Chuyên Đề Nhiệt Hóa Học

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    Chuyn NHIT HA HC Trang 11) KH L TNG:* Kh l tng l cht h ! h"#ng c$ch g%&a c$c 'h(n t) h a nhau+ c, th- ./ 0ua tng t$c g%&a ch2ng3* 45% h l tng th6 c, th- $' 78ng 9: ;hng tr6nh trT ?> = @+1B D!"l3K = E+E@F l3at!D!"l3KG

    - Trong bnh c hn h p khth: P = Pi = Vni.RT

    cn Pi= Ni.P = .Pnini

    2) H V MI TRNG:- H m:h tra" % cht J nng lLng J5% !M% trng3- H kn:H chO tra" % nng lLng J5% !M% trng3- H on n!"#:H hMng tra" % nh%t J5% !M% trng3* Quy c:H nhPn nng lLng cQa !M% trng nng lLng !ang 7u RH nhng nng lLng ch" !M% trng nng lLng !ang 7u :$) %I&N '(I TH*N NGH+,H:

    NSu h chuy-n t trn!cQa !Wt cht l lLng nh%t Lc 'h$t ra hay thu J" tr"ng 'h#n ^ng t

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    Chuyn NHIT HA HC Trang Fb$c [nh h%u ^ng nh%t cQa 'h#n ^ng9 F C R B HFHF R CFHmHH" t? calD!"l G : io+i :i@+ :Fi+o

    %>" #EF AF CDn #n! !" n n!"#

    1= b$c [nh h%u ^ng cQa 'h#n ^ng ]t ch$y gluc"Vp %u %n t%u chujn3 d%St9

    CiH1Fi?gluc"VpG CF?G HF?lGk%nh nh%t HV?calD!"lG :EB+E :B+m :i@+

    2= b$c [nh h%u ^ng cQa 'h#n ^ng thQy 'h(n urp thnh CFJ NH3 d%St9

    ?NHFGFC77?urpG HF?lG CF?77G NH?77Gk%nh nh%t HV ?calD!"lG :oi+ :i@+ :@+o :1+

    $= Cqn t%u t]n nh%t lLng .Ung .a" nh%u - %u chS 1EEE g can% cac.ua rn t Ca ?rnG J C ?rnG s

    Ca ?rG R C ?rG CaCF ?rG R C ?GH" V ?D!"lG : im+m :m+B : 11E+m \k9 oFom 'AF J?:- 1 k@

    = b$c [nh h%u ^ng nh%t cQa 'h#n ^ng9

    CiH1Fi?rG R i F?G

    i HF?lG R i CF?GH" V? calD!"l G : EB+i :i@+ :B+B'AF J?: - 4O14 k@

    = b$c [nh h%u ^ng nh%t cQa 'h#n ^ng9

    C R FNF FNF R CFH" V? calD!"l G 1o+o : B+B

    NSu chO c, FF g NF tha! g%a 'h#n ^ng th6 lLng nh%t g%#% 'h,ng l .a" nh%us'AF J?: $2 k@

    O) '+NH L*T HP..:H ?G cQa 1 0u$ tr6nh chO 'h8 thuWc J" tr

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    Chuyn NHIT HA HC Trang Ca ?rG : im+mm NaHC?rG : o1E+BB

    CF?G :+m1 NHBCl?rG : 1m+

    HF ?lG :F@m+@m NaFC?rG : 1BE+E

    NaCl ?rG : B1E+ CaClF?rG :oB+i

    Ca?HGF ?rG : @i+m

    '.= Tnh H"'thp" V%nh nh%t9H"'?1G = 1o@+EF H"'?FG = FF1+BF H"'?G = : i@@+mo H"'?BG = : im+1 H"'?mG = 1m@+ S=H"'?tngG = H"' ?1G R H"' ?FG R H"'?G R H"'?BG R H"'?mG = :1m+ @=CaC R F NaClCaClFR NaFC ?iGC=H"'?iG = :1m+ = H"'?tngG

    %>" #EF AF CDn n! E# HP..1= Tnh h%u ^ng nh%t cQa 'h#n ^ng9Ca R CFCaC ?aG+ H"

    Ch"9Ca R ?1DFG F Ca ?1G+ H" 1= : 1mF+ calC R F CF ?FG+ H" F= : B+BB calC R Ca R ?DFG F CaC ?G+ H" = : F@i+oo cal

    ?Trch V$ch d% tP' h,a hZc

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    Chuyn NHIT HA HC Trang BThp" [nh luPt HpVV ta c, V v9Thp" V v trn+ ta c,9 H" R H" = H" 1 R FH" F

    = H" = FH" F R H"1 : H" = : i+BF cal$= b$c [nh V%nh nh%t cQa apt%lpn nSu .%St th%u nh%t cQa n, l 1+i cal J V%nh nh%t cQa H F J CFtng ^ng

    .Ung i@+ cal J B+B cal3G"":Cqn tnh h%u ^ng nh%t cQa 'h#n ^ng9F C R HF CFHF ?cG+ H"

    Thp" .% ta c, 9

    CFHF R ?mDFGF F CFR HF ?1G+ H" t?CFHFG= : 1+i calC R F CF ?FG+ H" V?CFG= : B+BB calHF R ?1DFGFHF ?G+ H" V?HFG= : i@+ cal;h#n ^ng ?FG+?G ch" H" t?CG = : B+BB cal J H" t?HFG = : i@+ calTnh H" thp" th%u nh%t9H" = H" t?HFGR F H" t?CG :H" t?CFHFG= mi+BF cal= b$c [nh V%nh nh%t chujn Fm"C cQa 'r"'an %u %n zng $'+ zng tch3 d%St th%u nh%t cQa n, l FFFE D!"l JV%nh nh%t cQa HF J CFtng ^ng .Ung F@i D!"l J +m D!"l3G"":Cqn tnh h%u ^ng nh%t cQa 'h#n ^ng9 C R B HFCH@ H"

    Thp" .% ta c, 9CH@ R mF CFR B HF ?1G+ H" t?CH@G = : FFFE D!"lHF R ?1DFGF HF ?FG+ H" V?HFG = : F@i D!"lC R F CF ?G+ H" V?CFG = : +m D!"l;h#n ^ng ?FG+?G ch" H" t?HFG = : F@i D!"l H" t?CG = : +m D!"l: { %u %n zng $'9Tnh H" thp" th%u nh%t9H" = BH" t?HFGR H" t?CG : H" t?CH@G = : 1EB+m : { %u %n zng tch9

    H"

    = "

    R n >T = "

    = H"

    : n >T= :1EB+m ?1 : BG3@+1B3?1E : G3@ = : o+1 =b$c [nh nng lLng !

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    Chuyn NHIT HA HC Trang m: Tr"ng VY .%Sn % thuPn ngh[ch JM cXng nh/ T = c"nVt h tra" % J5% !M% trng !Wt lLng nh%t TNth6 VY .%Sn

    th%n pntr"'% tr"ng 0u$ tr6nh ny l9 7k=T

    QTN

    k l h! trln1

    F

    V

    V= n3>3ln

    F

    1

    P

    P

    12) ./ %I&N THI6N PNTRUI ,78 ,H0T NG56N ,H0T THPU NHIT '9=: u$ tr6nh ; = c"nVt9 \un n,ng 1 cht nguyn cht t T1TF+ hMng c, VY chuy-n 'ha9

    k = F

    1

    T

    T

    TN

    T

    Q45% = ;= 7H = n3C;37T

    k =T

    dTCn

    T

    T

    P33F

    1

    * Tr"ng h"#ng nh%t W h'+ c"% C;= c"nVt k = n3C;3ln1

    F

    T

    T

    : u$ tr6nh9 4 = c"nVt k = n 3C43ln1

    F

    T

    T

    1$) PNTRUI T5T '\I] NB^n III @_ n!"# `n !a@:: ntr"'% cQa cht nguyn cht 75% 7

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    Chuyn NHIT HA HC Trang i

    k = kT: k?T = EG= kT= =

    m

    1iiS

    kT=T

    dTCn

    T

    Ln

    T

    dTCn

    T

    Ln

    T

    dTCn

    T

    T

    hP

    S

    S

    T

    T

    lP

    nc

    nc

    T

    rP

    S

    S

    nc

    nc

    33333333 G?G?E

    G?

    1

    ++++%$ tr[ pntr"'% Lc $c [nh ; = 1 at! = c"nVt J nh%t W T n" , LcgZ% l g%$ tr[ pntr"'% chujn+ h%u l kET+ thng T = F@K kEF@1) ./ %I&N THI6N PNTRUI TRUNG HbN cNG HU3 H,:

    R Kh% 'h#n ^ng thYc h%n ; = c"nVt+ T = c"nVt th69 k = k?V'G : k?tDcGR NSu %u %n chujn J FmEC th69 kEF@= kEF@?V'G : kEF@?tDcGR 46 k cQa cht h cht rn+ l/ng nn nSu V] !"l h V#n 'hj! ?V'G V] !"lh tha! g%a th6 k E J ngLc lT3ln;?; tnh .Ung .ar ?at!GG31O) TNH G ,78 M9T .\ Q3 TRYNH:) G"n npn en n!"# k! #qn

    = n>T3ln1

    F

    P

    P= n>T3ln

    F

    1

    V

    V

    S) Tg`n rn en n!"# en AF 2 k! #qn:

    = nA3>TlnAR nd3>Tlnd@) QA #ghn! @!Bsn F! #!En n!@! ;#" n!"# ` @!Bsn F!): c= EC) QA #ghn! @!Bsn F! #!En n!@! T T@t

    Nguyn tc9 $' 78ng chu tr6nh nh%t Wng3 46 l h! tr

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    Chuyn NHIT HA HC Trang o

    1= Ch" 'h#n ng9 CaCCa R CF

    CaC Ca CFk%nh nh%t HV ?calD!"lG :F@@+m :1m1+ :B+1

    ntr"'% k ?calD!"l3"KG FF+F +m m1+1 b$c [nh ch%u tY #y cQa 'h#n ^ng ? tcG3 b$c [nh nh%t W t" 4: Tnh kEF@+ HEF@J EF@]% J5% 0u$ tr6nh 'h(n hQy nh%t CaC+ .%St9CaC Ca R CF ?*GkEF@?DK3!"lG RF+ @+1 F1+o HEht?D!"lG : 1FEi+E :im+1E :+mE%>" O: T" 1: Tnh EocQa 'h#n ^ng9 CHBR HF?G = C R HF3 d%St9

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    Chuyn NHIT HA HC Trang @Nh%t h6nh thnh chujn HEht F@cQa CHB+ HF?G J C lqn lLt .Ung :oB+@_ :FB1+@ J :11E+m D!"l3 ntr"'% chujn cQaCHB+ HF?G J C lqn lLt .Ung 1@i+F_ 1@@+o J 1o+i DK3!"l ?Tr"ng tnh t"$n g%# th%St rUng HEJ kEhMng 'h8thuWc TG3=T g%$ tr[ Et6! Lc c, th- St luPn g6 J h# nng tY 7%xn .%Sn cQa 'h#n ^ng oK3S=T" $:bt 0u$ tr6nh n,ng ch#y cQa n5c $ EEC J 1at! ta c, c$c 7& %n Vau (y9 Hnc?HF+ EEC+ 1at!G = i+EE@ D!"lC'?HF+ rG = o+F@ DK3!"lC'?HF+ lG = om+1F DK3!"lHy $c [nh .%Sn th%n pntan'% H+ .%Sn th%n pntr"'% k J .%Sn th%n cQa h tr"ng 0u$ tr6nh trn nhng #y razng $' t" ;hng tr6nh 'h#n ^ng9 HFR 1DFF= HFTa c,9 E= HE T3 kETr"ng ,9 kE= kE?HFG kE?HFG 1DFkE?FG = i+E1 1E+i@B :1DF3FEm+1@ = :1i+m DK3!"l= E= :F@m+@31E F@3?:1i+mG = Fo1m1+o D!"l = Fo+1mF D!"lG"" S>" 4Thp" 'hng tr6nh 'h#n ^ng ?*G ta tnh Lc9

    kE

    = k

    E

    ?CaG R k

    E

    ?CFG k

    E

    ?CaCG = @+1 R F1+o F+ = 1m@+ DK3!"l HE= HEht?CaG R HEht?CFG : HEht?CaCG = ?:im+1EG R ?:+mEG ?:1FEi+EG = 1o@+E D!"l= EF@= HEF@ T3 kEF@ = 1o@+E F@31m@+31E: = 1E+m D!"l EF@E ch^ng t/ FmEC J 1at! VY nh%t 'h(n CaChMng #y ra Lc3

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    Chuyn NHIT HA HC Trang G"" S>" OT%u chujn $nh g%$ ch%u h5ng tY 7%xn .%Sn cQa c$c 0u$ tr6nh #y ra %u %n zng nh%t+ zng $' l nng lLng tY 7"9 = H T3k = H T3 k ]% J5% 0u$ tr6nh zng nh%t3Kh% .ay h% cQa n5c ; = 1at!9

    HF ?lG = HF ?hG H = BEm@o+@E k = 1E@+i@ DK3!"l= = BEm@o+@E T3 1E@+i@

    Hy t6! nh%t W tG3?TF T1G 3n

    = ? PC : >G3?

    1

    F

    P

    P:1G3T13n = ?F+1 : @+1BG3? G1

    1

    m+1 3Fo+1m = 1B1B+EB?G

    .G 4"= G?@EB+FF3F@

    1EEl= 4= F4"= 1iE ?lG

    = :;3 4 = :1?1iE @EG = :@E ?l3atG = :@E 31E1+ = :@1Ei+B?G

    ;= H = PC 3n 3T =

    11

    1

    F 331+F3F@

    1EETT

    V

    V= F+13

    F@

    1EE?F3Fo+1m Fo+1mG = F@@@+1?G

    = R = F@@@+1 = @1Ei+B = FEF@1+o?GcG T = c"nVt = E_ H = E

    = : F

    1

    3V

    dVnRT = : n>T3ln

    1

    F

    V

    V

    = :F@

    1EE3@+1B 3Fo+1m3ln

    @E

    FEE= :oB1+io?G

    = R = E = : = oB1+io?G7G = E ?k = c"nVtGThp" ;T '"%VV"n9 T13 4

    11

    = TF3 41

    F

    TF= T13?F

    1

    V

    VG:1 45% B+1

    A1B+@1+Fl

    1+Fl

    =

    +==

    P

    P

    V

    P

    CR

    C

    C

    C

    = = n3 VC ?TFT1G =

    F@

    1EE?F+1:@+1BG3?1@+ :Fo+1mG = iFFF+B?G

    H = nPC 3T =

    F@

    1EE3F+1?1@+ Fo+1mG = : @o11+?G

    %>" 2:

    Tnho

    SH F@+ cQa Cl:?a0G3 d%St9

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    Chuyn NHIT HA HC Trang 1E

    ?aG9F

    1HFR

    F

    1ClF?GHCl?G

    o

    SH F@+ = :F+F?G

    ?.G9 HCl?GR a0 HR?a0GR Cl:?a0Go

    SH F@+ = :om+1?G

    ?cG9F

    1HFR a0 HR?a0GR p

    o

    SH F@+ = E

    ?ii:

    y ?aG R ?.G ?cG 9

    F

    1ClFR p R a0 = Cl:?a0G

    o

    SH F@+ = : 1io+?G

    %>" $:Tnh h%u ^ng nh%t cQa 'h#n ^ng9

    ~p?NGF?a0GR BHN?a0G~p?NG?a0GR N?GR FHF ?lGe%xn ra tr"ng n5c Fm"C3 Ch" .%St9 ~pFR?a0G ~pR?a0G N:?a0G N?G HF?lG

    o

    SH F@+ ?D!"lG :@o+@i : Bo+o :FEi+mo E+Fm :F@m+i?ii:;hng tr6nh %"n cQa 'h#n ^ng9~pFR?a0GR BHR?a0GR N:?a0G~pR?a0GR N?GR FHF ?lGH=3 oSH F@+ ?~pR+a0GR

    o

    SH F@+ ?NGRF3 o

    SH F@+ ?HF?lGG3 o

    SH F@+ ?~pFR+a0G: o

    SH F@+ ?N:+ a0G

    = 3?:Bo+oG R E+Fm R F3?:F@m+iG R 3@o+i R FEi+mo = :1m+?G%>" :1G k" V$nh H+ cQa c$c 'h#n ^ng9 CnHFnR HFCnHFnRF FG Kh% ]t ch$y h"n t"n F an"!p J cQa e gluc" !w% th^ 1 !"l $' Vut hMng %+ ng% ta " Lch%u ^ng nh%t cQa c$c 'h#n ^ng mEEK lqn lLt .Ung9:FoE+E J : F@Em+1aG Tnh ]% J5% !w% 'h#n ^ng3

    .G Tr"ng F 7T;h#n ^ng trn c,9 n = 1:F = :1 H = >T H FG CiH1FiR iFiCFR iHF?G= H?G: n3>T = : Fo i3@+1B31E:3mEE = :F@FB?G?G= H?G: n3>T = : F@Em+1 i3@+1B31E:3mEE = :F@E ?G

    oH = i3o

    COSH G? F R i3o

    OHSH G? F :o

    SH G?oH = i3

    o

    COSH G? F R i3o

    OHSH G? F :o

    SH G?

    oSH G? :o

    SH G? =oH :

    oH = :F@Em+1 R Fo = :i+1?G

    oSH G? o

    SH G? e

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    Chuyn NHIT HA HC Trang 11

    F

    AF?G _ C than ch6 C %! cng

    : y ?aG ?.G9

    C than ch6C %! cngo

    kcSH G? = 1+@ D!"l: y ?cG : ?7G9

    F

    AF?G?G

    o

    OSH G? = 1+@F D!"l

    FG NSu c"% c, cu tr2c J}ng n9

    o OSH G? =o

    OlkH G? :F

    A oOlkH G? F

    = 3?:1o+BG :F

    A3?: B+FBG = Fi+EB ?D!"lG 1+@F?D!"lG

    c, cu tr2c J}ng n rt hMng .n cu tr2c ny hMng ch' nhPn Lc3

    %>" 4:ntan'% V%nh t%u chujn cQa CH B?GJ CFHi?Glqn lLt .Ung :oB+@E J :@B+iE D!"l3 Tnh pntan'% t%u chujn cQa C BH1E?G3d%n luPn J St 0u# thu Lc3 Ch" .%St pntan'% thng h"a cQa than ch6 J nng lLng l%n St H: H lqn lLt .Ung9 o1E+iJ : B1+im D!"l3?ii:

    * ?1G C than ch6R FHF ?GCHB?Go

    CHSH B+ =:oB+@

    ?FG C than ch6C ?Go

    thH = o1E+i

    ?G HF ?GFH ?G lkH = B1+im y ?1G ?FG R F3?G ta Lc9

    C?GR BH?G CHB?Go

    CHtungSH B+D+ = :1iB@+o?D!"lG

    Nng lLng l%n St trung .6nh cQa l%n St C H l9B

    1?:1iB@+oG = : B1F+1om ?D!"lG3

    * ?BG FC than ch6R HFCFHi?Go

    KHCSH G+? iF = :@B+i ?D!"lG

    y ?BG F 3?FG R 3?G ta Lc9FC?GR iH?GCFHi?G

    o

    HCtungSHiF

    +D+ = :F@EE+om ?D!"lGC"% C Htr"ng CHBJ CFHinh nhau th69

    C: C= =1@EE+om i?: B1F+1omG = :Fo+o?D!"lG* C"% C:H_ C: Ctr"ng c$c cht CHB+ CFHi+ CBH1Eu nh nhau th69

    o

    HCtungSH1EB

    +D+ = 3 C: CR 1E3C: H = 3?: Fo+oG R 1E? :B1F+omG = :m11E+i ?D!"lG

    * ?mG BC?GR 1E H?GCBH1E?Go

    HCtungSH1EB

    +D+ = :m11E+i ?D!"lGy ?FG3 B R ?G3m R ?mG ta Lc9

    BCthan ch6R mHF?GCBH1E?Go

    HCSH1EB

    + = :1E+m?D!"lG

    * KSt 0u# thu Lc chO l gqn 2ng 7" c"% l?C CG+ l?C: HGtr"ng !Z% trng hL' l nh nhau3 4 J6 JPy V hMng tnh rLc

    o

    SH cQa c$c vng 'h(n h$c nhau3

    %>" O: Tnh H"cQa c$c 'h#n ^ng Vau91G ~pF?rGR FAl?rGF~p?rGR AlF?rG ? 1G

    Ch" .%Sto

    O!S rH

    G?F+ = :@FF+F D!"l_

    o

    O"lS rH

    G?F+ = :1ioi ?D!"lG

    FG k?rGRF

    AF?Gk?G ?FG

    d%St ?G 9 k?rGR F?GkF?GoHF@ = :Fi+i

    ?BG9 FkF?GR F?GFk?GoHF@ = :1m+i

    T St 0u# thu Lc J h# nng 7%xn .%Sn thYc tS cQa F 'h#n ^ng trn c, th- r2t ra St luPn g6s?ii:

    1Go

    #uH G1? =o

    O"lS rH

    G?F+ :

    o

    O!S rH

    G?F+ = :1ioi R @FF+F = : @m+@?G

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    Chuyn NHIT HA HC Trang 1F

    FGo

    #uH GF? =o

    #uH G? RF

    1 o#uH GB? = :Fi+i :

    F

    131m+i = :B+m@ ?G

    K9 Ha% 'h#n ^ng ?1G+ ?FG u t"# nh%t !Te" c$c 'h#n ^ng aG+ .G+ cG c, n = E nn " = H"

    ;h#n ^ng 7G9 "= H": n3>T = :1m+i R 13@+1B3 F@+1m3 1E: = :1+m ?GFG n?rGR HFkB?77GHF?GR nkB?77GTr"ng ."! nh%t lLng S c, 4 = c"nVt3

    = : o1+B@3@+imDi+F

    1= :1BF+i ?D!"lG

    H = R n3>T = : 1BF+i R 13 @+1B 3F@+1m 31E: = : 1BE+m ?D!"lG

    %>" W: Tnh H"cQa 'h#n ^ng tng hL' 1 !"l a7pn%np CmHmNm?rGt m !"l HCN?G3

    Ch" .%Sto

    kCHSH G++ B = : oB+@ ?D!"lG_o

    kNHSH ++ = :Bi+1D!"l_o

    r$d!ninSH G?+ = 1+1 D!"l

    4 CHB?GR NH?GHCN?GR HF?G H"= Fm1+F 3!"l:1

    ?ii:

    ?aG 9 Cgr R FHF?GCHBo

    kCHSH G++ B = :oB+@ ?D!"lG

    ?.G 9F

    1NF?GR

    F

    AHF?GNH?G

    o

    kNHSH ++ = : Bi+1D!"l

    ?cG 9 mCgrRF

    mHF?GR

    F

    mNF?GCmHmNm?rG

    o

    r$d!ninSH G?+ = 1+1 3!"l:1

    ?7G 9 CHB?GR NH?GHCN?GR HF?G H"= Fm1+F 3!"l:1

    Ta ly9 :m 3?aG R :m 3?.G R ?cG R :m3?7G ta Lc9mHCN?G CmHmNm?rGH"?BG= Fm1+F D!"l

    %>" 1X:

    Tnh nh%t th"$t ra h% tng hL' 1og NH 1EEEK3 d%Sto

    kNHSH G+?F@+ = :Bi+F 3!"l:1

    G+? kNHPC = FB+o R o+B@31E:T !"l:1K:1

    G+? F kNPC = Fo+@ R B+1@B31E:T !"l:1K:1

    G+? F kHPC = F@i R 1+1o31E:T !"l:1K:1

    ?ii:

    F

    1NF?GR

    F

    AHF?GNH?G

    o

    kNHSH ++ = : Bi+FD!"l

    C;= G+? kNHPC :F1 G+? F kNPC :

    FA G+? F kHPC

    = : FB+o R o+B@31E:T :F

    1Fo+@ R B+1@B31E: :

    F

    AF@+i R 1+1o 31E:T

    = : F+1 R 1+mB131E:T

  • 8/11/2019 Chuyn Nhit Ha Hc

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    Chuyn NHIT HA HC Trang 1

    = oH1EEEoHF@ R dTCP+

    1EEE

    F@ =

    oHF@ R dTTG1E3mB1+11+F?1EEE

    F@

    +

    =oHF@ R G

    F1E3mB1+11+F?

    F1EEE

    F@

    TT +

    = : Bi+F31ER1+mB1 31E:3F

    1?1EEEF:1@FG F+1?1EEE F@G= : mBiB+1@ ?D!"lG

    Kh% tng hL' 1o g NHth6 nh%t lLng t"# ra l9

    =1o

    1oEEE 3?:mBiB+1@ 31E:G = :mBiB+1@ ?G

    %>" 11:Tnh nng lLng ! J chP' nhPn hMng % tr"ng %u %n ch" cQa .% t"$n3

    Tnh th- tch cu]% cXng cQa h+ nh%t + .%Sn th%n nW% nng J cMng tr"ng !w% 0u$ tr6nh n,% trns?ii:

  • 8/11/2019 Chuyn Nhit Ha Hc

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    Chuyn NHIT HA HC Trang 1BaG T = c"nVt = E_ H = E = R = E = :

    = : =F

    1

    F

    1

    3V

    dVnRTdVP = : n>Tln

    1

    F

    V

    V

    45% h l tng9 ;1341= ;F34F 1

    F

    V

    V=

    F

    1

    P

    P 4F=

    F

    1

    P

    P3 41=

    1

    1E3 1E = 1EE?lG

    = :?n>TG3ln F

    1

    P

    P

    = :1E31E 3ln 1E = FE+Fm ?l3atG = FE+Fm 31E1+ 31E:= F+F ?G = : = :F+F ?G

    .G = E

    = = n3 VC 3 T = F

    33

    3

    1

    11

    TR

    VP3>?TF T1G

    = =F

    3

    3

    1

    11

    T

    VP?TF T1G

    Thp" ;T '"%VV"n9 T34: 1= c"nVt

    4 =P

    nRTT3

    1

    P

    nRT= c"nVt T3;: 1= c"nVt

    T .P =T# .P#

    TT#

    = P#P

    TT#

    P#P

    =

    1: 1:

    1:1:

    T#=T. =#2/+ .P#P

    1:

    1

    1:

    =!P!V

    !VR

    !V

    /# R R

    R=+

    /=

    -=- 1 = = /

    #

    1:

    +/

    +

    /

    /#

    T#=#2/+ .(1)-1=1*2 (7)

    % =8 = . (1*2 - #2/+) .1// =,*0(3)#2/01 .1

    V#= = /,* (") .#2/+1.1.1*2

    P#.T

    P.V.T#

    cG = E =

    n3 VC ?TF T1G = :;ng3?4F 41G = :;F3

    1

    1

    F

    F

    P

    nRT

    P

    nRT

    n3F

    A >?TF T1G = :n>31

    1E11F TT TF = E+iBT1

    V#= = 0(")T. 1.1.10T

    P#.T

    P.V.T#=

    = = :;ng?4F 41G = :1?iB 1EG = :mB?l3at!G= :mB?l3at!G 31E1+ 3Dl3at! = : mBo1+@F ?G

    %>" 1$ :

    ;h#n ^ng Vau9 Ag RF

    1ClF= AgCl

    b#y ra 75% $' Vut 1 at! J Fm"C t"# ra 1 nh%t lLng l 1Fi+mii 3

    NSu ch" 'h#n ^ng , #y ra tr"ng 1 nguyn t] ganJan% ;+ T = c"nVt th6 h"$ nng V Lc chuy-n thnh %n nng J V#nra cMng = 1E+iFF 3Hy ch^ng t/ rUng tr"ng c# F trng hL' trn+ .%Sn th%n nW% nng cQa h Jn chO l !Wt+ c}n nh%t th6 h$c nhau J tnhg%$ tr[ .%Sn th%n nW% nng ,3?ii:

  • 8/11/2019 Chuyn Nhit Ha Hc

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    Chuyn NHIT HA HC Trang 1m: e" l h! tr

  • 8/11/2019 Chuyn Nhit Ha Hc

    16/26

    Chuyn NHIT HA HC Trang 1i

    R E+m3E+F 3?oo oG RF

    1E F3E+m ?ooF oFG = m1oF?G

    %>" 1O: Tnh VY .%Sn th%n pntr"'% cQa 0u$ tr6nh un n,ng E+m !"l H F t mE"C Sn mEE"C ; = 1at!3 d%St nh%t n,ngch#y cQa n5c FoK = iEEBD!"l_ nh%t .ay h% cQa n5c FoK = BEiiED!"l3 Nh%t 7ung !"l zng $' oPC cQa n5c

    $ J n5c l/ng lqn lLt .Ung m+mi J om+D!"lK_ oPC cQa h% n5c l ?E+F R 1E:FTG D!"lK

    ?ii:

    HF?rG HF?rG HF?lG HF?lG HF?hG HF?hGk1 kF k kB km

    ooKoKoKFoKFoKFFK

    " " " " "

    kF kA kB km " " " "

    = R R R Rk"

    k1"

    = n3

    ++++

    Fo

    FF

    o

    Fo

    oo

    o

    G?G?G? 3o3

    Fo3

    T

    dTC

    L

    T

    dTC

    L

    T

    dTC hP

    hlP

    ncrP

    =E+m3

    +++++ Gooo?1E

    o

    ooln3F+E

    o

    BEiiE

    Fo

    oln3+om

    Fo

    iEEB

    FF

    Foln3mi+m F u W$;vwK)

    %>" 1:Tnh VY .%Sn th%n pntr"'% h% trWn ln FEEg n5c 1m "C J5% BEEg n5c iE"C3 d%St rUng h l cM lP' J nh%t7ung !"l cQa n5c l/ng l om+ D!"l3K

    ?ii:Z% T l nh%t W cQa h Vau h% 'ha trWn3e" thu= t"#nn9

    1@

    FEE3

    PC ?T F@@G = 1@

    BEE3

    PC ? TG

    T F@@ = F3 FT T =

    F@@3F += 1@?KG

    k h= k1R kF=T

    dT3+om3

    1@

    FEE1@

    F@@ R T

    dT3+om3

    1@

    BEE1@

    = 1@

    FEE3om+ ln F@@

    1@R 1@

    BEE3om+ ln AAA

    A1@

    = m+o@ ?DKG Eu$ tr6nh Van .Ung nh%t W ny tY #y ra3%>" 1W: Tnh VY .%Sn th%n pntr"'% J cQa VY h6nh thnh 1 !"l hwn hL' h l tng gv! FE NF_ mEHFJ ENHthp" th- tch3 d%St rUng hwn hL' h Lc t

  • 8/11/2019 Chuyn Nhit Ha Hc

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  • 8/11/2019 Chuyn Nhit Ha Hc

    18/26

    Chuyn NHIT HA HC Trang 1@dTN= : = FFo+F?Gkt'= k!tR kh

    kh?dTNG= kh?TNG=T

    QTN = =

    T

    &'F

    1 T

    dTnCV R dV

    V

    nRF

    1

    = n>ln1

    F

    V

    V= n>ln

    F

    1

    P

    P

    = 13@+1B 3ln1

    1m= FF+m1m?DKG

    k!t=T

    Qmt = :

    T

    Qh! =

    EE

    F+FFo= :o+oi?DKG kt'= FF+m1m : o+oi = 1B+omm ?DKG

    ?u$ tr6nh g%n n ny tY #y raGcG \"

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    19/26

    Chuyn NHIT HA HC Trang 1

    41=F

    F

    P

    nRT= 1+iB?lG

    = = 13F

    A3@+1B3?1@@: EEG = :1i+omF?G

    kt'= kh=T

    QTN = =

    T

    &'

    F

    1

    T

    T

    VT

    dTnC R dV

    T

    PV

    V

    F

    1

    = F

    1

    lnT

    T

    V TdnC R dVV

    nRV

    V

    F

    1

    = nC4ln 1

    F

    T

    T

    R n>ln 1

    F

    V

    V

    = 13 F

    A

    3@+1B3ln AEE

    1@@

    R 13 @+1B 3ln iB+1

    B1i+1m

    = 1F+@E1?DKG E

    %>" 2$: Tnh EFoG cQa 'h#n ^ng9 CHB?G R HF ?GC?GR HF?Gd%St9 CHB?G HF ?G C?G HF?G

    EF@+SH ?D!"lG : oB+@ : FB1+@ :11E+m E

    EF@S ?D!"lKG 1@i+F 1@@+o 1o+i 1E+i@B

    aG T g%$ tr[ Et6! Lc c, th- St luPn g6 J h# nng tY 7%xn .%Sn cQa h# nng 'h#n ^ng o"Ks.G T" 2: ntan'% tY 7" chujn cQa 'h#n ^ng t

  • 8/11/2019 Chuyn Nhit Ha Hc

    20/26

    Chuyn NHIT HA HC Trang FE

    cG ETG =ETH : T3

    ETS

    45% 'h#n ^ng h"$ hZc T = c"nVt3 NSuE

    G E ;h#n ^ng tY 7%xn .%Sn thp" ch%u ngh[ch3EG = E 9 ;h#n ^ng trTln ch^ hMng 'h#% 7Ya J" E3@uy nhiAn7 c thB coi rCng ETG -- . th0 )u( tr0nh c thB xy ra !#c c D !iEu kin chuFn G !iEu kin thHc' Ihi

    E

    TG -- . th0 GE nguyAn tJc chK c )u( tr0nh ng#c l&i mi xy ra7 khLng thB x(c !Mnh !#c chnh x(c gii h&n cOaE

    TG m tho ! )u( tr0nh xy ra tho chiEu ny hay chiEu kh(c' "t c(ch gRn !Sng c thB coi rCng c(c gii h&n nykhong chTng 6. kU9mol,'

    %>" 2O: Wt h l tng c, C4= > hMng 'h8 thuWc T Lc g%n n "" 2: Tnh cht nh%t Wng cQa !Wt V] 'h(n t) J %"n tr

  • 8/11/2019 Chuyn Nhit Ha Hc

    21/26

    Chuyn NHIT HA HC Trang F1

    : tt= : F

    1

    3dVP = :;3 4 = :n?G3>T

    = 3 @+1Bm3F@+1m = oBi+?G: = E

    .G u$ tr6nh thuPn ngh[ch9: TN= T3 k = F@+1m ?:oB+oBG = : 111oF@+o1?G: !a= = :F1E@+Fo?G E 9 H V%nh cMng: tt= : n?G3>T = oBi+?G E9 h nhPn cMng

    G aG u$ tr6nh .t thuPn ngh[ch9

    k!t =T

    Qmt = :T

    Q(TN = :T

    HE= :

    1m+F@

    1E3FFFE = oBBm+ 1i ?DKG

    k J tr8= k!t R k h= oBBm+1i : oB+oB = oEo1+1oi?DKG.G u$ tr6nh thuPn ngh[ch9

    k!t =T

    Qmt = :T

    QTN = GD?oB+oB1m+F@

    o1+111oF@K%=

    k J tr8= k!t R kh= EBG C$c n)a 'h#n ^ng9

    An"t9 CH@R FiH: FCO R 1oHF R FEpCat"t9 F R FHF R Bp BH:

    ;h#n ^ng tng cWng9

    CH@?G R mF?GR iH:?a0G F

    G? $)CO R oHF?lG

    k v '%n9?:G ;t+ CH@?1at!GDKH?mG+ KFC?1GD F?1at!G+ ;t ?RG

    E#uH = ?:ioo+1BG R o3?:F@m+@G R 1E+@m : m3E : i?:FF+G = :FmB@+BB?KGE

    #uS = 3?:mi+G R o3i+1 : Fi+1 : m3FEm+1@: i?:1E+oBG = :1F+B?KGE#uG =

    E#uH = T3

    E#uS = :FmB@+BB R F@+1m31F+B31E: = : FFoi+?KG

    E

    #u* = : nG

    E

    = iB@m3FEFFoi

    = 1+1@?4G

    = E: mi

    F

    F@33

    lg

    FE

    EmF+E

    OHC PPOH

    CO

    = 1+1@ :FE

    EmF+Elg?mG:i= 1+1?4G

    ; = 3I = 1+1 3E+1 = E+11?G

    %>" 2W: Tnh .%Sn th%n pntr"'% h% chuy-n B1@+B nh%t t JPt c, tE= 1mE"C Sn JPt c, tE= mE"C3?ii:u$ tr6nh .%Sn % trn l hMng thuPn ngh[ch Lc c"% nh gv! 0u$ tr6nh .%Sn th%n thuPn ngh[ch91G 4Pt 1mE"C truyn nh%t thuPn ngh[ch T = c"nVt3

    k1= T

    Q= 1m+Fo1mE

    B+B1@

    +

    = : E+@?DKG

    FG H .%Sn th%n "

  • 8/11/2019 Chuyn Nhit Ha Hc

    22/26

    Chuyn NHIT HA HC Trang FF

    +o! &o" $#9 " -+o! &o" $#9(r)

    (/)

    ABTN=J

    ()(K@< trnh TN Lo$#9 hMi bo ho;nO& cn bOng Q i $#9("))

    - +o! &o" $#9

    #* Torr

    (#)-+o! &o" $

    #9 (h)

    #+ Torr

    ?1G+ ?G l 0u$ tr6nh chuy-n 'ha thuPn ngh[ch1 = = E

    = F= n>Tln1

    F

    P

    P= 13@+1B3 Fm@+1m ln

    BF@+1

    F1m+1 = :Bi+i@o?G

    %>" $1: C, 1 !"l Fnguyn cht Fm"C+ Fat!+ 1 !"l Fnguyn cht Fm"C+ 1at!1 !"l F Fm"C tr"ng hMng h trn !`t t ?; = 1at!+ Fch%S! F1 4 hMng hG: k" V$nh g%$ tr[ h! cQa 1 !"l Ftr"ng trng hL' trn hn ! nhau .a" nh%u s3 T , r2t ra St luPn9 Kh# nng

    'h#n ^ng cQa Ftr"ng !w% trng hL' trn ca" hay th' hn V" J5% trng hL' h$cs?ii:

    * El h! %.. cQa 1 !"l F 1at!: 1 !"l F+ 1at!+ Fm"C 1 !"l F+ Fat!+ Fm"C ?EG ?1G

    1= 1: E= n>Tln1

    F

    P

    P= 13 @+1Bm 3F@+1m3ln

    1

    F = 1o1@+F?G

    1 E3: Z% F l h! %.. cQa 1!"l F Fm"C tr"ng hMng h ?E+F1 at!G1!"l F+ Fm"C+ 1at! 1 !"l F+ Fm"C+ E+F1at! ?EG ?FG

    F= F: E= 13 @+1Bm 3F@+1m3ln1

    F1+E = :@i@+@?G

    F E34Py9F?1!"l F+ Fm"C+ E+F1at!G E?1 !"l F+ Fm"C+ 1at!G 1?1 !"l HF+ Fm"C+ Fat!G: 1 cht c, h! cng ca" th6 cng ! .n 1 !"l F Fm"C+ Fat! c, h# nng 'h#n ^ng ca" nht c}n 1 !"l FnU!tr"ng hMng h th6 . nht c, h# nng 'h#n ^ng ! nht3

    %>" $2: Nh%t h" tan ?HhtG E+ioFg 'hpn"l tr"ng 1m+g cl"r""! l :@@ J cQa 1+mig 'hpn"l tr"ng 1B@+igcl"r""! l :1oF3Tnh nh%t 'ha l"ng ]% J5% 7ung 7[ch c, nvng W nh 7ung 7[ch th^ F ch^a 1 !"l 'hpn"l h% 'ha l"ng Sn nvng W cQa7ung 7[ch th^ nht .Ung cl"r""!3?ii:

    ,g phGno" !$!"/ LL # LL $ pha "ong!$!"/$ht (#)

    $ht()

    $ pha "ong= $ht()- $ht(#)

    =- .(-2#) (-**) =- #11*2(3)102#,

    +0,,

    %>" $$: Nh%t h" tan 1 !"l KCl tr"ng FEE !l n5c 75% $' Vut ; = 1a!t l9 tEC F1 F

    H 1@+1mB 1o+@FB ?Gb$c [nh HF@J V" V$nh J5% g%$ tr[ thYc ngh%! l 1o+mo@ ?G?ii:Thp" [nh luPt K%rchh"9HFB= HF@R C;3?FB : F@G = 1@+BmB ?GHF@i= HF@R C;3?Fi : F@G = 1o+@FB?G

  • 8/11/2019 Chuyn Nhit Ha Hc

    23/26

    Chuyn NHIT HA HC Trang F

    HFl@ = 1o+BB ?G

    C;= :E+1im ?DKG

    HFl@?TG: HFl@?TNGHFl@?TNG

    E+B@

    4Py HF@tnh Lc thp" l thuySt Va% h$c J5% g%$ tr[ TN l E+B@3

    %>" $: Tnh

    k cQa 0u$ tr6nh h"$ h% !"l HF ?lG Fm"C+ 1at!3

    Ch"9 Hhh+ HF?lG= BE+imi D!"l_ G?+ F lOHPC = om+F1 ?DK3!"lG_ G?+ F hOHPC = +m@ ?D!"lKG?ii:bt chu tr6nh9

    #+o! / &o" $#9(") at& #+o! / &o" $#9(r) at&

    11o! /&o" $#9(")at& 11o! /&o" $#9 (h)at&

    5

    5

    5#

    5/

    k1=TQ1 =

    F

    1

    33 G?

    T

    T

    lPTdTCn = nC;?lGln

    1

    F

    TT = 3 om+F13ln

    1m+F@1m+o = mE+i@FF?DKG

    kF=T

    QF =T

    Hn lhh33 = 31m+o

    1E+imi+BE = Fi+@iEm?DKG

    k=T

    Q = 1

    F

    33 G?

    T

    T

    hPT

    dTCn = nC;?hGln

    1

    F

    T

    T= 3 +m@3ln

    1m+o

    1m+F@= : FF+iEBB?DKG

    k = k1R kFR k= mB+@ ?DKG

    %>" $:

    aG Tnh cMng tr"ng 0u$ tr6nh ]t ch$y 1 !"l rLu ptyl%c c J Fm"

    C3.G NSu HF 73T = @+1B3F@1m = FBo@+@F ?G

    .G NSu HF 7T = :F 3@+1B 3F@+1m = : Bmo+iB?G

    %>" $4: Tnh k+ tr"ng 0u$ tr6nh g%n hMng thuPn ngh[ch F !"l h l tng t Blt Sn FE lt mB"C3?ii:46 k+ l c$c h! tr" $O: Wt .6nh c, th- tch 4 = m?lG Lc ngn l! F 'hqn .Ung nhau3 ;hqn 1 ch a NF F@K J $' Vut Fat!+ 'hqnF F@K J $' Vut 1at!3 Tnh + H+ k cQa 0u$ tr6nh trWn ln F h h% ng% ta ./ J$ch ngn %3

    ?ii:

    T = F@K _ 4.?NFG = 4.?FG =F

    m?lG

    k = k?NFG R k?FG = FNn 3>ln1

    F

    V

    VR

    FOn >ln

    1

    F

    V

    V =

    RT

    VP NN FF 3 >lnm+F

    mR

    RT

    VP OO FF 3 >lnm+F

    m

  • 8/11/2019 Chuyn Nhit Ha Hc

    24/26

    Chuyn NHIT HA HC Trang FB

    = Fln33

    FFFF

    T

    VPVP OONN + = E+E1oB?l3atDKG = E+E1oB 31E1+Fm = 1+oi ?DKG

    : u$ tr6nh zng nh%t H = E = H : T3 k = : F@ 31+oi = : mFm+oB ?G

    %>" $: Ch" c$c 7& l%u Vau (y F@K

    Cht ESH ?D!"lKG kE?D!"lKG 4?!D!"lGCthan ch6 E+EE m+ii m+131Ei

    C%! cng 1+E F+BFo +B1i31E:i1G F@K c, th- c, !Wt 'hqn rt nh/ %! cng cXng tvn t" $W: ;h#n ^ng g%&a n J 77 CukB#y ra tr"ng ]ng ngh%! t"# ra lLng nh%t FE+oi3 Cng 'h#n ^ng trnch" #y ra tr"ng '%n %n th6 !Wt 'hqn h"$ nng chuy-n thnh %n nng3 CMng %n cQa '%n l F1E+ioF3 Ch^ng !%nhrUng9 cQa F 0u$ tr6nh hMng %+ nhng nh%t t"# ra thay %3 Tnh k cQa 'h#n ^ng+ k!tJ kt's Ch" T = EEK?ii: n R CukB= nkB R Cu: Kh% thYc h%n tr"ng ]ng ngh%!9 ?T%Sn hnh .t thuPn ngh[chG4n

    4Cu

    tt= E _ = E

    dTN = dTN= H = :FE+oi: Kh% thYc h%n 'h#n ^ng tr"ng '%n %n ?0u$ tr6nh thuPn ngh[chG!a= : F1E+ioF ?G = !a= :F1E+ioF?GHTN= HdTN= : FE+oi?GTN= T3 k = H : = :FE+oi R F1E+ioF = :FE+EiB?G

  • 8/11/2019 Chuyn Nhit Ha Hc

    25/26

    Chuyn NHIT HA HC Trang FmTN= R R ;3 4 = :FE+EiB = F1E+ioF R E = :FE+oi ?G = dTN

    : kh=T

    QTN = :EE

    1E3EiB+FE = ii+@@?DKG

    k!tdTN= :T

    Q(TN =EE

    1E3oi+FE = oi+1F?DKG

    kt'?dTNG= oEF+FB?DKG

    k!t?TNG= :

    T

    QTN = :khkt'?TNG= E

    %>" X:: '= !a

    bt 1 'h#n ^ng thuPn ngh[ch tr"ng '%n %n th6 '= !a E : Nhng !Wt hZc V%nh J%St rUng9Tr"ng !Z% 0u$ tr6nh luMn c,9 k J tr8= k!tR k h ?1G H!t= : H h ?FG

    k!t=T

    Hmt = :T

    Hh! k J tr8= :T

    Hh! R k h

    T3 k J tr8= : H hR T3 k h = : h45% 0u$ tr6nh thuPn ngh[ch th6 k J tr8= E h= E '= EHy g%#% thch !(u thun ny3?ii:?FG chO 2ng h% ng"% cMng g%n n h hMng thYc h%n cMng n" h$c9H = R ;3 4 = H : ;3 4 = : = ?H : ;3 4G : ?:;3 4 R G h= H h: = : H !tChO h% = E th6 H!t= : H h* Tr"ng '%n9 !a= E nn H!tH h3%>" 1: bt 'h#n ^ng9 n?rG R CuFR?a0GnFR?a0GR Cu?rG7%xn ra tr"ng tc Fm"C3aG Tnh + + + H+ + k cQa 'h#n ^ng %u %n trn3d%St9 nFR?a0G n?rG Cu?rG CuFR?a0G

    EF@+SH ?D!"lG :1mF+B E E iB+

    EF@S ?D!"l3KG : 1Ei+m B1+i + : @+o

    .G bt h# nng tY 7%xn .%Sn cQa 'h#n ^ng thp" F c$ch h$c nhau3cG NSu thYc h%n 'h#n ^ng trn 1 c$ch thuPn ngh[ch tr"ng '%n %n th6 c$c St 0u# trn c, g6 thay %s Tnh '%ns?ii:

    aGE#uH =

    E

    + F+

    +nSH R

    E+CuSH : +

    E++nSH

    E

    + F+

    CuSH = :1mF+B : iB+ = :F1i+o ?G

    E

    #uS =E

    G?F $)+nS + R

    EG?rCuS :

    EG?r+nS :

    E

    G?F $)CuS + = :1Ei+m R + : B1+i R @+o = :1i+1 ?DKG

    E

    #u

    G

    =

    EH

    : T3

    ES

    = :F1i+o R F@+1m 31i+131E:= :F11+?G

    "= ;=E#uH = :F1i+o ?G

    = E_ 0u$ tr6nh dTN_ = E

    .G *E#uG = :F11+ ?G E ? : BE G

    e"E#uG rt (! nn 'h#n ^ng tY #y ra hMng nh&ng c ! c}n c# c$c %u %n h$c n&a3

    * k!t=T

    Qmt =T

    Hh!E

    =1m+F@

    1E3o+F1i = oFo+1F ?DKG

    k J tr8= k hR k!t= :1i+1 R oFo+1F = o11+EF ?DKG46 k h cM lP'= k J tr8= o11+EF ?DKG E

    u$ tr6nh l .t thuPn ngh[ch 'h#n ^ng tY #y ra3cG Kh% thYc h%n 'h#n ^ng trn TN tr"ng '%n %n th6 c$c g%$ tr[ HE+ kE+ E+ EhMng thay % 7" H+ k+ + l c$ch! tr

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    Chuyn NHIT HA HC Trang Fi

    k!t=T

    Qmt =T

    Qh! = 1i+1 ?DKG k J tr8= k!tR kh= E

    '%n= :n

    G E=

    iB@m3F

    F11E1+1?4G

    %>" 2:\]% J5% nguyn t] \an%pn 1m "C ng% ta $c [nh Lc V^c %n Wng = 1+Eo4 J h V] nh%t W cQa V^c %n

    WngT

    *

    = E+EEEBF 4DK3 Hy tnh h%u ^ng nh%t cQa 'h#n ^ng h"$ hZcs

    ?ii:

    = : n~ T

    G

    = : n~3

    T

    *

    = : k k = n~ 3

    T

    *

    H = R T3 k = n~3?T3T

    *

    : G

    H = F3 iB@m 3?F@+1m3E+EEEBF : 1+EoG : : 1@o1iF+m?G%>" $: Ch" 'h#n ^ng h"$ hZc9 n R CuFRnFRR Cu#y ra !Wt c$ch thuPn ngh[ch zng nh%t+ zng $' Fm"C tr"ng nguyn t] anJan%3k^c %n Wng cQa nguyn t] " Lc l 1+14 J h V] nh%t W cQa V^c %n Wng l

    PT

    *

    = +31E:m

    ?4DKG3aG Tnh h%u ^ng nh%t + .%Sn th%n %' J .%Sn th%n pntr"'% k cQa 'h#n ^ng h"$ hZc ch"3

    .G Tnh tncQa 0u$ tr6nhscG NSu cng 'h#n ^ng h"$ hZc trn thYc h%n cXng nh%t W J cXng $' Vut nhng tr"ng !Wt .6nh cqu thng th6 c$c g%$tr[ cQa + k V l .a" nh%us?ii:aG = : n~ = : F 31+1 3iB@m = : F1FFio?G

    k = :T

    G

    = n3~ 3T

    *

    = F 3iB@m 3+ 31E:m= i+i@ ?DKG

    H = R T3 k = F1FFio R F@+1m 3i+i@ = :F1Ei@+B?G

    .G tn= T 3 k = F@+1m 3i+i@ = 1@@+iF ?GcG NSu 'h#n ^ng h"$ hZc thYc h%n cXng nh%t W+ $' Vut nhng tr"ng 1 .6nh cqu thng t^c l thYc h%n 0u$ tr6nh !Wtc$ch .t thuPn ngh[ch th6 + k cQa 'h#n ^ng Jn nh c(u ?aG3 e" + k l c$c h! tr