrates that hot gasconsist of fast moving molecules transferring energy tothe vanes

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    First Law of ThermodynamicsConservation of energy

    E int is the internal energy of the system Q is the heat flow

    W is the work

    Significance is that that Q - W is path independent. Thatis it only depends on the initial and final states. Similar toconservation of energy. Found experimentally.

    Q and W are path dependent. Also Q+W and Q-2W.

    The first law extends the conservation of energy to

    systems that include heat and work done by the system.

    ( E int

    ! Q W

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    18-1 Changes in Thermal Systems

    Change where system is always in thermalequilibrium: reversible process

    Change where system is not always in thermalequilibrium: irreversible process

    Examples of irreversible processes:Free expansion

    melting of ice in warmer liquid

    frictional heating

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    18-1 Changes in Thermal Systems

    Example of a Reversible Process:

    Cylinder must be pulled or pushed slowlyenough that the system remains in thermalequilibrium

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    18-1 Changes in Thermal Systems

    Example of an Irreversible Process:

    The gas expands freely when the valve isopened.

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    Work and Heat Consider a system

    consisting of a gas and a piston in the figure.

    Lead shot rest on the piston and is part of theenvironment.

    The bottom of the cylinder rest on a thermal reservoir that we can use to controlthe temperature with a

    knob. The system is insulatedfrom everything else.

    d W ! F .ds ! p A.ds ! pd V

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    Shaded area is the work done by the system

    p depends on V in general

    Below are many ways to take the system from i to f.The work W done and Q depends on the path.

    W ! dV V i

    V f

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    43) A sample of gas expands from 1. 0 m3 to 4. 0 m3

    while its pressure decreases from 4 0 Pa to 1 0 Pa.How much work is done by the gas if its pressurechanges with volume via each of the three pathsshown in the Figure below?

    1.0 4.01

    0

    40 Path A: W = +12 0 JPath B: W =+75 JPath C: W =+3 0 J

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    Problem 42)

    Fill in the table +, _, or 0 for Q,W and ( E int for each path.

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    Heating Effects Demo

    Cooling coke can cause pressure reduction inside.Atmosphere crushes the can as it is placed upside

    down in water.

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    Special Cases of the First Law

    Adiabatic process

    Constant - volume process

    Cyclical process

    Free expansion

    (gas is not in equilibrium during expansion)

    Q! 0

    ( E ! W

    W ! 0

    ( E ! Q

    ( E ! 0

    Q!

    W

    Q ! W ! 0

    ( E ! 0

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    Which is the largest unit: oneCelsius degree, one Kelvindegree, or one Fahrenheit

    degree?

    1) one Celsius degree

    2) one Kelvin degree3) one Fahrenheit degree4) both one Celsius degree and

    one Kelvin degree

    5) both one Fahrenheit degreeand one Celsius degree

    ConcepTest 17.1 D egree s

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    Which is the largest unit: oneCelsius degree, one Kelvindegree, or one Fahrenheit

    degree?

    1) one Celsius degree

    2) one Kelvin degree3) one Fahrenheit degree4) both one Celsius degree and

    one Kelvin degree5) both one Fahrenheit degree

    and one Celsius degree

    The Celsius degree and the Kelvin degree are the same size. The

    scales only differ by an offset, not by the size of the degree unit. For

    Fahrenheit, there are 180 degrees between boiling and freezing(212F32F). For Celsius, there are 100 degrees between the same

    points, so the Celsius (and Kelvin) degrees must be larger.

    ConcepTest 17.1 D egree s

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    You may notice that if a

    mercury-in-glass thermometer is inserted into a hot liquid, themercury column first drops,and then later starts to rise (asyou expect). How do you

    explain this drop?

    1) the mercury contracts before theglass contracts

    2) the glass contracts before themercury contracts3) the mercury contracts before the

    glass expands4) the glass expands before the

    mercury expands5) the mercury expands before the

    glass contracts

    The hot liquid touches the glass first, so initially the glass

    expands slightly. This increases the volume inside the glass,and so the mercury level drops slightly. Once the mercuryheats up, it begins to expand and then the characteristic risein the mercury column follows, indicating the increase intemperature that you expected to measure.

    ConcepTest 17.3 Therm ometer s

    FollowFollow- -up:up: Is it possible to have the mercury first rise and later drop?Is it possible to have the mercury first rise and later drop?

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    A steel tape measure ismarked such that it givesaccurate length measurementsat room temperature. If thetape measure is used outsideon a very hot day, how will its

    length measurements beaffected?

    1) measured lengths will be too small

    2) measured lengths will still be accurate

    3) measured lengths will be too big

    ConcepTest 17.5a S tee l Exp an s ion I

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    A steel tape measure ismarked such that it givesaccurate length measurementsat room temperature. If thetape measure is used outsideon a very hot day, how will its

    length measurements beaffected?

    1) measured lengths will be too small

    2) measured lengths will still be accurate

    3) measured lengths will be too big

    The tape measure will expand, so its markings will spread outfarther than the correct amount. When it is laid down next to anobject of fixed length, you will read too few markings for that givenlength, so the measured length will be too small.

    ConcepTest 17.5a S tee l Exp an s ion I

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    ConcepTest 17.9b Idea l Ga s L aw II

    1) cylinder A

    2) cylinder B

    3) both the same

    4) it depends on the

    pressure P

    Two identical cylinders at the same

    pressure contain the same gas. If Acontains three times as much gas as B ,

    which cylinder has the higher

    temperature ?

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    Ideal gas law: PV PV = = nRT nRT

    Solve for pressure: P P == nRT / V nRT / V

    For constant V and T , the one with more

    gas ( the larger value of the larger value of nn ) has the

    higher pressure P .

    ConcepTest 17.9a Idea l Ga s L aw I

    1) cylinder A

    2) cylinder B

    3) both the same

    4) it depends on temp. T

    Two identical cylinders at the same

    temperature contain the same gas. If Acontains three times as much gas as B ,

    which cylinder has the higher pressure ?

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    ConcepTest 17.10 S od a Bo ttle

    1) it expands and may burst

    2) it does not change3) it contracts and the sides collapse

    inward

    4) it is too dark in the fridge to tell

    A plastic soda bottle is emptyand sits out in the sun, heatingthe air inside. N ow you put thecap on tightly and put the bottlein the fridge. What happens tothe bottle as it cools?

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    ConcepTest 17.11 Ba lloon in Freezer

    1) it increases

    2) it does not change

    3) it decreases

    What happens to the volume of a

    balloon if you put it in the freezer?

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    According to the Ideal Gas Law, when the temperature iswhen the temperature is

    reduced at constant pressurereduced at constant pressure , the volume is reducedvolume is reduced as well.

    The volume of the balloon therefore decreases.

    ConcepTest 17.11 Ba lloon in Freezer

    nRT PV !

    1) it increases

    2) it does not change

    3) it decreases

    What happens to the volume of a

    balloon if you put it in the

    freezer?

    FollowFollow- -up:up: What happens to the volumeWhat happens to the volume

    h th b ll i i th i ?h th b ll i i th i ?