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  • 7/27/2019 Carnot's Theorem

    1/12

    Tc

    Th

    heat pump

    Tc

    Th

    heat engine

    Carnots Theorem

    We introduced already the Carnot cycle with an ideal gas

    Now we show:1 Energy efficiency of the Carnot cycle is independent of the working substance

    2 Any cyclic process that absorbs heat at one temperature, and rejects heat at

    one other temperature, and is reversible has the energy efficiency of a Carnot

    cycle

    W

    hQ

    cQ

    W

    WQQ ch

    cQ

    W

    QhP

    reversibleRemark:

    Note:P>1

    Textbook:

    coefficient

    of performance

  • 7/27/2019 Carnot's Theorem

    2/12

    Tc

    Thheat engine X

    XW

    XhQ

    XcQ

    Lets combine a fictitious heat engine X with CX with a heat pumprealized by a reversed Carnot cycle

    Tc

    Thheat pump

    ChQ

    CcQ

    X C

    CW

    CX

    WWW

    We can design the engine X such that CcXc QQ

    Lets calculate XWXhQ

    XcQ with X

    h

    XX

    Q

    W

    X

    XXh

    WQ

    XWXcQ

    X

    XW

    XW

    X

    cX

    X Q1

  • 7/27/2019 Carnot's Theorem

    3/12

    If X would be a Carnot engine it would produce the work CWXc

    C

    C Q1

    with CX XWXc

    X

    X Q1

    > CW

    Xc

    C

    C Q1

    T

    c

    Thheat engine X

    XW

    XhQ

    XcQ T

    c

    Thheat

    pumpChQ

    CcQ

    X C

    CW

    CX WWW

    We can design the engine X such thatCc

    Xc QQ

    However:

    CX WWW >0

    0.0 0.2 0.4 0.6 0.8 1.00

    2

    4

    6

    8

    10

    2

    10

    1 1

    d

    d

    X/(1-X)

    /(1

    -)

    C X


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