Phys2 Ch2 Heat Temp Law0

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    PROGRAM OF PHYSICSLecturer:Dr. DO Xuan Hoi

    Room 413

    E-mail : [email protected]

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    PHYSICS 2(FLUID MECHANICS AND THERMAL PHYSICS)

    02 credits (30 periods)

    Chapter 1 Fluid Mechanics

    Chapter 2 Heat, Temperature and the Zeroth

    Law of Thermodynamics

    Chapter 3 Heat, Work and the First Law of

    Thermodynamics

    Chapter 4 The Kinetic Theory of Gases

    Chapter 5 Entropy and the Second Law of

    Thermodynamics

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    References :

    Halliday D., Resnick R. and Walker, J. (2005),Fundamentals of Physics, Extended seventh edition.John Willey and Sons, Inc.

    Alonso M. and Finn E.J. (1992). Physics, Addison-WesleyPublishing Company

    Hecht, E. (2000). Physics. Calculus, Second Edition.Brooks/Cole.

    Faughn/Serway (2006), Serways College Physics,Brooks/Cole.

    Roger Muncaster (1994), A-Level Physics, StanleyThornes.

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    http://ocw.mit.edu/OcwWeb/Physics/index.htmhttp://www.opensourcephysics.org/index.html

    http://hyperphysics.phy-

    astr.gsu.edu/hbase/HFrame.htmlhttp://www.practicalphysics.org/go/Default.ht

    ml

    http://www.msm.cam.ac.uk/

    http://www.iop.org/index.html...

    http://www.opensourcephysics.org/index.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.htmlhttp://www.practicalphysics.org/go/Default.htmlhttp://www.practicalphysics.org/go/Default.htmlhttp://www.msm.cam.ac.uk/http://www.iop.org/index.htmlhttp://www.iop.org/index.htmlhttp://www.msm.cam.ac.uk/http://www.practicalphysics.org/go/Default.htmlhttp://www.practicalphysics.org/go/Default.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.htmlhttp://www.opensourcephysics.org/index.html
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    CHAPTER 2

    Heat, Temperature and the Zeroth

    Law ofThermodynamics

    Temperature and the ZerothLaw of

    ThermodynamicsThermal Expansion (of Solids and Liquids)

    Heat and the Absorption of Heat by Solidsand Liquids

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    1. Temperature and the ZerothLaw of

    Thermodynamics

    What is HEAT ?

    Heat is the transfer of energyfrom one object to another

    object as a result of a difference in temperaturebetween

    the two.Two objects are in thermal contactwith each other if

    energy can be exchanged between them

    Thermal equilibriumis a situation in which two objects inthermal contact with each other cease to exchange energy

    by the process of heat.

    These two objects have the same temperature

    1.1 Notions

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    Heat is the energy transferred between a

    system and its environment because of atemperature difference that exists betweenthem.

    Units: 1 cal = 4.1868 J

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    A C

    thermal

    equilibrium

    BC

    thermal

    equilibrium

    AB?thermal

    equilibrium

    1.2 The zerothlaw of thermodynamics

    (the law of equilibrium) : If objects A and B are separately in thermal equilibriumwith a third object C, then objects A and B are in thermalequilibrium with each other

    thermometer

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    If objects A and B are separately in thermalequilibrium with a third object C, then A andB are in thermal equilibrium with each other.

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    1.3 Temperature Scales

    Thermometers can be calibrated by placing them inthermal contact with an environment that remains atconstant temperature

    Environment could be mixture of ice and water inthermal equilibrium

    Also commonly used is water and steam in thermalequilibrium

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    Comparing Temperature Scales

    273.15

    9325

    9

    5

    C K

    F C

    F C

    T T

    T T

    T T

    =

    = +

    =

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    TEST 1

    What is the physical significance of the factor 9/5 in

    Equation 9 325

    F CT T= +

    SOLUTION100 0 232 32 ;C C F F T T T T = 100 180C FT T=

    180 91 ;100 5

    C F FT T T= =

    32 ;F FT T = 0C CT T =

    915

    C FT T=

    1;

    9 /5F C

    F C

    F

    T TT T

    T

    =

    5

    9F CT T =

    5( 32) 0 ;

    9F CT T =

    932

    5F CT T= +

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    PROBLEM 1

    A healthy person has an oral temperature of 98.6 F. Whatwould this reading be on the Celcius scale?

    SOLUTION

    32 98.6 32 66.6F FT T F F F = = =

    9

    5 F CT T

    66.6 166.6

    9 /5

    F CF

    F

    37.0 CC T= =

    37.0 0C CT T=

    37.0CT C=

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    PROBLEM 2

    A time and temperature sign on a bank indicates the outdoortemperature is -20.0C. Find the corresponding temperature onthe Fahrenheit scale.

    SOLUTION9

    1 5C FT T

    20.0 9 /520.0

    1

    C FC

    C

    36.0 FF T= =

    36.0 32FF T F =

    4.0FT F=

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    PROBLEM 3

    On a day when the temperature reaches 50F, what is thetemperature in degrees Celsius and in kelvins?

    SOLUTION

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    PROBLEM 4

    A pan of water is heated from 25C to 80C. What is thechange in its temperature on the Kelvin scale and on theFahrenheit scale?

    SOLUTION

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    2. Thermal expansion of solids

    Thermalexpansion

    Joints are used to

    separate sections of

    roadways on bridges

    2.1 Notions

    Thermal expansionis a consequence of thechange in the average separation betweenthe constituent atoms in an object

    0

    10A

    0

    11A

    0

    10A>

    0

    11A>

    As the temperature of the solid increases, the atoms oscillate withgreater amplitudes the average separation between themincreases the object expands.

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    2.2 Average coefficient of linear expansion

    Li:initial length along some direction at some temperature Ti

    L : amount of the increase in lengthT :change in temperature

    The average coefficient of linear expansionis defined :

    / iL LT

    = f i iL L L L T

    The change in length of an object is proportional to thechange in temperature

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    2.3 Average coefficient of volume expansion

    Vi:initial volumeat some temperature

    TiV : amount of the increase in volumeT :change in temperature

    The average coefficient of volume expansionis defined :

    / iV VT

    = f i iV V V V T

    Relationship between and ?

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    Consider a box of dimensions l, w, and h.Its volume at some temperature Ti is Vi= lwh

    If the temperature changes to Ti+ T ,its volume changes to Vi+ V ,where each dimensionchanges according to :

    ( )( )( )iV V l l w w h h + = + + +

    Relationship between and

    i f iL L L L T =

    ( )( )( )l l T w w T h h T = + + + 3(1 )lwh T = + 2 31 3 3( ) ( )

    iV T T T = + + +

    Because for typical values of T < 100C, T

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    The change in areaAi

    of a rectangular platewhen the temperature change an amount of Tis

    TEST

    A. A = AiT

    B.

    A = 2

    AiTC. A = 3AiT

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    Principle of a thermostats:b im eta l l i c s t r ip

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    A steel railroad track has a length of 30.000 m

    when the temperature is 0.0C.

    (a)What is its length when the temperature is 40.0C?

    SOLUTION

    The increase in length(a)

    PROBLEM 5

    iL L T = 6 111 10 ( ) (30000 )(40.0 )o oC m C =

    The length of the track at 40.0C :

    0.013 m=

    0.013 30.013f iL L m m = + =

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    A steel railroad track has a length of 30.000 mwhen the temperature is 0.0C.(a)What is its length when the temperature is 40.0C?

    (b)Suppose that the ends of the rail are rigidly clampedat 0.0C so that expansion is prevented. What is the thermalstress set up in the rail if its temperature is raised to 40.0C?Knowing that the Youngs modulus for steel : 20 1010 N/m2.

    SOLUTION (b)

    PROBLEM 5

    /

    / i

    F AY

    L L=

    stress

    Thermal stress : /i

    LF A Y

    L

    =

    10 7 20.013(20 10 / ) 8.7 10 /

    30.000

    F mN m N m

    A m

    = =

    Youngs modulus:measuresthe resistance of a solid to a changein its length :

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    A glass flask with volume 200 cm3is filled tothe brim with mercury at 20oC. How much mercury overflowswhen the temperature of the system is raised to 1OOC? The

    coefficient of linear expansion of the glass is 0.40 1O-5

    K-1

    .SOLUTION

    PROBLEM 6

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    A metal rod is 40.125 cm long at 20.0oC and

    40.148 cm long at 45.0C. Calculate the average coefficient of

    linear expansion of the rod for this temperature range.

    SOLUTION

    PROBLEM 7

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    A glass flask whose volume is 1000.00 cm3at0.0oC is completely filled with mercury at this temperature.When flask and mercury are warmed to 55.OoC, 8.95 cm3of

    mercury overflow. If the coefficient of volume expansion ofmercury is 18.0 x 10-5K-1, compute the coefficient of volumeexpansion of the glass.

    SOLUTION

    PROBLEM 8

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    3. Heat and the Absorption of Heat by Solidsand

    Liquids

    3.1 The specific heatThe heat capacity of a particular sample of asubstance is defined as the amount of energyneeded toraise the temperature of that sample by 1C.

    If heat Q produces a change T in the temperature ofa substance :

    Q C T=

    J/0

    CThe specific heat c of a substance is the heat capacityper unit mass

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    If energy Q transferredby heat to mass m of asubstance changes thetemperature of the sample byT, then the specific heat ofthe substance:

    Qc

    m T

    =

    J/kg.0C

    Q mc T =

    N.B.: if c varies with temperature

    over the interval (Ti , Tf) :f

    i

    T

    T

    Q m cdT =

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    Consequences of Different Specific Heats

    Water has a highspecific heat comparedto land

    On a hot day, the airabove the land warmsfaster

    The warmer air flows

    upward and cooler airmoves toward thebeach

    CkgJc

    CkgJc

    OH

    Si

    4186

    700

    2 =

    =What happens at night?

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    A 0.050 0-kg ingot of metal is heated to

    200.0C and then dropped into a beaker containing 0.400 kg

    of water initially at 20.0C.

    (a)If the final equilibrium temperature of the mixed system is22.4C, find the specific heat of the metal.

    SOLUTION

    Conservation of energy : The energy leaving the hotpart of the system by heat is equal to that entering thecold part of the system

    (a)

    PROBLEM 9

    cold hot Q Q=

    The energy transfer for the water : ( ) ( 0)w w f w m c T T >The energy transfer for the sample of unknown specific heat :

    ( ) ( 0)x x f x m c T T