CML100 Physical Lectures I II

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Thermodynamics

Transcript of CML100 Physical Lectures I II

  • 28-Jul-15 5

    Thermodynamics Variables: , P, T, V, M, E, S, Avogadro number of particles, NA=6.023 X 10

    23

    Thermodynamic Limit: N , V

    In Statistical Thermodynamics, we do care about the molecular details, establish connection between molecular details (microscopic states) and macroscopic properties.

    In Thermodynamics, we talk only about Macroscopic properties, dont pay attention to molecular details of the system

    Thermodynamic Equilibrium State: A state at which macroscopic properties stop changing

  • System: A system is the part of the world in which we are interested.

    System

    Surroundings

    Boundary or wall

    System

    Boundary or wall

    Surroundings Surroundings

    Surroundings

    Surroundings: the rest is surrounding.

    SYSTEM AND SURROUNDING

    Boundary could be real, imaginary; thermally conducting, insulating, rigid, flexible, permeating, non-permeating etc.

  • Surroundings

    OpenSurroundings

    Surroundings

    Closed System

    IsolatedSystem

  • Diathermal /Adiabatic Walls

    Adiabatic Container

    Endothermic

    Exothermic

    Diathermal Container

  • Open ~IsolatedClosed

    System is Coffee

  • 28-Jul-15 10

    Suppose an object A (which we can think of as a block of iron) is in thermal equilibrium with an object B (a block of copper), and that B is also in thermal equilibrium with another object C (a ask of water). Then it has been found experimentally that A and C will also be in thermal equilibrium when they are put in contact. This observation is summarized by the Zeroth Law of thermodynamics as:

    If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then C is also in thermal equilibrium with A. The Zeroth Law justies the concept of temperature and the use of a thermometer, a device for measuring the temperature.

    Zeroth Law of Thermodynamics and Thermal Equilibrium

    If TA=TB and TB=TC, then TC=TA

    To achieve thermal equilibrium the objects have to be in contact through a diathermic boundary

  • First Law of Thermodynamics, Internal Energy, Enthalpy, and Heat Capacities

  • First Law of Thermodynamics

    The internal energy of an isolated system is constant (or conserved).

    U=Constant

    SSYSTEM

    U

    SURROUNDINGS

    ADIABATIC/INSULATING WALL

    SUR

    RO

    UN

    DIN

    GS

    SUR

    RO

    UN

    DIN

    GS

    SURROUNDINGS

    Isolated system

    ADIABATIC/INSULATING WALL

    System: GAS, LIQUID, SOLID,

    for Isolated system

  • wqUSys ddd

    Supply heat

    Do someWork

    To change the energy of the system by amount dU:

    SSYSTEM

    U

    SURROUNDINGS

    ADIABATIC WALL AD

    IAB

    ATIC

    WA

    LL

    AD

    IAB

    ATI

    C W

    ALL

    ADIABATIC WALL

    SUR

    RO

    UN

    DIN

    GS

    SUR

    RO

    UN

    DIN

    GS

    SURROUNDINGS

    wd qd and/orS

    SYSTEMU+dU

    SURROUNDINGS

    ADIABATIC WALL AD

    IAB

    ATIC

    WA

    LL

    ADIABATIC WALL

    SUR

    RO

    UN

    DIN

    GS

    SURROUNDINGS

    It has been found experimentally that the internal energy of a system may be changed either by doing work on the system or by heating it.

    Heat and work are equivalent ways of changing a systems internal energy.

  • SSYSTEMU+dUdU >0

    SURROUNDINGS

    ADIABATIC WALL AD

    IAB

    ATIC

    WA

    LL

    ADIABATIC WALL

    SUR

    RO

    UN

    DIN

    GS

    SURROUNDINGSSSYSTEM

    U

    SURROUNDINGS

    ADIABATIC WALL AD

    IAB

    ATIC

    WA

    LL

    AD

    IAB

    ATI

    C W

    ALL

    ADIABATIC WALL

    SUR

    RO

    UN

    DIN

    GS

    SUR

    RO

    UN

    DIN

    GS

    SURROUNDINGSS

    SYSTEMU+dUdU >0

    ADIABATIC WALL AD

    IAB

    ATIC

    WA

    LL

    ADIABATIC WALL

    SUR

    RO

    UN

    DIN

    GS

    SURROUNDINGS

    Dia

    the

    rmal

    Wal

    l

    wd

    dq

  • If energy of the system increases, then U is +ve

    If energy of the system decreases, then U is -ve

    If work is done on the system, then w is +ve

    If work is done by the system, then w is ve

    If heat is supplied to the system, then q is +ve

    If heat is liberated by the system, then q is -ve

    WORK

    HEAT

    WORK

    HEAT

    ENERGY, U

    w < 0

    w > 0

    q < 0

    q > 0

    The Sign Convention

  • i.e. internal energy plus the surrounding energy is also conserved.

    wq dddUSys

    Supply heat Do some Work

    Work done or heat supplied is by the surroundings, so

    )dd(dUSurr wq

    0dUdU SurrSys

    ConstantUU SurrSys

    Different forms of FirstLaw of Thermodynamics

    ConstantUUniverse Universe is an isolated system

  • wqU ddd Sys Differential form of First Law

    Function)(Path d

    Function)(Path - d

    function) state is (U dU

    12

    2

    1

    12

    2

    1

    12

    2

    1

    Sys

    -wwww

    qqqq

    UUU

    wqU Sys

    Integrated form of First Law

    Exact Inexact Inexact

    2

    1

    2

    1

    2

    1

    Sys ddd wqU

    Total change in internal energy when the system goes from state 1 to 2 is

  • Thermodynamic Variables

    State Function Path Function

    PATH 1

    State A State B

    System System

    321 www (UB-UA)1= (UB-UA)2= (UB-UA)3

    PA, VA, TA, nAPB, VB, TB, nB

    PATH 2

    PATH 3

    For fixed number of moles: nA=nB

    Depends on how the process has been carried out from one

    state to another. Example: Work

    Depends on the states (initial and final), does matter

    how those states have been attained. Example:

    Internal Energy

  • Between two states the change in a state variable is always the same regardless of the

    path the system travels.

    Differential of a state function is called exact differential, df in this case.

    fffdf AB

    AB

    A

    B

    AB fffd Differential of a path function is called inexact differential, df in this case.

    Exact Differential and State Function:

    Inexact Differential and Path Function:

    df=Infinitesimal change in f

    f=Macroscopic change in f

    A

    D

    C

    B

    B

    A

    fdfdfdfdf 0... Cyclic Integral is zero for state function

    A

    D

    C

    B

    B

    A

    fdfdfdfd ... will depend on the path

  • xa xb

    yb

    ya a

    bExamples: (i)dz=ydx

    (ii)dz=ydx+xdy

    AREA I

    AREA II

    b

    a

    b

    a

    ydxdz I Area

    II AreaI Area)( b

    a

    b

    a

    xdyydxdz

    AREA I and AREA II are path dependentAREA I+AREA II is not path dependent i.e. the sum of these areas is independent of the shape of the curve (path).

  • Test to know about exact and inexact differentials

    dyyxNdxyxMdz ),(),(

    dyy

    zdx

    x

    zdz

    xy

    yx

    zyxM

    ),(

    xy

    zyxN

    ),(

    yxxyy

    z

    xx

    z

    y

    yxx

    N

    y

    M

    Exact or not ??Examples: (i)dz=ydx

    (ii)dz=ydx+xdy

    Consider, as if dz was exact then

    As mixed partial derivatives are equal

    (1)

    (2)

    Comparing (1) and (2),

    Then has to be satisfied if dz in Eq. 1 is exact.

    Eulers Criteria for exactness

    and

  • o Inexact differentials can be made exact by multiplication of integrating factor.dq is inexact but dq/T is exact!

    o Sum of two inexact differentials can be an exact differential.dz=ydx+xdy is exact but ydx and xdy are inexact differentials.

  • ENERGY, WORK, AND HEAT

    Work and Heat are two forms of energy transfer

    Mechanical

    Electrical

    Thermal

    Energy (U) is State Function Heat (q) and Work(w) Both are Path Functions, not state functions

    UUUdU AB

    AB

    A

    B

    AB wwdw

    A

    B

    AB qqdq

  • coordinatereaction

    theoft independen ;)( FF

    Work done GeneralizedForce

    GeneralizedReaction Coordinate

    )(2

    1

    2

    1

    FdFwdw

    Generalized Work

    Examples:

  • dQfdLddVPqdU ext d

    When volume expansion, surface expansion, elongation or electrical work are involved, first law can be written as

    2

    1

    2

    1

    2

    1

    2

    1

    2

    1

    dQfdLddVPqdUU ext

  • Reversible and Irreversible Process

    fA fA +df fA +2df fA +3df fB

    fA fA +df fA +2df fA +3df fB

    Reversible Process: Changes in the system are brought in infinitesimal amount step by step, so that the system can adjust the changes.

  • Isothermal Reversible P-V Work for Compression

    A reversible change in thermodynamics is a change that can be reversed by an infinitesimal modification of a

    variable.

    PPP Gasex

    External pressure is changed by infinitesimal amount that at every step the pressure exerted by the gas is equal to external pressure i.e. at each step one ensures mechanical equilibrium

    S

    DIATHERMAL

    SUR

    RO

    UN

    DIN

    GS

    M

    L

    S

    DIATHERMAL

    M

    L

    m S

    DIATHERMAL

    SUR

    RO

    UN

    DIN

    GS

    M

    L

    m

    2/ LMgPex 2/)( LgmMPex

    2/)2( LgmMPex

    m

    GAS GASGAS

    Reversible and Irreversible Process

  • PPP Gasex

    S

    DIATHERMAL

    SUR

    RO

    UN

    DIN

    GS

    M

    L

    S

    DIA

    THER

    MA

    LDIATHERMAL

    SUR

    RO

    UN

    DIN

    GS

    M

    L

    2/ LMgPP exi 2/)( LgMMPP exf

    GAS GAS

    M

    Isothermal Irreversible Compression against Constant External Pressure

    VPVVPdVPw exifex

    V

    V

    ex

    f

    i

    )(

    )( if VVV

    Vf ,T

    Vi ,T

    Vf Vi

    P

    V

    Pf

    Pi

    Pex

    irrevifexirrev AreaVVPw )(

    Areairrev

    Reversible and Irreversible Process

  • When a piston of area A moves out through a distance dz, it sweeps out a volume

    The work required to move an object a distance dz against an opposing force of magnitude F is

    dw=|F|dz

    |F|=Pex A

    dV=Adz

    The external pressure Pex is equivalent to a weight pressing on the piston, and the force opposing expansion is

    When the system expands through a distance dz against anexternal pressure Pex, it follows that the work done is

    dw=PexAdz=-PexdV Total work done when the volume changes from Vi to Vf

    f

    i

    V

    V

    exdVPw

    Pex

    P

    of the Piston

    Force (F) exertedby the piston

    |F| is the magnitude of force exerted by the pistonbecause of its mass, lets say.

    wqU ddd Sys

  • 2

    1

    d

    dVPqU

    dVPqdU

    ext

    ext

    First law for isothermal expansion

    First law for adiabatic process

    2

    1

    0d

    dVPU

    dVPdU

    q

    ext

    ext

    Change in Temperature of theSystem is expected in an adiabaticprocess

  • Supporting Slides

  • Work is a Path Function

    SS

  • Free Expansion or Expansion in Vacuum

    0 f

    i

    V

    V

    exdVPw0exP

    Expansion/Compression against Constant External Pressure

    VPVVPdVPw exifex

    V

    V

    ex

    f

    i

    )( )( if VVV

    veiswssionfor CompreVVV

    veiswionfor ExpansVVV

    if

    if

    0)(

    0)(

  • Vf Vi

    P

    V

    Pf

    Pi

    Pex

    Isothermal Reversible P-V Work for Compression

    rev

    V

    V

    exrev AreadVPwf

    i

    Arearev < Areairrev

    ArearevWork done on the gas in reversiblecompression is less than that in irreversiblecompression.

  • Adiabatic Process (Compression/Expansion)

    System

    Surroundings

    ADIABATIC

    AD

    IAB

    ATI

    C ADIA

    BA

    TIC

    ADIABATIC Adiabatic Wall (Isolated system)

    No heat is allowed to be transferred between System and Surroundings

    dq=0

    Change in Temperature of the System is expected. Pex=Pmechanical

    dVPwddUdU exSys

  • Adiabat and Isotherm

    T1

    T1

    T2

    System

    ADIABATIC

    AD

    IAB

    ATI

    C AD

    IAB

    ATIC

    ADIABATIC

    System

    ADIABATIC

    AD

    IAB

    ATIC A

    DIA

    BATIC

    ADIABATIC

    (P1, V1, T1) (P2, V2, T2)

    The P-V curve for reversible adiabatic process are steeper than those of isothermal process

    Adiabatic Cooling Adiabatic Heating