+ All Categories
Home > Documents > solution manual for fundamental thermodynamic sixth edition chapter 16

solution manual for fundamental thermodynamic sixth edition chapter 16

Date post: 30-May-2018
Category:
Upload: alfasel
View: 216 times
Download: 0 times
Share this document with a friend

of 68

Transcript
  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    1/68

    62/87,210$18$/

    6,81,7352%/(06

    &+$37(5

    FUNDAMENTALS

    ofThermodynamics

    Sixth Edition

    SONNTAG BORGNAKKE VAN WYLEN

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    2/68

    )XQGDPHQWDOVRI7KHUPRG\QDPLFVWK(GLWLRQ

    6RQQWDJ%RUJQDNNHDQGYDQ:\OHQ

    &217(17&+$37(5

    68%6(&7,21 352%12

    &RUUHVSRQGHQFHWDEOH

    6WXG\JXLGHSUREOHPV

    6WDJQDWLRQ3URSHUWLHV

    0RPHQWXP(TXDWLRQDQG)RUFHV

    $GLDEDWLF')ORZDQG9HORFLW\RI6RXQG

    5HYHUVLEOH)ORZ7KURXJKD1R]]OH

    1RUPDO6KRFNV 1R]]OHV'LIIXVHUVDQG2ULILFHV

    5HYLHZSUREOHPV

    3UREOHPVVROYHGZLWKWKH3UYUIXQFWLRQV

    (QJOLVKXQLWSUREOHPV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    3/68

    &+$37(5WKHG&255(6321'$1&(7$%/(

    1RWLFHWKDWPRVWRIWKHVROXWLRQVDUHGRQHXVLQJWKHFRPSXWHUWDEOHVZKLFK

    LQFOXGHVWKHVWHDPWDEOHVDLUWDEOHFRPSUHVVLEOHIORZWDEOHDQGWKHQRUPDOVKRFN

    WDEOH7KLVVLJQLILFDQWO\UHGXFHVWKHDPRXQWRIWLPHLWZLOOWDNHWRVROYHD

    SUREOHPVRWKLVVKRXOGEHFRQVLGHUHGLQSUREOHPDVVLJQPHQWVDQGH[DPV

    &KDQJHVRISUREOHPVIURPWKHWKHGLWLRQ&KDSWHUDUH

    3UREOHPVDUHDOOQHZ

    1HZ WK(G 1HZ

    WK(G 1HZ

    WK(G

    QHZ E

    QHZ

    QHZ

    QHZ QHZ

    QHZ

    QHZ

    D

    QHZ DE

    F

    DE

    QHZ F

    1HZ WK 6, 1HZ WK 6,

    ( (

    ( (

    ( (

    ( (

    ( (

    ( ( ( (

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    4/68

    &RQFHSW6WXG\*XLGH3UREOHPV

    ,VVWDJQDWLRQWHPSHUDWXUHDOZD\VKLJKHUWKDQIUHHVWUHDPWHPSHUDWXUH":K\"

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    5/68

    7KHMHWHQJLQHWKUXVWLVIRXQGIURPWKHRYHUDOOPRPHQWXPHTXDWLRQ:KHUHLVWKH

    DFWXDOIRUFHDFWLQJLWLVQRWDORQJUDQJHIRUFHLQWKHIORZ"

    7KHFRPSUHVVRULVJHQHUDWLQJWKHKLJKSUHVVXUHIORZVRWKHEODGHVSXVKHVKDUGRQWKHIORZDQGWKXVDIRUFHDFWVLQWKHIRUZDUGGLUHFWLRQRQWKHVKDIWKROGLQJ

    WKHURWDWLQJEODGHV7KHKLJKSUHVVXUHLQWKHFKDPEHUZLWKFRPEXVWLRQDOVRKDVD

    QHWIRUFHLQWKHIRUZDUGGLUHFWLRQDVWKHIORZOHDYHVLQWKHEDFNZDUGVGLUHFWLRQVR

    OHVVZDOODUHDWKHUH7KHSUHVVXUHGURSLQWKHWXUELQHPHDQVLWVEODGHVSXVKHVLQ

    WKHRWKHUGLUHFWLRQEXWDVWKHWXUELQHH[LWSUHVVXUHLVKLJKHUWKDQWKHDPELHQW

    SUHVVXUHWKHD[LDOIRUFHLVOHVVWKDQWKDWRIWKHFRPSUHVVRU

    +LJK3/RZ3

    cb

    +RZODUJHDIRUFHPXVWEHDSSOLHGWRDVTXLUWJXQWRKDYHNJVZDWHUIORZRXW

    DWPV":KDWSUHVVXUHLQVLGHWKHFKDPEHULVQHHGHG"

    )

    GPV

    GW P

    V

    NJPV

    1

    (TY3V

    3VY3DN3D

    %\ORRNLQJDW(TUDQNWKHVSHHGRIVRXQGIRUDVROLGDOLTXLGDQGDJDV

    6SHHGRIVRXQG 3 VF

    )RUDVROLGDQGOLTXLGSKDVHWKHGHQVLW\YDULHVRQO\VOLJKWO\ZLWK

    WHPSHUDWXUHDQGFRQVWDQWVLVDOVRQHDUO\FRQVWDQW7:HWKXVH[SHFWWKH

    GHULYDWLYHWREHYHU\KLJKWKDWLVZHQHHGYHU\ODUJHFKDQJHVLQ3WRJLYH

    VPDOOFKDQJHVLQGHQVLW\

    $JDVLVKLJKO\FRPSUHVVLEOHVRWKHIRUPXODUHGXFHVWR(TZKLFK

    JLYHVPRGHVWYDOXHVIRUWKHVSHHGRIVRXQG

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    6/68

    'RHVVSHHGRIVRXQGLQDQLGHDOJDVGHSHQGRQSUHVVXUH":KDWDERXWDUHDOJDV"

    1R)RUDQLGHDOJDVWKHVSHHGRIVRXQGLVJLYHQE\(T

    F N57

    DQGLVRQO\DIXQFWLRQRIWHPSHUDWXUH7 )RUDUHDOJDVZHGRQRWUHFRYHUWKHVLPSOHH[SUHVVLRQDERYHDQGWKHUHLV

    DGHSHQGHQF\RQ3SDUWLFXODUO\LQWKHGHQVHJDVUHJLRQDERYHWKHFULWLFDO

    SRLQW

    &DQDFRQYHUJHQWDGLDEDWLFQR]]OHSURGXFHDVXSHUVRQLFIORZ"

    1R)URP(TDQGDQR]]OHVRG3LWLVUHTXLUHGWRKDYHG$!WR

    UHDFK0!$FRQYHUJHQWQR]]OHZLOOKDYH0DWWKHH[LWZKLFKLVWKH

    VPDOOHVWDUHD)RUORZHUEDFNSUHVVXUHVWKHUHPD\EHDVKRFNVWDQGLQJLQ

    WKHH[LWSODQH

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    7/68

    6NHWFKWKHYDULDWLRQLQV73DQG0IRUDVXEVRQLFIORZLQWRDFRQYHUJHQWQR]]OHZLWK0DWWKHH[LWSODQH"

    V0F0 N57 &S7R7 6LQFHZHGRQRWNQRZWKHDUHDYHUVXVOHQJWKZHSORWLWYHUVXVPDFKQXPEHU0

    73DQGUHODWLYHWRWKHVWDJQDWLRQVWDWHLVOLVWHGLQ7DEOH$DQGJLYHQLQHTV$VPDOOVSUHDGVKHHW0VWHSGLGWKHFDOFXODWLRQV

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    0.8

    0.9

    1

    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

    Mach number

    V

    P

    T

    7KHFXUYHVDUH

    SORWWHGDVWKH

    YDULDEOHV

    77RR33R

    9 &S7R

    DQGIRUN

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    8/68

    6NHWFKWKHYDULDWLRQLQV73DQG0IRUDVRQLF0IORZLQWRDGLYHUJHQWQR]]OHZLWK0DWWKHH[LWSODQH"

    V0F0 N57 &S7R7 6LQFHZHGRQRWNQRZWKHDUHDYHUVXVOHQJWKZHSORWLWYHUVXVPDFKQXPEHU0

    73DQGUHODWLYHWRWKHVWDJQDWLRQVWDWHLVOLVWHGLQ7DEOH$DQGJLYHQLQHTV

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    0.8

    0.9

    1

    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

    Mach number

    V

    P

    T

    7KHFXUYHVDUH

    SORWWHGDVWKH

    YDULDEOHV

    77R

    R33R

    9 &S7R

    DQGIRUN

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    9/68

    To maximize the mass flow rate of air through a given nozzle, which properties

    should I try to change and in which direction, higher or lower?

    The mass flow rate is given by Eq.16.41 and if we have M= 1 at the throatthen Eq.16.42 gives the maximum mass flow rate possible.

    Max flow for:

    Higher upstream stagnation pressure

    Lower upstream stagnation temperature

    +RZGRWKHVWDJQDWLRQWHPSHUDWXUHDQGSUHVVXUHFKDQJHLQDQLVHQWURSLFIORZ"

    7KHVWDJQDWLRQWHPSHUDWXUHDQGVWDJQDWLRQSUHVVXUHDUHFRQVWDQW

    &DQDQ\ORZHQRXJKEDFNXSSUHVVXUHJHQHUDWHDQLVHQWURSLFVXSHUVRQLFIORZ"

    1R2QO\RQHEDFNSUHVVXUHFRUUHVSRQGVWRDVXSHUVRQLFIORZZKLFKLV

    WKHH[LWSUHVVXUHDWVWDWHGLQ)LJXUH+RZHYHUDSUHVVXUHORZHUWKDQWKDW

    FDQJLYHDQLVHQWURSLFIORZLQWKHQR]]OHFDVHHZLWKDGURSLQSUHVVXUHRXWVLGH

    WKHQR]]OH7KLVLVLUUHYHUVLEOHOHDGLQJWRDQLQFUHDVHLQVDQGWKHUHIRUHQRW

    LVHQWURSLF

    ,VWKHUHDQ\EHQHILWWRRSHUDWHDQR]]OHFKRNHG"

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    10/68

    7RLQFUHDVHWKHIORZWKURXJKDFKRNHGQR]]OHWKHIORZFDQEHKHDWHGFRROHGRU

    FRPSUHVVHGH[SDQGHGIRXUSURFHVVHVEHIRUHRUDIWHUWKHQR]]OH([SODLQZKLFK

    RIWKHVHHLJKWSRVVLELOLWLHVZLOOKHOSDQGZKLFKZLOOQRW

    7KHPDVVIORZUDWHWKURXJKDFKRNHGQR]]OHLVJLYHQE\(T6LQFHNDQG5

    DUHFRQVWDQWLWYDULHVZLWKWKHXSVWUHDPVWDJQDWLRQSURSHUWLHV3RDQG7R

    $IWHUQR]]OH$Q\GRZQVWUHDPFKDQJHVKDYHQRHIIHFWV

    %HIRUHQR]]OH8SVWUHDPFKDQJHVLQ3RDQG7RKDVDQLQIOXHQFH

    D+HDW7KLVORZHUVPDVVIORZUDWH7RLQFUHDVHV

    E&RRO7KLVUDLVHVPDVVIORZUDWH7RGHFUHDVHV

    F&RPSUHVV5DLVHV3RDQG7RRSSRVLWHHIIHFWV

    ,VHQWURSLF3RQHZ3RUSDQG7RQHZ7R USN

    N

    3RQHZ 7RQHZ USNN >3R 7R@!>3R 7R@

    6RWKHPDVVIORZUDWHLQFUHDVHV

    G([SDQG/RZHUV3RDQG7RRSSRVLWHHIIHFWV$VVXPH

    LVHQWURSLFWKHQPDVVIORZUDWHGHFUHDVHV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    11/68

    :KLFKRIWKHFDVHVLQ)LJDKKDYHHQWURS\JHQHUDWLRQDQGZKLFKGRQRW"

    D7KHUHLVQRIORZVRVJHQ

    E6XEVRQLFIORZUHYHUVLEOHVRVJHQ F/LPLWIRUVXEVRQLFIORZUHYHUVLEOHVRVJHQ

    G7KHRQO\VXSHUVRQLFUHYHUVLEOHIORZVROXWLRQVRVJHQ

    H6XSHUVRQLFUHYHUVLEOHLQQR]]OHVJHQLUUHYHUVLEOHRXWVLGH

    I6XSHUVRQLFUHYHUVLEOHLQQR]]OHVJHQFRPSUHVVLRQRXWVLGH

    J6KRFNVWDQGVDWH[LWSODQHVJHQ!DFURVVVKRFN

    K6KRFNLVORFDWHGLQVLGHQR]]OHVJHQ!DFURVVVKRFN

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    12/68

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    13/68

    +RZGRHVWKHVWDJQDWLRQWHPSHUDWXUHDQGSUHVVXUHFKDQJHLQDQDGLDEDWLFQR]]OH

    IORZZLWKDQHIILFLHQF\RIOHVVWKDQ"

    7KHVWDJQDWLRQWHPSHUDWXUHVWD\VFRQVWDQWHQHUJ\HT 7KHVWDJQDWLRQSUHVVXUHGURSVVLVJHQHUDWHGOHVVNLQHWLFHQHUJ\

    +RZKLJKFDQDJDVYHORFLW\0DFKQXPEHUEHDQGVWLOOWUHDWLWDVLQFRPSUHVVLEOH

    IORZZLWKLQHUURU"

    7KHUHODWLYHHUURULQWKH3YHUVXVNLQHWLFHQHUJ\(TEHFRPHV

    H

    V

    FR

    0

    V

    FR

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    14/68

    6WDJQDWLRQ3URSHUWLHV

    6WHDPOHDYHVDQR]]OHZLWKDSUHVVXUHRIN3DDWHPSHUDWXUHRI&DQGDYHORFLW\RIPV:KDWLVWKHLVHQWURSLFVWDJQDWLRQSUHVVXUHDQGWHPSHUDWXUH"

    6WDJQDWLRQHQWKDOS\IURPHQHUJ\HTXDWLRQDQGYDOXHVIURPVWHDPWDEOHV%

    K

    K

    9

    N-NJ

    V

    V

    N-NJ.

    ,WFDQEHOLQHDUO\LQWHUSRODWHGIURPWKHSULQWHGWDEOHV

    &RPSXWHUVRIWZDUHKR

    VR

    7R

    &3R

    N3D

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    15/68

    $QREMHFWIURPVSDFHHQWHUVWKHHDUWKVXSSHUDWPRVSKHUHDWN3D.ZLWKD

    UHODWLYHYHORFLW\RIPVRUPRUH(VWLPDWHWKHREMHFWCVVXUIDFHWHPSHUDWXUH

    KRK9N-NJ

    KR

    K

    N-NJ!7.

    7KHYDOXHIRUK

    IURPLGHDOJDVWDEOH$ZDVHVWLPDWHGVLQFHWKHORZHVW7LQWKH

    WDEOHLV.

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    16/68

    6WHDPLVIORZLQJWRDQR]]OHZLWKDSUHVVXUHRIN3D7KHVWDJQDWLRQSUHVVXUH

    DQGWHPSHUDWXUHDUHPHDVXUHGWREHN3DDQGR&UHVSHFWLYHO\:KDWDUH

    WKHIORZYHORFLW\DQGWHPSHUDWXUH"

    6WDJQDWLRQVWDWH7DEOH%K

    RN-NJV

    RN-NJ.

    6WDWHN3DV

    VR

    N-NJ.

    7

    R&

    K

    N-NJ

    (QHUJ\HTXDWLRQJLYHV

    V

    KRKN-NJ

    V KRK PV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    17/68

    7KHSURGXFWVRIFRPEXVWLRQRIDMHWHQJLQHOHDYHWKHHQJLQHZLWKDYHORFLW\

    UHODWLYHWRWKHSODQHRIPVDWHPSHUDWXUHRI&DQGDSUHVVXUHRIN3D$VVXPLQJWKDWN=&S=N-NJ.IRUWKHSURGXFWVGHWHUPLQHWKH

    VWDJQDWLRQSUHVVXUHDQGWHPSHUDWXUHRIWKHSURGXFWVUHODWLYHWRWKHDLUSODQH

    (QHUJ\(T KR

    K

    9N-NJ

    7R

    7

    KR

    K

    &S.

    7R

    .

    ,VHQWURSLFSURFHVVUHODWHVWRWKHVWDJQDWLRQSUHVVXUH

    3R

    3

    7R

    7

    NNN3D

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    18/68

    $PHWHRULWHPHOWVDQGEXUQXSDWWHPSHUDWXUHVRI.,ILWKLWVDLUDWN3D

    .KRZKLJKDYHORFLW\VKRXOGLWKDYHWRH[SHULHQFHVXFKDWHPSHUDWXUH"

    $VVXPHZHKDYHDVWDJQDWLRQ7.

    K

    9K

    VWDJQ

    8VHWDEOH$KVWDJQ

    N-NJK

    N-NJ

    9N-NJUHPHPEHUFRQYHUWWR-NJPV

    9

    PV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    19/68

    ,GULYHGRZQWKHKLJKZD\DWNPKRQDGD\ZLWK&N3D,SXWP\KDQGFURVVVHFWLRQDODUHDPIODWRXWWKHZLQGRZ:KDWLVWKHIRUFHRQP\

    KDQGDQGZKDWWHPSHUDWXUHGR,IHHO"

    7KHDLUVWDJQDWHVRQWKHKDQGVXUIDFH K

    9K

    VWDJQ

    8VHFRQVWDQWKHDWFDSDFLW\

    7VWDJQ

    7

    9

    &S

    &

    $VVXPHDUHYHUVLEOHDGLDEDWLFFRPSUHVVLRQ

    3VWDJQ

    3

    7VWDJQ

    7

    NN

    N3D

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    20/68

    $LUOHDYHVDFRPSUHVVRULQDSLSHZLWKDVWDJQDWLRQWHPSHUDWXUHDQGSUHVVXUHRI

    &N3DDQGDYHORFLW\RIPV7KHSLSHKDVDFURVVVHFWLRQDODUHDRIP'HWHUPLQHWKHVWDWLFWHPSHUDWXUHDQGSUHVVXUHDQGWKHPDVVIORZUDWH

    KR

    K

    9N-NJ

    7R

    7

    KR

    K

    &S

    .

    7

    7R

    7&.

    3

    3R

    7

    7R

    NNN3D

    P

    $9$9

    Y

    3

    $9

    57

    NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    21/68

    $VWDJQDWLRQSUHVVXUHRIN3DLVPHDVXUHGIRUDQDLUIORZZKHUHWKHSUHVVXUHLV

    N3DDQG&LQWKHDSSURDFKIORZ:KDWLVWKHLQFRPPLQJYHORFLW\"

    $VVXPHDUHYHUVLEOHDGLDEDWLFFRPSUHVVLRQ

    7R

    7

    3R

    3

    NN

    .

    9K

    RK

    &

    S7

    R7

    N-NJ

    9

    PV

    1

    2

    cb

    7RWKHOHIWD3LWRWWXEHEOXHLQQHUWXEHPHDVXUHVVWDJQDWLRQSUHVVXUHDQG\HOORZ

    RXWHUWXEHZLWKKROHVLQLWPHDVXUHVVWDWLFSUHVVXUH7RWKHULJKWLVDVWDJQDWLRQ

    SRLQWRQDZDOOUHODWLYHWRWKHIUHHVWUHDPIORZDWVWDWH

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    22/68

    $MHWHQJLQHUHFHLYHVDIORZRIPVDLUDWN3D&DFURVVDQDUHDRIPZLWKDQH[LWIORZDWPVN3D.)LQGWKHPDVVIORZUDWHDQGWKUXVW

    P

    $9LGHDOJDV357

    P

    357$9 (

    NJV

    )QHW

    P

    9H[

    9LQ

    1

    ,QOHW+LJK3/RZ3H[LW

    cb

    )QHW

    7KHVKDIWPXVWKDYHD[LDOORDGEHDULQJVWRWUDQVPLWWKUXVWWRDLUFUDIW

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    23/68

    $FPLQQHUGLDPHWHUSLSHKDVDQLQOHWIORZRINJVZDWHUDWR&N3D

    $IWHUDGHJUHHEHQGDVVKRZQLQ)LJ3WKHH[LWIORZLVDWR&N3D

    1HJOHFWJUDYLWDWLRQDOHIIHFWVDQGILQGWKHDQFKRULQJIRUFHV)[DQG)\

    'P =

    'P

    VDYJ

    P

    $

    PV

    1RZZHFDQGRWKH[DQG\GLUHFWLRQPRPHQWXPHTXDWLRQVIRUVWHDG\IORZ

    DQGWKHVDPHPDJQLWXGHRIWKHYHORFLW\EXWGLIIHUHQWGLUHFWLRQV

    ;GLU P

    V

    DYJ)[P

    33R$

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    24/68

    $ZDWHUFDQQRQVSUD\VNJVOLTXLGZDWHUDWDYHORFLW\RIPVKRUL]RQWDOO\

    RXWIURPDQR]]OH,WLVGULYHQE\DSXPSWKDWUHFHLYHVWKHZDWHUIURPDWDQNDW

    &N3D1HJOHFWHOHYDWLRQGLIIHUHQFHVDQGWKHNLQHWLFHQHUJ\RIWKHZDWHUIORZLQWKHSXPSDQGKRVHWRWKHQR]]OH)LQGWKHQR]]OHH[LWDUHDWKHUHTXLUHGSUHVVXUHRXWRIWKHSXPSDQGWKHKRUL]RQWDOIRUFHQHHGHGWRKROGWKHFDQQRQ

    P

    $V$VY$P

    YV

    P

    :

    SP

    Z

    SP

    Y3

    H[3

    LQP

    V

    H[

    3H[

    3LQ

    VH[ Y N3D

    )PV

    H[1

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    25/68

    $QLUULJDWLRQSXPSWDNHVZDWHUIURPDODNHDQGGLVFKDUJHVLWWKURXJKDQR]]OHDV

    VKRZQLQ)LJ3$WWKHSXPSH[LWWKHSUHVVXUHLVN3DDQGWKH

    WHPSHUDWXUHLV&7KHQR]]OHLVORFDWHGPDERYHWKHSXPSDQGWKHDWPRVSKHULFSUHVVXUHLVN3D$VVXPLQJUHYHUVLEOHIORZWKURXJKWKHV\VWHPGHWHUPLQHWKHYHORFLW\RIWKHZDWHUOHDYLQJWKHQR]]OH

    $VVXPHZHFDQQHJOHFWNLQHWLFHQHUJ\LQWKHSLSHLQDQGRXWRIWKHSXPS

    ,QFRPSUHVVLEOHIORZVR%HUQRXOOLVHTXDWLRQDSSOLHV9

    9

    9

    Y3

    3

    99

    J=

    =

    3

    3

    J=

    =

    Y

    N3D

    9

    Y33

    9

    Y3

    3

    PV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    26/68

    $MHWHQJLQHDWWDNHRIIKDVDLUDWR&N3DFRPLQJDWPVWKURXJKWKH

    PGLDPHWHULQOHW7KHH[LWIORZLVDW.N3DWKURXJKWKHH[LWQR]]OHRI

    PGLDPHWHU1HJOHFWWKHIXHOIORZUDWHDQGILQGWKHQHWIRUFHWKUXVWRQWKH

    HQJLQH

    =

    'P

    =

    'P

    Y

    57

    3

    PNJY

    PNJ

    P

    $VYV

    Y

    NJV

    V

    P

    Y

    $

    PV

    1RZZHFDQGRWKH[GLUHFWLRQPRPHQWXPHTXDWLRQIRUVWHDG\IORZDQGWKHVDPH

    PDVVIORZUDWHLQDQGRXW

    ;GLU P

    V

    )[

    3

    3R

    $

    P

    V

    3

    3R

    $

    )[

    P

    V

    3

    3R

    $

    P

    V

    3

    3R

    $

    P

    V

    V

    1

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    27/68

    $ZDWHUWXUELQHXVLQJQR]]OHVLVORFDWHGDWWKHERWWRPRI+RRYHU'DPP

    EHORZWKHVXUIDFHRI/DNH0HDG7KHZDWHUHQWHUVWKHQR]]OHVDWDVWDJQDWLRQ

    SUHVVXUHFRUUHVSRQGLQJWRWKHFROXPQRIZDWHUDERYHLWPLQXVGXHWRORVVHV

    7KHWHPSHUDWXUHLV&DQGWKHZDWHUOHDYHVDWVWDQGDUGDWPRVSKHULFSUHVVXUH,IWKHIORZWKURXJKWKHQR]]OHLVUHYHUVLEOHDQGDGLDEDWLFGHWHUPLQHWKHYHORFLW\DQG

    NLQHWLFHQHUJ\SHUNLORJUDPRIZDWHUOHDYLQJWKHQR]]OH

    3J=J=

    Y

    N3D

    3DF

    3N3D

    Y39H[ 9

    H[ Y3

    9H[

    PV

    9H[ Y3N-NJ

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    28/68

    $ZDWHUWRZHURQDIDUPKROGVPOLTXLGZDWHUDW&N3DLQDWDQNRQWRSRIDPWDOOWRZHU$SLSHOHDGVWRWKHJURXQGOHYHOZLWKDWDSWKDWFDQRSHQD

    FPGLDPHWHUKROH1HJOHFWIULFWLRQDQGSLSHORVVHVDQGHVWLPDWHWKHWLPHLWZLOO

    WDNHWRHPSW\WKHWDQNIRUZDWHU

    ,QFRPSUHVVLEOHIORZVRZHFDQXVH%HUQRXOOL(TXDWLRQ

    3H3LVL=H=L+

    VHJ=

    L VH J= PV

    P

    $VH$VHYPW

    P9Y$' P

    WPY$VH9$VH

    W VHFPLQ

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    29/68

    )LQGWKHH[SUHVVLRQIRUWKHDQFKRULQJIRUFH5[IRUDQLQFRPSUHVVLEOHIORZOLNHLQ

    )LJXUH6KRZWKDWLWFDQEHZULWWHQDV

    5 [

    VLVH

    VLVH>3L3R$L3H3R$H@

    $SSO\WKH;GLUPRPHQWXPHTXDWLRQIRUDVWHDG\IORZ

    5 [3L3R$L3H3R$HPV

    LP

    VH

    %HUQRXOOLHTXDWLRQIRUWKHIORZLV

    V

    H V

    L Y3H3L VHVLY3L3H

    VLVH

    &RQWLQXLW\HTXDWLRQJLYHV

    P $LVLY$HVHY

    6ROYHIRU5 [IURPWKHPRPHQWXPHTXDWLRQ

    5 [P

    VHVL3H3R$H3L3R$L

    $LVL

    YY3L3H

    VLVH3H3R$H3L3R$L

    0XOWLSO\LQDQGXVHFRQWLQXLW\HTXDWLRQIRUVHFRQGWHUP

    5[

    VLV

    H

    >3L$LVL3H$HVH@3H3R$H3L3R$L

    VLVH>3L$LVL3H$HVH

    3H3R$HVH

    3L3R$LVL

    3H3R$HVL

    3L3R$LVH@

    1RZSXWWKHILUVWIRXUWHUPVWRJHWKHU

    5[

    VLVH>3L3R$LVL

    3H3R$HVH

    3H3R$HVL

    3L3R$LVH@

    VLVH>3L3R$LVLVH

    3H3R$HVLVH@

    VLVH

    VLVH>3L3R$L3H3R$H@

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    30/68

    )LQGWKHVSHHGRIVRXQGIRUDLUDWN3DDWWKHWZRWHPSHUDWXUHV&DQG&5HSHDWWKHDQVZHUIRUFDUERQGLR[LGHDQGDUJRQJDVHV

    )URPHTZHKDYH

    F

    N57 PV

    F

    PV

    )RU&DUERQ'LR[LGH5N-NJ.N

    F

    PV

    F

    PV

    )RU$UJRQ5N-NJ.N

    F

    PV

    F

    PV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    31/68

    ,IWKHVRXQGRIWKXQGHULVKHDUGVHFRQGVDIWHUWKHOLJKWQLQJLVVHHQDQGWKH

    ZHDWKHULV&+RZIDUDZD\LVWKHOLJKWQLQJWDNLQJSODFH"

    7KHVRXQGWUDYHOVZLWKWKHVSHHGRIVRXQGLQDLULGHDOJDV8VHWKH

    IRUPXODLQ(T

    /F W N57 W P

    )RUHYHU\

    VHFRQGVDIWHUWKH

    OLJKWQLQJWKH

    VRXQGWUDYHOV

    DERXWNP

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    32/68

    (VWLPDWHWKHVSHHGRIVRXQGIRUVWHDPGLUHFWO\IURP(TDQGWKHVWHDP

    WDEOHVIRUDVWDWHRI03D&8VHWDEOHYDOXHVDWDQG03DDWWKHVDPHHQWURS\DVWKHZDQWHGVWDWH(TLVWKHQGRQHE\ILQLWHGLIIHUHQFH)LQGDOVR

    WKHDQVZHUIRUWKHVSHHGRIVRXQGDVVXPLQJVWHDPLVDQLGHDOJDV

    (T F3V3

    V

    6WDWH03D& VN-NJ.

    03DV YPNJYNJP

    03DVYPNJYNJP

    F

    FPV

    )URP7DEOH$&S

    N-NJ.

    &Y&S5N-NJ.

    N&S&Y5N-NJ.IURP$

    1RZGRWKHVSHHGRIVRXQGIURP(T

    F N57 PV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    33/68

    7KHVSHHGRIVRXQGLQOLTXLGZDWHUDWR&LVDERXWPV)LQGWKHVWDJQDWLRQ

    SUHVVXUHDQGWHPSHUDWXUHIRUD0IORZDWR&N3D,VLWSRVVLEOHWRJHW

    DVLJQLILFDQWPDFKQXPEHUIORZRIOLTXLGZDWHU"

    V 0FPV

    KKV

    %HUQRXOOL(T3VY

    3D03D

    333N3D

    77V&S

    R&

    5HPDUN1RWLFHWKHYHU\KLJKSUHVVXUH7RJHWDKLJKHUYHORFLW\\RXQHHGDKLJKHU

    SUHVVXUHWRDFFHOHUDWHWKHIOXLGWKDWLVQRWIHDVLEOHIRUDQ\ODUJHIORZUDWH

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    34/68

    $FRQYHUJHQWQR]]OHKDVDPLQLPXPDUHDRIPDQGUHFHLYHVDLUDWN3D

    .IORZLQJZLWKPV:KDWLVWKHEDFNSUHVVXUHWKDWZLOOSURGXFHWKH

    PD[LPXPIORZUDWHDQGILQGWKDWIORZUDWH"

    3

    3R

    N

    N

    N &ULWLFDO3UHVVXUH5DWLR

    )LQG3R

    KKVN-NJ

    77L.IURPWDEOH$

    33L77LNNN3D

    7KHPDVVIORZUDWHFRPHVIURPWKHWKURDWSURSHUWLHV

    33RN3D

    77R.

    3

    57

    NJP

    9F N57 PV

    P

    $9NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    35/68

    $FRQYHUJHQWGLYHUJHQWQR]]OHKDVDWKURDWDUHDRIPPDQGDQH[LWDUHDRI

    PP7KHLQOHWIORZLVKHOLXPDWDVWDJQDWLRQSUHVVXUHRI03DVWDJQDWLRQ

    WHPSHUDWXUHRI.:KDWLVWKHEDFNSUHVVXUHWKDWZLOOJLYHVRQLFFRQGLWLRQDW

    WKHWKURDWEXWVXEVRQLFHYHU\ZKHUHHOVH"

    )RUWKLVIORZZHKDYHKHOLXPZLWKN+H

    VRZHFDQQRWXVHWKHWDEOHVIRUDLU

    :HQHHGWKHVROXWLRQWRWKHFXUYHODEHOHGFLQ)LJ)RUFULWLFDOIORZDWWKH

    WKURDWZHKDYHIURP7DEOHODVWFROXPQ

    33RN3D

    1RZZHQHHGWRILQGWKHFRQGLWLRQVZKHUHWKHDUHDUDWLRLV

    $(

    $

    WKDWLVVROYHIRU0LQ(TJLYHQWKHDUHDUDWLR7KLVLVQRQOLQHDUVRZHKDYHWR

    LWHUDWHRQLW+HUHNNVRORRNDOVRDW)LJIRUWKHJHQHUDOVKDSH

    0$$>@

    0$$>@

    0$$>@

    0$$>@ 1RZGRDOLQHDULQWHUSRODWLRQIRUWKHUHVWWRJHW0

    (

    (T3(

    3R>@

    3(

    N3D

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    36/68

    $MHWSODQHWUDYHOVWKURXJKWKHDLUZLWKDVSHHGRINPKDWDQDOWLWXGHRI

    NPZKHUHWKHSUHVVXUHLVN3DDQGWKHWHPSHUDWXUHLV&&RQVLGHUWKHLQOHWGLIIXVHURIWKHHQJLQHZKHUHDLUOHDYHVZLWKDYHORFLW\RIPV'HWHUPLQHWKH

    SUHVVXUHDQGWHPSHUDWXUHOHDYLQJWKHGLIIXVHUDQGWKHUDWLRRILQOHWWRH[LWDUHDRIWKHGLIIXVHUDVVXPLQJWKHIORZWREHUHYHUVLEOHDQGDGLDEDWLF

    9NPKPVY

    573 PNJ

    K

    N-NJ

    KR

    N-NJ

    7R

    .

    3R

    3

    7R

    7

    NNN3D

    K

    N-NJ 7

    .

    3

    3R

    7

    7R

    NNN3D

    Y

    PNJ

    $

    $

    Y

    Y

    9

    9

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    37/68

    $LULVH[SDQGHGLQDQR]]OHIURPDVWDJQDWLRQVWDWHRI03D.WRD

    EDFNSUHVVXUHRI03D,IWKHH[LWFURVVVHFWLRQDODUHDLVPILQGWKH

    PDVVIORZUDWH

    7KLVFRUUHVSRQGVWRFDVHFDQGLVDUHYHUVLEOHIORZ

    3(

    3R[

    7DEOH$ 0(

    7(

    77R

    (

    7R

    .

    F(

    N57(

    PV

    V(

    0(

    F(

    PV

    Y(

    573 PNJ

    P $(9

    (Y

    ( NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    38/68

    $LUIORZVLQWRDFRQYHUJHQWGLYHUJHQWQR]]OHZLWKDQH[LWDUHDRIWLPHVWKH

    WKURDWDUHDRIP7KHLQOHWVWDJQDWLRQVWDWHLV03D.)LQGWKH

    EDFNSUHVVXUHWKDWZLOOFDXVHVXEVRQLFIORZWKURXJKRXWWKHHQWLUHQR]]OHZLWK0

    DWWKHWKURDW:KDWLVWKHPDVVIORZUDWH"

    7KLVFRUUHVSRQGVWRFDVHFDQGLVDUHYHUVLEOHIORZ

    $(

    $ /RRNDWWRSLQ7DEOH$0

    0(

    DQG3(

    3R

    3(

    3R

    N3D

    7RILQGWKHPDVVIORZUDWHZHQHHGWKHWKURDWFRQGLWLRQVVHH7DEOH

    77 N.

    Y573PNJ

    F N57 PV

    P

    $FY

    NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    39/68

    $LUIORZVLQWRDFRQYHUJHQWGLYHUJHQWQR]]OHZLWKDQH[LWDUHDRIWLPHVWKH

    WKURDWDUHDRIP7KHLQOHWVWDJQDWLRQVWDWHLV03D.)LQGWKH

    EDFNSUHVVXUHWKDWZLOOFDXVHDUHYHUVLEOHVXSHUVRQLFH[LWIORZZLWK0DWWKH

    WKURDW:KDWLVWKHPDVVIORZUDWH"

    7KLVIORZLVFDVHGLQ)LJWKHRQO\UHYHUVLEOHVXSHUVRQLFIORZ

    $(

    $VHH7DEOH$0!

    0(

    DQG3(

    3R

    3(

    N3D

    7RILQGWKHPDVVIORZUDWHZHQHHGWKHWKURDWFRQGLWLRQVVHH7DEOH

    77 N.

    33R

    N

    N

    NN3D

    3

    57

    NJP

    P

    $V$F$ N57

    NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    40/68

    $LULVH[SDQGHGLQDQR]]OHIURPDVWDJQDWLRQVWDWHRI03D.WRDVWDWLF

    SUHVVXUHRIN3D7KHPDVVIORZUDWHWKURXJKWKHQR]]OHLVNJV$VVXPHWKH

    IORZLVUHYHUVLEOHDQGDGLDEDWLFDQGGHWHUPLQHWKHWKURDWDQGH[LWDUHDVIRUWKH

    QR]]OH

    9HORFLW\

    'HQVLW\$UHD

    0DFK

    03D 03D3

    33R

    N

    N

    N

    03D

    77R

    N.

    Y573 PNJ

    F N57 PV

    $P

    YFP

    3

    3R

    0

    9

    F

    &ROXPQZLWKPDFKQREDVHGRQWKURDWVSHHGRIVRXQG

    9

    PV

    7

    7R

    7

    7R

    .

    Y

    57

    3

    PNJ

    $

    P

    Y

    9

    P

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    41/68

    $LUDWN3D.H[SDQGVWRWKHDWPRVSKHUHDWN3DWKURXJKDFRQYHUJHQW

    QR]]OHZLWKH[LWDUHDRIP$VVXPHDQLGHDOQR]]OH:KDWLVWKHSHUFHQW

    HUURULQPDVVIORZUDWHLIWKHIORZLVDVVXPHGLQFRPSUHVVLEOH"

    7H7L3H3L

    N

    N .

    9HKLKH&S7L7HN-NJ

    9HPVYH57H3H

    PNJ

    P

    $9HYH

    NJV

    ,QFRPSUHVVLEOH)ORZYL573P

    NJ 9H

    Y3YL3L3HN-NJ

    !9HPV!P

    $9HYLNJV

    P

    LQFRPSUHVVLEOH

    P

    FRPSUHVVLEOH

    DERXWRYHUHVWLPDWLRQ

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    42/68

    $FRQYHUJHQWGLYHUJHQWQR]]OHKDVDWKURDWGLDPHWHURIPDQGDQH[LW

    GLDPHWHURIP7KHLQOHWVWDJQDWLRQVWDWHLVN3D.)LQGWKHEDFN

    SUHVVXUHWKDWZLOOOHDGWRWKHPD[LPXPSRVVLEOHIORZUDWHDQGWKHPDVVIORZUDWH

    IRUWKUHHGLIIHUHQWJDVHVDVDLUK\GURJHQRUFDUERQGLR[LGH

    7KHUHLVDPD[LPXPSRVVLEOHIORZZKHQ0DWWKHWKURDW

    7

    N7

    R33

    R

    N

    N

    NR

    N

    N

    P

    $9$F3$ N57 $'P

    N 7 3 F P

    D

    E F

    $(

    $'(

    '7KHUHDUHSRVVLEOHVROXWLRQVFRUUHVSRQGLQJWRSRLQWV

    FDQGGLQ)LJDQG)LJ)RUWKHVHZHKDYH

    6XEVRQLFVROXWLRQ 6XSHUVRQLFVROXWLRQ

    0(

    3(

    3R

    0(

    3(

    3R

    D

    E

    F

    3

    %3

    (N3DDOOFDVHVSRLQWF

    D 3%

    3(

    N3DSRLQWG

    E 3%

    3(

    N3DSRLQWG

    F 3%

    3(

    N3DSRLQWG

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    43/68

    $QR]]OHLVGHVLJQHGDVVXPLQJUHYHUVLEOHDGLDEDWLFIORZZLWKDQH[LW0DFK

    QXPEHURIZKLOHIORZLQJDLUZLWKDVWDJQDWLRQSUHVVXUHDQGWHPSHUDWXUHRI

    03DDQG&UHVSHFWLYHO\7KHPDVVIORZUDWHLVNJVDQGNPD\EHDVVXPHGWREHDQGFRQVWDQW'HWHUPLQHWKHH[LWSUHVVXUHWHPSHUDWXUHH[LWDUHDDQGWKHWKURDWDUHD

    )URP7DEOH$ 0(

    3(

    03D

    &ULWLFDOSURSHUWLHVIURP7DEOH

    7 .

    3 03D

    F PV

    Y573 PNJ

    $P

    YF P

    $(

    $$(

    $ P

    7(

    7R

    7(

    7R

    .

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    44/68

    $PLQVXODWHGWDQNFRQWDLQVDLUDW03D.7KHWDQNLVQRZGLVFKDUJHG

    WKURXJKDVPDOOFRQYHUJHQWQR]]OHWRWKHDWPRVSKHUHDWN3D7KHQR]]OHKDV

    DQH[LWDUHDRIP

    D)LQGWKHLQLWLDOPDVVIORZUDWHRXWRIWKHWDQN

    E)LQGWKHPDVVIORZUDWHZKHQKDOIWKHPDVVKDVEHHQGLVFKDUJHG

    D 7KHEDFNSUHVVXUHUDWLR

    3%

    3R

    33R

    FULW

    VRWKHLQLWLDOIORZLVFKRNHGZLWKWKHPD[LPXPSRVVLEOHIORZUDWH

    0(

    3(

    N3D

    7(

    7 .

    9(F N57

    PV Y

    (573

    (PNJ

    P

    $9

    (Y

    ( NJV

    E 7KHLQLWLDOPDVVLV

    P

    3

    957

    NJ

    ZLWKDPDVVDWVWDWHDVP

    P

    NJ

    $VVXPHDQDGLDEDWLFUHYHUVLEOHH[SDQVLRQRIWKHPDVVWKDWUHPDLQVLQWKHWDQN

    3

    3

    Y

    Y

    N N3D

    7

    7

    Y

    Y

    N .

    7KHSUHVVXUHUDWLRLVVWLOOOHVVWKDQFULWLFDODQGWKHIORZWKXVFKRNHG

    3%

    3R

    33R

    FULW

    0(

    3(

    N3D

    7(

    7 .

    9(

    F N57 PV

    P

    $9

    (3

    (57

    (

    NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    45/68

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    46/68

    $PXQLQVXODWHGWDQNFRQWDLQVDLUDW03D.7KHWDQNLVQRZ

    GLVFKDUJHGWKURXJKDVPDOOFRQYHUJHQWQR]]OHWRWKHDWPRVSKHUHDWN3DZKLOH

    KHDWWUDQVIHUIURPVRPHVRXUFHNHHSVWKHDLUWHPSHUDWXUHLQWKHWDQNDW.7KH

    QR]]OHKDVDQH[LWDUHDRIP D)LQGWKHLQLWLDOPDVVIORZUDWHRXWRIWKHWDQN

    E)LQGWKHPDVVIORZUDWHZKHQKDOIWKHPDVVKDVEHHQGLVFKDUJHG

    D 6DPHVROXWLRQDVLQD

    E )URPVROXWLRQEZHKDYHP

    P

    NJ

    3

    3

    N3D7

    7

    3%

    3

    33R

    FULW

    7KHIORZLVFKRNHGDQGWKHYHORFLW\LV

    7(

    7 .

    9(

    F N57 PV

    3(

    N3D0(

    P

    $9

    (3

    (57

    (

    NJV

    3

    $,5

    H

    FE

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    47/68

    $VVXPHWKHVDPHWDQNDQGFRQGLWLRQVDVLQ3UREOHP$IWHUVRPHIORZRXW

    WKHQR]]OHIORZFKDQJHVWREHFRPHVXEVRQLF)LQGWKHPDVVLQWKHWDQNDQGWKH

    PDVVIORZUDWHRXWDWWKDWLQVWDQW

    7KHLQLWLDOPDVVLV

    P

    3

    957

    NJ

    )ORZFKDQJHVWRVXEVRQLFZKHQWKHSUHVVXUHUDWLRUHDFKHVFULWLFDO

    3%

    3R

    3

    3R

    3%

    N3D

    P

    P

    3

    3

    NJ

    7

    7

    7(

    7 .

    9(

    F N57 PV

    P

    $9

    (3

    (57

    (

    NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    48/68

    1RUPDO6KRFNV

    7KHSURGXFWVRIFRPEXVWLRQHQWHUDFRQYHUJHQWQR]]OHRIDMHWHQJLQHDWDWRWDOSUHVVXUHRIN3DDQGDWRWDOWHPSHUDWXUHRI&7KHDWPRVSKHULFSUHVVXUHLVN3DDQGWKHIORZLVDGLDEDWLFZLWKDUDWHRINJV'HWHUPLQHWKHH[LWDUHD

    RIWKHQR]]OH

    7KHFULWLFDOSUHVVXUH3FULW3 N3D!3DPE

    7KHIORZLVWKHQFKRNHG 7 .

    VF PV

    Y P

    NJ $P

    Y9 P

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    49/68

    &RQVLGHUWKHQR]]OHRI3UREOHPDQGGHWHUPLQHZKDWEDFNSUHVVXUHZLOO

    FDXVHDQRUPDOVKRFNWRVWDQGLQWKHH[LWSODQHRIWKHQR]]OH7KLVLVFDVHJLQ)LJ

    :KDWLVWKHPDVVIORZUDWHXQGHUWKHVHFRQGLWLRQV"

    :HDVVXPHUHYHUVLEOHIORZXSWRWKHVKRFN

    7DEOH$3(

    3R

    0(

    0[

    6KRFNIXQFWLRQV7DEOH$ 0\

    3\

    3[

    3%

    3\

    3[

    N3D

    P

    NJVVDPHDVLQ3UREOHPVLQFH0DWWKURDW

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    50/68

    $WZKDW0DFKQXPEHUZLOOWKHQRUPDOVKRFNRFFXULQWKHQR]]OHRI3UREOHP

    IORZLQJZLWKDLULIWKHEDFNSUHVVXUHLVKDOIZD\EHWZHHQWKHSUHVVXUHVDWF

    DQGGLQ)LJ"

    )LUVWILQGWKHWZRSUHVVXUHVWKDWZLOOJLYHH[LWDWFDQGG6HHVROXWLRQWRD

    $(

    $'(

    '

    3(

    N3DFN3DG

    3(

    N3D

    $VVXPH0[0\3R\3R[

    $[

    $[

    $[

    $\

    $(

    $\

    $(

    $[

    $[

    $\

    $[

    $[

    0(

    3(

    3R\

    3(3(3R\3R\3R[3R[ N3D

    5HSHDWLI0[3(N3D

    ,QWHUSRODWHWRPDWFKWKHGHVLUHGSUHVVXUH!0[

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    51/68

    7KHQR]]OHLQ3UREOHPZLOOKDYHDWKURDWDUHDRIPDQGDQH[LW

    DUHDWLPHVDVODUJH6XSSRVHWKHEDFNSUHVVXUHLVUDLVHGWR03DDQGWKDW

    WKHIORZUHPDLQVLVHQWURSLFH[FHSWIRUDQRUPDOVKRFNZDYH9HULI\WKDWWKHVKRFN

    PDFKQXPEHU0[LVFORVHWRDQGILQGWKHH[LWPDFKQXPEHUWKHWHPSHUDWXUHDQGWKHPDVVIORZUDWHWKURXJKWKHQR]]OH

    D )URP7DEOH$ 0(

    3(

    03D

    7 . 3 03D F PV Y PNJ

    $

    P

    $

    ( P

    7(

    .

    $VVXPH0[

    WKHQ

    0\

    3R\

    3R[

    $(

    $[

    $[

    $[$

    [$

    \

    $(

    $\

    0(

    3(

    3R\

    3( 03D2. 7

    ( .P

    NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    52/68

    &RQVLGHUWKHGLIIXVHURIDVXSHUVRQLFDLUFUDIWIO\LQJDW0=DWVXFKDQDOWLWXGHWKDWWKHWHPSHUDWXUHLV&DQGWKHDWPRVSKHULFSUHVVXUHLVN3D&RQVLGHUWZRSRVVLEOHZD\VLQZKLFKWKHGLIIXVHUPLJKWRSHUDWHDQGIRUHDFKFDVHFDOFXODWH

    WKHWKURDWDUHDUHTXLUHGIRUDIORZRINJV

    D7KHGLIIXVHURSHUDWHVDVUHYHUVLEOHDGLDEDWLFZLWKVXEVRQLFH[LWYHORFLW\

    E$QRUPDOVKRFNVWDQGVDWWKHHQWUDQFHWRWKHGLIIXVHU([FHSWIRUWKHQRUPDO

    VKRFNWKHIORZLVUHYHUVLEOHDQGDGLDEDWLFDQGWKHH[LWYHORFLW\LVVXEVRQLF

    7KLVLVVKRZQLQ)LJ3

    D $VVXPHDFRQYHUJHQWGLYHUJHQWGLIIXVHUZLWK0=DWWKHWKURDW

    5HODWHWKHLQOHWVWDWHWRWKHVRQLFVWDWH

    3

    3R

    33R

    3

    N3D7

    .

    F N57 PV

    Y573 PNJ

    $P

    YF P E $FURVVWKHVKRFNZHKDYH

    0\

    3\

    N3D

    7\

    .

    3

    N3D

    7

    .FPV

    Y PNJ

    $ P

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    53/68

    &RQVLGHUWKHQR]]OHLQSUREOHPIORZLQJDLU:KDWVKRXOGWKHEDFNSUHVVXUH

    EHIRUDQRUPDOVKRFNWRVWDQGDWWKHH[LWSODQH"7KLVLVFDVHJLQ)LJ:KDW

    LVWKHH[LWYHORFLW\DIWHUWKHVKRFN"

    5HYHUVLEOHIORZXSWRWKHVKRFNZLWK0DWWKHWKURDW

    3[R

    3R

    7[R

    7R

    $(

    $

    7DEOH$0(

    0[

    3[

    3[R

    7[

    7[R

    1RZZHFDQGRWKHQRUPDOVKRFNIURP7DEOH$

    0[

    0\

    3\

    3[

    7\

    7[

    7\

    7[

    7[R

    .

    3\3[3[RN3D

    V\0\F\0\ N57\

    PV

    A*

    M Mx y

    AE

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    54/68

    1R]]OHV'LIIXVHUVDQG2ULILFHV

    $LULVH[SDQGHGLQDQR]]OHIURPN3D&WRN3DLQDQR]]OHKDYLQJDQHIILFLHQF\RI7KHPDVVIORZUDWHLVNJV'HWHUPLQHWKHH[LWDUHDRIWKH

    QR]]OHWKHH[LWYHORFLW\DQGWKHLQFUHDVHRIHQWURS\SHUNLORJUDPRIDLU&RPSDUH

    WKHVHUHVXOWVZLWKWKRVHRIDUHYHUVLEOHDGLDEDWLFQR]]OH

    7V

    7

    3

    3

    NN.

    9V

    -NJ

    9

    9

    PV

    K

    9

    K

    7

    7

    9

    &S

    7

    .

    Y

    PNJ

    $

    PPP

    VV

    OQ

    OQ

    N-NJ.

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    55/68

    5HSHDW3UREOHPDVVXPLQJDGLIIXVHUHIILFLHQF\RI

    6DPHDVSUREOHPH[FHSW

    '

    :HWKXVKDYHIURP

    K

    K

    KR

    K

    K

    K

    N-NJ7

    .

    3R

    3

    3

    (/

    )NN

    N3D

    h

    01

    02

    3

    1

    2

    s

    7R

    7R

    .

    KN-NJ7.

    33R77RNN N3D

    Y PNJ

    $$YY99

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    56/68

    $LUHQWHUVDGLIIXVHUZLWKDYHORFLW\RIPVDVWDWLFSUHVVXUHRIN3DDQGD

    WHPSHUDWXUHRI&7KHYHORFLW\OHDYLQJWKHGLIIXVHULVPVDQGWKHVWDWLFSUHVVXUHDWWKHGLIIXVHUH[LWLVN3D'HWHUPLQHWKHVWDWLFWHPSHUDWXUHDWWKH

    GLIIXVHUH[LWDQGWKHGLIIXVHUHIILFLHQF\&RPSDUHWKHVWDJQDWLRQSUHVVXUHVDWWKHLQOHWDQGWKHH[LW

    7R

    7

    9&

    S .

    7R

    7R

    7

    7R

    9&

    S .

    7

    R7

    7

    N

    N3

    R3

    3

    3R

    3

    3R

    N3D

    7

    R7

    7

    N

    N3

    R3

    3

    3R

    3

    3R

    N3D

    7H[

    V 73R3NN .

    '

    7

    H[

    V 77

    R7

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    57/68

    6WHDPDWDSUHVVXUHRI03DDQGWHPSHUDWXUHRI&H[SDQGVLQDQR]]OHWRDSUHVVXUHRIN3D7KHQR]]OHHIILFLHQF\LVDQGWKHPDVVIORZUDWHLV

    NJV'HWHUPLQHWKHQR]]OHH[LWDUHDDQGWKHH[LWYHORFLW\

    )LUVWGRWKHLGHDOUHYHUVLEOHDGLDEDWLFQR]]OH

    VV

    V

    N-NJ.K

    N-NJ

    7V

    &KV

    N-NJ

    1RZWKHDFWXDOQR]]OHFDQEHFDOFXODWHG

    K

    KDF

    '

    K

    KV

    N-NJ

    KDF

    N-NJ7

    &Y

    PNJ

    9

    PV

    $

    P

    Y

    9

    P

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    58/68

    $VKDUSHGJHGRULILFHLVXVHGWRPHDVXUHWKHIORZRIDLULQDSLSH7KHSLSH

    GLDPHWHULVPPDQGWKHGLDPHWHURIWKHRULILFHLVPP8SVWUHDPRIWKH

    RULILFHWKHDEVROXWHSUHVVXUHLVN3DDQGWKHWHPSHUDWXUHLV&7KHSUHVVXUHGURSDFURVVWKHRULILFHLVN3DDQGWKHFRHIILFLHQWRIGLVFKDUJHLV'HWHUPLQHWKHPDVVIORZUDWHLQWKHSLSHOLQH

    77L

    N

    N

    33

    L

    .

    YL57

    L3

    LPNJ

    3HN3D7

    H.Y

    HPNJ

    P

    LP

    HV

    LV

    H'

    H'

    LY

    LY

    H

    KLK

    HV

    H&

    S7

    L7

    H

    VHV

    PV

    P

    &'$VYNJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    59/68

    $FULWLFDOQR]]OHLVXVHGIRUWKHDFFXUDWHPHDVXUHPHQWRIWKHIORZUDWHRIDLU

    ([KDXVWIURPDFDUHQJLQHLVGLOXWHGZLWKDLUVRLWVWHPSHUDWXUHLV&DWDWRWDOSUHVVXUHRIN3D,WIORZVWKURXJKWKHQR]]OHZLWKWKURDWDUHDRIPPE\

    VXFWLRQIURPDEORZHU)LQGWKHQHHGHGVXFWLRQSUHVVXUHWKDWZLOOOHDGWRFULWLFDOIORZLQWKHQR]]OHDQGWKHPDVVIORZUDWH

    33R

    N3D77R

    .

    Y573PNJ

    F N57 PV

    P

    $FY NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    60/68

    6WHDPDWN3D&IORZVWKURXJKDFRQYHUJHQWGLYHUJHQWQR]]OHWKDWKDVDWKURDWDUHDRIPP7KHSUHVVXUHDWWKHH[LWSODQHLVN3DDQGWKHH[LW

    YHORFLW\LVPV7KHIORZIURPWKHQR]]OHHQWUDQFHWRWKHWKURDWLVUHYHUVLEOH

    DQGDGLDEDWLF'HWHUPLQHWKHH[LWDUHDRIWKHQR]]OHWKHRYHUDOOQR]]OHHIILFLHQF\DQGWKHHQWURS\JHQHUDWLRQLQWKHSURFHVV

    KR

    N-NJVR

    N-NJ.

    33R

    NNN3N3D

    $W3VVR

    KN-NJYPNJ

    K99 PV

    P

    $9

    Y

    NJV K

    HK

    R9

    H N-NJ

    ([LW3HK

    HY

    HPNJV

    HN-NJ.

    $HP

    Y

    H9

    HP

    VJHQ

    VHV

    RN-NJ.

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    61/68

    6WHDPDWN3D&LVIHGWRDVHWRIFRQYHUJHQWQR]]OHVLQDVWHDPWXUELQH7KHWRWDOQR]]OHH[LWDUHDLVPDQGWKH\KDYHDGLVFKDUJHFRHIILFLHQWRI

    7KHPDVVIORZUDWHVKRXOGEHHVWLPDWHGIURPWKHPHDVXUHPHQWRIWKH

    SUHVVXUHGURSDFURVVWKHQR]]OHVZKLFKLVPHDVXUHGWREHN3D'HWHUPLQHWKHPDVVIORZUDWH

    ,QOHW%KLN-NJV

    LN-NJ.

    ([LW3HV

    HV3

    H3

    LN3DV

    HVV

    LN-NJ.

    KHV

    N-NJDQGYHV

    PNJ

    9HV

    PV

    P

    V$9HVYHV NJV

    P

    D&

    'P

    VNJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    62/68

    $FRQYHUJHQWQR]]OHLVXVHGWRPHDVXUHWKHIORZRIDLUWRDQHQJLQH7KH

    DWPRVSKHUHLVDWN3D&7KHQR]]OHXVHGKDVDPLQLPXPDUHDRIPPDQGWKHFRHIILFLHQWRIGLVFKDUJHLV$SUHVVXUHGLIIHUHQFHDFURVVWKH

    QR]]OHLVPHDVXUHGWRN3D)LQGWKHPDVVIORZUDWHDVVXPLQJLQFRPSUHVVLEOHIORZ$OVRILQGWKHPDVVIORZUDWHDVVXPLQJFRPSUHVVLEOHDGLDEDWLFIORZ

    $VVXPH9LY

    L57

    L3

    L PNJ

    9HV

    KLK

    HVY

    L3

    L3

    HN-NJ

    9HV

    PV

    P

    V$9

    VY

    L NJV

    H

    P

    D&

    'P

    VNJV

    7HV7L3H3LNN.

    K&S

    7 9HV

    9HV

    PV

    YHV

    PNJ

    P

    V$9

    VY

    HV NJV

    H

    P

    D&

    'P

    VNJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    63/68

    7KHFRHIILFLHQWRIGLVFKDUJHRIDVKDUSHGJHGRULILFHLVGHWHUPLQHGDWRQHVHWRI

    FRQGLWLRQVE\XVHRIDQDFFXUDWHO\FDOLEUDWHGJDVRPHWHU7KHRULILFHKDVD

    GLDPHWHURIPPDQGWKHSLSHGLDPHWHULVPP7KHDEVROXWHXSVWUHDP

    SUHVVXUHLVN3DDQGWKHSUHVVXUHGURSDFURVVWKHRULILFHLVPPRIPHUFXU\7KHWHPSHUDWXUHRIWKHDLUHQWHULQJWKHRULILFHLV&DQGWKHPDVVIORZUDWHPHDVXUHGZLWKWKHJDVRPHWHULVNJPLQ:KDWLVWKHFRHIILFLHQWRIGLVFKDUJH

    RIWKHRULILFHDWWKHVHFRQGLWLRQV"

    3 N3D

    77L

    N

    N33

    L

    YL57

    L3

    LPNJY

    H57

    H3

    HPNJ

    9L

    9H

    $H

    YL

    $L

    YH

    9H

    9H9

    L9

    HK

    LK

    H&

    S7

    9H PV

    P

    $H9

    HY

    H

    NJV

    &'

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    64/68

    $FRQYHUJHQWQR]]OHZLWKH[LWGLDPHWHURIFPKDVDQDLULQOHWIORZRI&N3DVWDJQDWLRQFRQGLWLRQV7KHQR]]OHKDVDQLVHQWURSLFHIILFLHQF\RIDQGWKH

    SUHVVXUHGURSLVPHDVXUHGWRFPZDWHUFROXPQ)LQGWKHPDVVIORZUDWH

    DVVXPLQJFRPSUHVVLEOHDGLDEDWLFIORZ5HSHDWFDOFXODWLRQIRULQFRPSUHVVLEOHIORZ

    &RQYHUW3WRN3D

    3FP+

    2N3D

    7

    &. 3

    N3D

    $VVXPHLQOHW9L 3

    H3

    3N3D

    7H7

    3H

    3

    N

    N

    9HK

    LK

    H&

    S7

    L7

    H

    N-NJ-NJ !9HPV

    9HDF

    9HV 9

    HDFPV

    7HDF

    7L

    9HDF

    &S

    .

    HDF

    3H

    57S

    NJP

    P

    $9

    NJV

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    65/68

    5HYLHZ3UREOHPV

    $WZKDW0DFKQXPEHUZLOOWKHQRUPDOVKRFNRFFXULQWKHQR]]OHRI3UREOHPLIWKHEDFNSUHVVXUHLV03D"WULDODQGHUURURQ0

    [

    5HODWHWKHLQOHWDQGH[LWFRQGLWLRQVWRWKHVKRFNFRQGLWLRQVZLWKUHYHUVLEOH

    IORZEHIRUHDQGDIWHUWKHVKRFN,WEHFRPHVWULDODQGHUURU

    $VVXPH0[

    0\

    3R\

    3R[

    $(

    $[

    $

    $

    $[

    $[

    $[

    $\

    $(

    $\

    $(

    $[

    $[

    $\

    $[

    $[

    0(3(3R\ 3

    (3

    (3

    R\3

    R\3

    R[3

    R[ N3D03D

    6RVHOHFWWKHPDFKQXPEHUDOLWWOHOHVV

    0[

    0\

    3R\

    3R[

    $[

    $[

    $[

    $\

    $(

    $\

    $(

    $[

    $[

    $\

    $[

    $[

    0(

    3(

    3R\

    3(

    3(

    3R\

    3R\

    3R[

    3R[

    N3D

    1RZLQWHUSRODWHEHWZHHQWKHWZR 0

    [0

    \3

    R\3

    R[

    $[

    $[

    $[

    $\

    $(

    $\

    0(

    3(

    3R\

    3(

    N3D2.

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    66/68

    $WPRVSKHULFDLULVDW&N3DZLWK]HURYHORFLW\$QDGLDEDWLFUHYHUVLEOHFRPSUHVVRUWDNHVDWPRVSKHULFDLULQWKURXJKDSLSHZLWKFURVVVHFWLRQDODUHDRI

    PDWDUDWHRINJV,WLVFRPSUHVVHGXSWRDPHDVXUHGVWDJQDWLRQSUHVVXUHRI

    N3DDQGOHDYHVWKURXJKDSLSHZLWKFURVVVHFWLRQDODUHDRIP :KDWDUHWKHUHTXLUHGFRPSUHVVRUZRUNDQGWKHDLUYHORFLW\VWDWLFSUHVVXUHDQG

    WHPSHUDWXUHLQWKHH[LWSLSHOLQH"

    &9FRPSUHVVRURXWWRVWDQGLQJDLUDQGH[LWWRVWDJQDWLRQSRLQW

    P

    KR

    :

    "FP

    K9

    H[P

    K

    RH[

    P

    VR

    P

    VRH[

    3URH[

    3UR

    3VWH[

    3R

    7RH[

    .KRH[

    N-NJKR

    N-NJ

    :

    FP

    K

    RH[K

    RN:

    3H[

    3RH[

    7H[

    7RH[

    NN7H[

    7RH[

    9 H[

    &S

    P

    NJV$9H[

    3H[

    $9H[

    57H[

    1RZVHOHFWXQNQRZQDPRQJVW3H[

    7H[

    9H[

    DQGZULWHWKHFRQWLQXLW\HTP

    DQGVROYHWKHQRQOLQHDUHTXDWLRQ6D\XVH7H[

    WKHQ

    9H[

    &S

    7RH[

    7H[

    P

    NJV3RH[

    7H[

    7RH[

    NN$ &S

    7RH[

    7H[

    57H[

    VROYHIRU7H[7RH[FORVHWR

    7H[

    .9H[

    PV3H[

    N3D

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    67/68

    6ROXWLRQXVLQJWKH3URUYUIXQFWLRQV

    $MHWSODQHWUDYHOVWKURXJKWKHDLUZLWKDVSHHGRINPKDWDQDOWLWXGHRI

    NPZKHUHWKHSUHVVXUHLVN3DDQGWKHWHPSHUDWXUHLV&&RQVLGHUWKHLQOHWGLIIXVHURIWKHHQJLQHZKHUHDLUOHDYHVZLWKDYHORFLW\RIPV'HWHUPLQHWKH

    SUHVVXUHDQGWHPSHUDWXUHOHDYLQJWKHGLIIXVHUDQGWKHUDWLRRILQOHWWRH[LWDUHDRI

    WKHGLIIXVHUDVVXPLQJWKHIORZWREHUHYHUVLEOHDQGDGLDEDWLF

    9NPKPVY

    57

    3

    PNJ

    K

    N-NJ3U

    KRN-NJ

    7R

    .3UR

    7KHUDWLRRIWKHSUHVVXUHVHTXDOVWKHUDWLRRIWKH3UIXQFWLRQVZKHQVFRQVWDQW

    3R

    33UR

    3U

    N3D

    K

    7

    .3U

    3

    N3D

    Y

    PNJ

    $

    $

    Y

    Y

    9

    9

  • 8/14/2019 solution manual for fundamental thermodynamic sixth edition chapter 16

    68/68

    5HSHDW3UREOHPDVVXPLQJDGLIIXVHUHIILFLHQF\RI

    6DPHDVSUREOHPH[FHSW

    '

    :HWKXVKDYHIURP

    K

    K

    KR

    K

    K

    K

    N-NJ3U

    3R

    3

    N3D

    h

    01

    02

    3

    1

    2

    s

    3UR3UR

    KN-NJ7.3U

    33R3U3UR N3D

    Y PNJ

    $$


Recommended