Lecture 3 – The First Law (Ch. 1)
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Lecture 3 – The First Law (Ch. 1) Friday January 11 th. Test of the clickers (HiTT remotes) I will not review the previous class Usually I will (certainly after Ch. 2) Internal energy The equivalence of work and heat The first law (conservation of energy) Functions of state

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Lecture 3 – The First Law (Ch. 1)

Friday January 11th

  • Test of the clickers (HiTT remotes)

  • I will not review the previous class

    • Usually I will (certainly after Ch. 2)

  • Internal energy

  • The equivalence of work and heat

  • The first law (conservation of energy)

  • Functions of state

  • Reversible work

  • Reading: All of chapter 1 (pages 1 - 23)

    1st homework set due next Friday (18th).

    Homework assignment available on web page.

    Assigned problems: 2, 6, 8, 10, 12


    Functions of state: internal energy U

    Adiabatic

    Joule’s paddle wheel

    experiment

    Work = -DUgrav

    W = -(-mgh)

    = mgh

    Measured as a change in temperature, q

    Gravitational energy is lost. 1st law is about conservation of energy. This energy goes into thermal (‘internal’) energy associated with the fluid.


    Functions of state: internal energy U

    Adiabatic

    Joule’s paddle wheel

    experiment

    DUfluid= W = mgh

    Measured as a change in temperature, q

    !!!!!!!!!!!!!!!!!!!!!!!

    Gravitational energy is lost. 1st law is about conservation of energy. This energy goes into thermal (‘internal’) energy associated with the fluid.


    Functions of state: internal energy U

    Stirring

    Adiabatic

    Rise in q

    (temperature)

    DU = W = torque × angular displacement = tdf


    Functions of state: internal energy U

    Electrical

    work

    Adiabatic

    Rise in q

    (temperature)

    R

    i

    DU = W = i2R


    Functions of state: internal energy U

    Reversible

    work

    Force, F

    Adiabatic

    Rise in q

    (temperature)

    DU = W = Force × distance = -PDV


    Equivalence of work and heat

    Heat, Q

    Adiabatic

    Same rise in q

    (temperature)

    DU = Q


    The First Law of Thermodynamics

    These ideas lead to the first law of thermodynamics (a fundamental postulate):

    DU = Q + W

    or

    dU = đQ+đW

    “The change in internal energy of a system is equal to the heat supplied plus the work done on the system. Energy is conserved if the heat is taken into account.”

    Note that đQand đW are notfunctions of state. However, dU is, i.e. the correct combination of đQ and đW which, by themselves are not functions of state, lead to the differential internal energy, dU, which is a function of state.


    How to know if quantity is a function of state

    Significant

    heat flows in

    How can U be state function, but not W?

    Heat is involved (not adiabatic).

    đQ + đW

    U1

    U2


    How to know if quantity is a function of state

    z

    dS

    y

    x

    dr

    There is a mathematical basis.....

    Consider the function F = f(x,y):


    How to know if quantity is a function of state

    In general, F is a state function if the differential dF is ‘exact’. dF (= Adx + Bdy) is exact if:

    • See also:

    • Appendix E

    • PHY3513 notes

    • Appendix A in Carter book

    • In thermodynamics, all state variables are by definition exact. However, differential work and heat are not.

    There is a mathematical basis.....

    Consider the function F = f(x,y):


    How to know if quantity is a function of state

    This is by no means true for any function!

    If integration does depend on path, then the differential is said to be ‘inexact’, i.e. it cannot be integrated unless a path is also specified. An example is the following:

    đF = ydx - xdy.

    Note: is a differential đF is inexact, this implies that it cannot be integrated to yield a function F.

    Differentials satisfying the following condition are said to be ‘exact’:

    This condition also guarantees that any integration of dF will not depend on the path of integration, i.e. only the limits of integration matter.


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