Termodinamik - Prof.dr. Ali Pınarbaşı Çözümlü Sorular

8/10/2019 Termodinamik - Prof.dr. Ali Pnarba zml Sorular

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0. Jir pistfe sioiemir mzlelieml j` oèd t`, 0;; h[` j`s et` mfybu sv-jun`r h`r b < hd sujuoueb`ht`mr. Quyue : hdo h job sv g`z em`, dlri hòè isl jun`r g`z em`mr. Jumurubm`yhle pistfe murmuruauo`r zlriemlmir. M`n` sfer` suy`s dlii fob`ht`, j`s e

yhsloblhtl vl :;; h[` fomu uem` pistfe n`rlhlt ltblyl j` o`b`ht`m r. Is dlii tfpo`b nàib

7,;:< b1

fouea`y` h`m`r mlv`b ltblhtlmir. Jue` drl8`) oh vl sfe nòmlhi sa`hoho`r ,j) [istfe yuh`r mfru n`rlhlt ltblyl j` o`m èm`hi s v g`zem`hi suyue htolsieia) Nò mliibi s r`s em` y`poè ii juoueuz.

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:. -:; ; Aml mfybu jun`r fo`r`h juoueè sf utuau `hhè-0:eie, jir hfbprlsr y`rm b yo` ;.4B[` j`s ea` h`m`r sh t r ob`s istleblhtlmir. Qf utuau `hhèe mljisi 0.: hd/smir.

`) Hfbprlsre `my j`tih vl h s a`ho ee >; ; A fob`s murubuem`, hfbprlsr iiedlrlhoi da juoueuz.

j) @ye hfbprlsrml sf utb` y`p ob`s murubuem`, sfutuau `hhèmè < hc/hd slhioblhtl jueue sfeuauem` h sa`ho 4; ; A fob`ht`mr. Ju murubm`, hfbprlsr iie dlrlhoida juoueuz.

a) ` vl jml loml lmiole sfeuo`r dz eel ò`r`h, hfbprlsrml y`p oè sfutbè ebnlemisoih `semè elbiei `ho`yez.

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a) Qfutb` y`p ob`s murubuem` n`raèè i m`n` `z fob`ht`mr. Bnlemisoih `semè i n`ra`yè mzlelholrml iie `z` bieibub` iemirioblsi istleir.

1. Jun`ro jir s tb` sistlbieml huooè oè r`my`tre nàbi :; otmir. Z`my`tr ;.0< B[` j`s et`mfybu jun`ro` mfomuu z`bè jun`r diri vl h vèò`r h`p`t ob`ht`m r. J`s e


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0. @ m` zlooiholri vlriole b`mmlolr iie jioieblyle zlooiholri mfomurueuz.

B`mml [(h[`) ]( ; A) v(b 1/hd) x G`z MurubuZ-0: :; ;.;::N: F :;;; 09;N: F 1:< ;.=

Z-01=` 7; ;,07;N: F 04; Mfybu jun`r

B`mml [(h[`) ]( ; A) v(b 1/hd) x G`z MurubuZ-0: Mfybu s v -jun`rN: F :;;; 09; ;.;;00=0 - Q h tr ob s v N: F 1:< 017.1; ;.::< ;.= Mfybu s v jun`r

Z-01=` 07> 7; ;,07; - H zde jun`rN: F 490.4 04; ;.:=:> 0 Mfybu jun`r

:. Jir pistfe sioiemir mzlelieml ;.7 B[` vl =; ; Aml juoueè 0; hd sfutuau `hhè-0: , :; ; As a`ho h`m`r s`jit j`s et` sf utuob`ht`mr.

`) Nò mliibiei ]-v miy`dr`b em`, mfybu sv jun`r l riolriei ml dstlrlrlh izieiz.j) Nàibmlhi mliblyi juoueuza) ]fpo`b letòpi ml iibiei letòpieie tè b e huooè`r`h juoueuzm) ]fpo`b letòpi ml iibiei t`jof huooè`r`h juoueuz

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j) [ 02;.7 B[` vl ] 02=; ; A Hzd e jun`r v 02;.;1094b 1 /hd n02:;9.10hc/hd u0209;.01hc/hd

[ : 2;.7 B[` vl ] : 2:; ; A Qht r ob sv v: 2vgK:; ; A 2;.;;;4


4/67

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0-: Nò mliibi (1;;h[` fouea`y` mlh s`jit nàibml)[ : 21;;h[` vl v : 2;.1197b1/hdvg?v: ?vd fomuuemè r` jodlml

:-1 Nò mliibi (1;;h[` s`jit j`s et` dlei olbl)[121;;h[`st murmuruauy` ml mii èm` zdo nàib8v2;.7/0.04>v2;.


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6/67

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7/67

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0) @ m` vlriole b`mmlolr iie t`jofm`hi jf ouho`r mfomurueuz.

B`mml [(h[`) ]( ; A) v(b1/hd) x N`o`) N : F 09>,


8/67


9/67

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10/67

Aubnuriylt eivlrsitlsiB`hie` Bnlemisoi i Job]lrbfmie`bih I Gieò Q e`v Qfruo`r

rleaieie, 0 1 < 4@m : = 7Eub`r`s ]F[O@B

0-Jir `ymèo h suyue `) jir fa` e zlrieml, j) iiel lolhtrihoi s t a hfe`r`h s t om e mee.Quyu s tb`h iie nèdi yfo m`n` vlriboimir6 @ ho`y e. (< puè)

(j) bltfmu m`n` vlriboimir. eh suyue iieml juoueè s t a lolbèmè lvrlyl foè soh`y po`r mi lriel drl m`n` `zm r. @b` m`n` `z lolhtrih lelrcisi dirmisiyol s tb`y s` o`b`h fomu uemè ihieai yetlbie m`n` vlriboi fomu u ` ih`rm r.

:-Jir lolhtrihoi fa`ht` su s t om e mee. Ju i olb lse`s em` lelrcieie nèdi jiibolrmljuouemuueu vl nèdi lelrci me bolri fomuueu jloirtie. (< puè)

Lelrcieie gfrbu lolhtrih lelrcisi vl muyuour i lelrcimir. Lolhtrih lelrcisi suy` foè s trèsglri eltialsieml muyuour i lelrciyl me blhtlmir.

1-@ m` jloirtiole i olbolrmle nèdisi m`n` g`zo` lelrci dlrlhtirir. `) 0 @tb j`s et` 0 hdmfybu s v nòieml suyu tbyol jun`ro` t rb`h, j) > @tb j`s et` 0 hd mfybu s v nòieml suyutbyol jun`ro` t rb`h. (< puè)

Yhslh j`s e, m`n` `z jun`ro` b` lelrcisi dlrlhtirmi iemle, 0 @tb j`s et` 0 hd mfybu s v y jun`ro` t rb`h m`n` g`zo` lelrci dlrlhtirir.

=- Yhslh jir jieè

e tlplsiemle `t

oè jir hutu d`zfz m ee. @

mlrhle d`zfzue s

a`ho

pftèsiylo lelrcimlhi zò`b`mè mfo`y `rt`r b 6 (< puè)

N`y r eh hutueue pftèsiylo lelrcisi m bl lse`s em` i lelrciyl ml io, hieltih lelrciylmer.


11/67

Aubnuriylt eivlrsitlsiB`hie` Bnlemisoi i Job]lrbfmie`bih I Gie`o Q e`v Qfruo`r


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12/67

Aubnuriylt eivlrsitlsiB`hiel Bnlemisoi i Job]lrbfmie`bih I - Gie`o Q e`v Qfruo`r zbolri 0;.;0.:;;:

0-) @ m` zlooiholri jloirtiole b`mmlolr iie jioieblyle zlooiholri mfomurueuz.

B`mml [ (h[`) ] ( ; A) v (b 1/hd) n (hc/hd) x G`z murubuN: F 07; 07>:N: F 9


13/67

Aubnuriylt eivlrsitlsiB`hiel Bnlemisoi i Job]lrbfmie`bih I - Gie`o Q e`v Qfruo`r zbolri 0;.;0.:;;:

0-)

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14/67

0. Nlr jiri :;; O nàbiel s`nip @ vl J tèho`r lhio 0 ml dstlriomii diji jir vè` y`rm b yo` jirjiriel j` oèb t r. J` oèd t` @ tèh em` := ; Aml, nàibal %0; s v , %9; jun`rfob`h zlrl sf utuau `h hè 0: juoueur ihle J tèh t`b`ble jf tur. M`n` sfer` vè` ` o`r`hmfybu jun`r e @ tèh emè J tèh e` `h , J tèh e e j`s ea @ tèh em`hi j`s ea` uo` ea`y`h`m`r s` oèb`ht`m r. Ju efht`m` vè` tlhr`r h`p`t ob`ht`m r. Nò mliibieie y`v`

dlrlhol blsi elmleiyol s a`ho h nò mliibi jfyuea` := ; A fo`r`h hòb`ht`m r. @ tèh em`hihuruouh mlrlalsiemlhi ml iibi juoueuz.

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15/67

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1. Jun`ro jir s tb` tlsis`t em` huooè oè r`my`tre nàbi :; otmir. Z`my`tr 0


16/67

7. H`pò jir sistlbml dlrlhol le jir lvrib iie, elt i buto`h` s g r b m r6 El trsistlbolr iie ju murub dllroimir.

N`y r. @my`j`tih sistlbolr iie elt i s g r four.4. Qrlhoi `h o jir n`v` hfbprlsr m ee. Hfbprlsr diri vl h em`hi nàibslomljiolri h`r o t r e.

Hfbprlsr diri iemlhi nàibslo mlji m`n` jyhtr. eh h t` zdo nàib`zòb`ht`m r.>. 0h[` . b 1 20hc fomuueu dstlrieiz.

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17/67

:. @ m` zlooiholri vlriole b`mmlolr iie jioieblyle zlooiholri mfomurueuz.

B`mml [(h[`) ]( ; A) v(b 1/hd) x G`z Murubu

N: F 0;; 99.>1 0.79< - H zd e jun`rN: F 09>.7< - H zd e jun`rZ-0: 0 Mfybu jun`r

1. Zicit jir tèh ihi l it p`r` nòiemlmir. J` oèd t` tèh e jir t`r`g em` < hd su, :;; h[`vl :< ; Amlmir. Milr t`r`g isl jf tur. @r`m`hi aim`r hòm r om em` su tèh e jte nàbieldlei olblhtlmir. ]èh e s a`ho :< ; Aoih jòèd s a`ho e` lri iealyl h`m`r s trèsglri

fob`ht`m

r.`) ]èh e nàbieij) Qfe j`s ea e a) Ju lse`m`hi s trèsglriei nls`po`y`r`h [-W miy`dr`b em` dstlrieiz.

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21/67

Aubnuriylt eivlrsitlsi

B`hiel Bnlemisoi i Job]lrbfmie`bih I Gieò Q e`v sfruo`r

rleaieie, 0 =@m :

Qfy`m 1Eub`r`s ]F[O@B

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22/67

Aubnuriylt eivlrsitlsi

B`hiel Bnlemisoi i Job]lrbfmie`bih I Gie`o Q e`v sfruo`r

rleaieie, 0 =@m :

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23/67

]LZBFM E@BH QFZ\O@ZI

0. @ m zlooiholri vlriole b`mmlolr iie t`jofyu mfomurueuz.

:. Jir pistfe sioiemir mzlel ieml j` oèd t` :;; h[` j`s et` ;,< b 1 mfybu su jun`r juoueb`ht`m r. Ju murubm`yhle pistfe ihi murmuruau zlrieml juoueb`ht`m r. [istfeuhòm rb`h iie 1;; h[` j`s ea` dlrlh v`rm r. M`n` sfer` jun`r` foè s dli i sfeuem` nàibihi h`t e` hb`ht`m r. Nò ml iibi iie8`) [-W miy`dr`b e izieiz.j) Qfe murubm`hi s a`ho a) Y`p oè iim) ]fpo`b s dli iei nls`po`y e z

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`) Y`p oè ii juoueuz.j) Qfe murubm`hi j`s ea juoueuz.a) D`z e aiesiei jloirolyieiz.

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D`z e aiesi fhsicle (F : ) mir.

=. Z`myò `h o jir hfbprlsrl 0;; h[` vl :>; H murubuem` dirle ;,;: hd/s n`v`,7;; h[` j`s ea` s h t r ob`ht`m r. Nò ml iibi srlsieal 07 hC/hd s h`yj fob`ht`m r.Hfbprlsr ò t rb`h iie dlrlhoi d :,41: hT fomu ue` drl, hieltih vl pftèsiylo lelrcimliibolriei inbò lmlrlh sfe murubm`hi s a`ho juoueuz.

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7. Bhlbblo jir d`z jir pistfe sioiemir mzlel ieml `my`j`tih fo`r`h vl s`jit s a`ho ht`s h t r o`jioir bi6

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Q h t rb`h iie i n`raèbò , mfo`y s yo` ju murubm` s h t r o`b`z.

4. Jir buait =;; H s a`ho ht`hi jir h`ye`htè >;; hC s òè, :.

Z`h b 0:>< b foè Qiv`st` st ` h jir `ymèo ht`hi jir su h` ; A ml h`ye`r6

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etlrpfo`syfeo` Qiv`st` hi `tbfsglr j`s ea [ `tb 2>7,7> h[ètlrpfo`syfe ju j`s ea` mleh dlole mfyb` s a`ho ]299,


27/67

Aubnuriylt eivlrsitlsiB`hie` Bnlemisoi i Job]lrbfmie`bih I Wizl Q e`v Qfruo`r


0-Mfybu s v iol s ht r ob s v , vl mfybu jun`r iol h zd e jun`r `r`s em`hi g`rh elolrmir,` ho`y e z. (< puè)

Jir s v htolsieie jun`r nòiel dlljiolal i oibit ml lrimir. @hsi t`hmirml sv s ht r ob fo`r`h h`juo lmioir. Mfybu jun`r iol h zde jun`r `r`s em`hi g`rh isl, mfybu jun`rilrisieml s v p`rtihoolri ilrblyle `h hè foup, nlrnèdi jir s a`hoh `rt b em` sht r ob jun`r yèi h zde jun`r nòiel meljiolal i oibit efht` fo`r`h tè boèr.

:-Mfybu s v jun`r h`r b jodlsieml s a`ho h vl j`s e elmle jirjiriel j` o zlooiholrmir.(>< b 1/hdNàib s`jit fomu uemè8

sf utb` i olbiemle ealhi zdo nàib2sf utb` sfer`s zdo nàib

;.< x 2 2 (4.< puè)

a) I. Y`s` dlrl i8P u T 2 +

s`jit nàib i olbi sljljiyol T2;, mfo`y syo`8P u2

0 0 0

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g gd

u n [v x hC hd n n xn x hC hd u n [v x hC hd zdoilelrciml i ibiisl

u u u hC hd ]rèsglr lmiole s i

2 2 22 + 2 + 2

2 2 2

2 2 2

8

0.4>..=

slP b u x hC 2 2 2

(0; puè)

4-Jir d`z 0.= BE/b : j`s e vl 17; f A s a`ho ht` `my`j`tih fo`r`h 0;; hE/b : j`s ea` s ht r o yfr.D`z m`n` sfer` s`jit nàibml s a`ho h 17; f AUyl dloiealyl h`m`r s t o yfr vl ju efht`m` j`s ea e::; hE/b : fomuu tlsjit lmioiyfr. Qfe fo`r`h m` izftlrbò fo`r`h j` oèd j`s ea foè 0.=BE/b : foè` h`m`r tlhr`r s h t r o`r`h lvrib t`b`boè yfr. Htolsi ;.:1 hd foè ju d`z e nòmliib dr`gi iei [-v miy`dr`b em` dstlrlrlh8 (d`z iie A p20.;;< hC/hd H) (1; puè) `) @my`j`tih s foè h y ,j) @my`j`tih s ht rb` lse`s em`hi i lelrci ml iibiei juoueuz.


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Aubnuriylt eivlrsitlsiB`hie` Bnlemisoi i Job]lrbfmie`bih I Wizl Q e`v Qfruo`r


`) zftlrbò i olb iie8 100 0 1 11 0

0=;; 7.17::;

W [ [W [W [ W

2 2 2 2 (< puè)

@my`j`tih iolb iie8 10 : :0 0 : : 1 :: 0 0 0

h h h W [ W W [W [W vl jyolal W W

[ W W W

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0=;;7.17 0.=:7 .

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j)0.;;4.4

::; [ [ [ ] ] H ] ] x H ] ] [

2 2 2 + 2 2 2 2 (4.< puè)

@my`j`tih nò ml iibi lse`s em` i lelrci ml iibi8

: 0 : 0( ) ;.:1 ;.4;4.4 711)


30/67

0. @ m` zlooiholri vlriole b`mmlolr iie jioieblyle zlooiholri mfomurueuz.

B`mml [(h[`) ]( ; A) v(b 1/hd) x G`z MurubuN: F 0;; 0.79

Z-0: :;; -1 0.79< - H zd e jun`r

N: F 09>.7< - H zd e jun`rZ-0: 0 Mfybu jun`r

:- Qrlhoi `h o ` h jir sistlbml `h hè =hd/s mlji iol `hb`ht`m r. @h hè sistlbl 7;;hE/b : j`s e, ::; b/s n z, ::;;hC/hd i lelrci vl ;,=: b 1/hd zdo nàbiel s`nip fo`r`h dirip, 0


32/67

a)

hcP

hd hcu

u

v

vv x

hd hc

uu

uubP

[L HL \ T P

gd

g

g

:>.0;=91.0;=(>.0;=

0;1.:;;0.;17.=1;;0.;;;:.;

>>.0;=

)(

:

>.;,/;;0;==.;0;;

ububnbPububnbnbT P

hdH hC x x s x s s

hd hC x xu xuu x x

A ]

xv

vv xhd bbW v

hd bbbbbbb

hd bbhd vW

b

hdH hC s shd hC nn s vmfybu

A ]

hdH hC s shd hC uuhd bvv s vmfybu

A ]

HN d d

sd s

sd s

gd

g

HN d

A g A g

A g A g A g

h`ye`h

h`ye`h

lvrl

lvrl

lvrl

lvrl d d rltib ]

P

]

P sb sb sb]

P sb sb sb sbQ

hC x xP

+++2++2

2+2

)()(

4>,:749=,=0>0=0.1>1:=,=:;


35/67

]LZBFM E@BH-: MLZQ GE@O QFZ\O@ZI WL ALW@[O@ZI0:.7.:;;4

1

ALW@[3

hC.)..(x.)uu(bxPT\TPhC.)..(xx)ss(]bQ]P

hdH /hC.s,hd/hC.u]]A[

hdH /hC.s,hd/hC.ujun.mfy

A]

>:9:1:17:=1:17>07:=41

>077:71;:;;

=1:171:


36/67

]LZBFM E@BH-: MLZQ GE@O QFZ\O@ZI WL ALW@[O@ZI0:.7.:;;4

=

ZELH-73

0;; h[` vl :: A mlhi n`v` jir hfbprlsrl `r`a o yo`,


37/67

Aubnuriylt eivlrsitlsiB`hiel Bnlemisoi i Job]lrbfmie`bih I Gieò Q e`v sfru vl zbolri

Yrm.Mf.Mr. @oi [IE@ZJ@ I

0

0-

@

m`hi izlodlml lhsih zlooiholri juo`r`h, nòie nèdi g`zm` fomu ueu su iie jloirtieiz. (Ml lrolri juob`h iie y`pt e z iolbolr alv`p h` m e` y`z oà`ht r.)

] ( f A) [ (h[`) u (hC/hd) x G`z @ ho`b`s

` 0:;,:1 :;; 0409,=9 ;.7 Mfybu s v +Jun`rj 0:< :1:,0 07;; ;,


38/67


39/67

]lrbfmie`bih I- Gieò s e`v sfru vl alv`po`r 9.0.:;;>

0. Llr jiri t`r`g emè vly` hlemi hlemieizl yzezl tfh`t `t`r`h vurmu ueuzm`, loieizmlvly` yzezml yèb` nissi fou tu ueu jioirsieiz. ]òinsiz jir fo`yo` h`r o` r`h h zd e jirhii t`r`g emè yzezl tfh`t `t om e n`yò lmieiz. Ju murub yzeze fo`ymè lthiolelejodlsieml 0.> f Al s a`ho h `rt e` elmle foà`ht r. ]fh`t `tè loie htolsi 0.: hd, vurb`fo`y emè lthiolele lo vl yze mfhuo`r e e y`ho` h htolsi isl ;.0hC/hd f A fo`r`h ò e. (Eft3 Mlri

yzlyiemle lvrlyl s h`yj fob`m e h`juo lmieiz)

Lo vl yze lthiolele h sbo`r sistlb fo`r`h slioirsl8: :

: 0

:0

0

;:

;;.0< 1.> 0.> 0.: =0.1< /

: 0;;;

mlri lo mlri lo

W W P T \ HL b a ] b

W W b s

2 + 2 +

2 + 2

: . Jloiroi jir htolyl s`nip bhlbblo d`z > 04=.:

17;;( ) ( ;.0< 0; ) 04=.: ;.40> 0< .04

0v f

[W bZ] b b hd

hC se hcP T \ ba ] ] s``t hd ] ] A

s s``t hd A

2 2 2

2 2 2 2


40/67

; ;.:< ;.0: 0 ;.;< 0.=: hC/hdAmir.Lholeblsi dlrlhle juz biht`r e juoueuz.

Qu :; fAmle ; fAyl dloirhle vlrmii s, juzu lritblhtlmir.;.=< =.0> :; 11= ;.00:7su juz su juz gd juz juz L L b a ] b n b b h 2 2 2 2

4. Qrlhoi `o b` rto`r em`, j`s ea 0 bb : fomuue` drl (`) jun`r e h htol mljisiei vl n z e (j) Jun`r e jirib htolmlhi `h lelrcisiei vl tfpo`b lelrcisiei (a) Jirib z`b`em` mmhotlealrlyi tlrh lmle jun`r e lelrcisiei juoueuz.

`) 0


41/67

Aubnuriylt eivlrsitlsiB`hiel Bnlemisoi i Job

]lrbfmie`bih I Wizl Q e`v sfruo`r

@m Qfy`m Eub`r`s

0. < f A s a`ho em`hi ;.0 hd yuburtè e zdo s s 1.1: hC/hd f Amir. Yuburt` 9< f Amlh`ye`yè suy` t o rs`, yuburt`y` foè b`hsibub s dli iei juoueuz .

hC>>.:9)

P T n n n hc hd

n n]`jof @ ] H A

2 2

2 2 2


42/67


]lrbfmie`bih I Wizl Q e`v sfruo`r

@m Qfy`m Eub`r`s

7. H zd e su jun`r s`jit s a`ho ht` mfybu jun`r loml lmioiealyl h`m`r s h t r o yfr. [-v vl ]-vmiy`dr`bo`r e izieiz.

4. : hT daemlhi jir lolhtrihoi s t a < hd su iiel mòm r ob`ht` vl 0; m`hih` srlyolò t r ob`ht`m r. olb s r`s em` sumè 1;; hC s h`yj fob`ht`m r. Quyue s a`ho em`hi `rt juoueuz (Quyue zdo s s =.0> hC/hd f A ò e`jioir).

7;1;; ( : *0; * ) * =1.;7

0

v

f

P T \ ba ]

hc shC mh ] ] A

s mh

2 2

2 2

>. Jir s b`hielsi 0;;; f A s a`ho ht`hi jir mlpfmè s òb`ht` vl


43/67


44/67


]lrbfmie`bih II :. Wizl Q e`v sfruo`r :9.; b/s n zo`

dirblhtl, ;; hC/hd n`v`m r.

`- lvribie nlr jir i olbi sfeuem`hi j`s e vl s a`ho ,j- Is o vlribi,a- Frtò`b` lglhtig j`s ea nls`po`y e z.

Eft3 ]lrbfmie`bih t`jofo`r ` ht r J` `r o`r]`b sfeuo`r ml lrolemirblml mihh`tl ò eà`ht r . Mf.Mr. @oi [IE@ZJ@ I

( ) ( ) ( ): :. .

0 :tr 0 : ; 0 : 0 :

h 0 (h 0) h h

elt: 0 : : : 0

0 : 0 0 0 : 0 :

W WT b n n ] s s d z z

:

w] v ] [ [ vFLJ

] v ] [ [ v v v

2 + +

2 2 2 2


45/67


]lrbfmie`bih II :. Wizl Q e`v sfruo`r :9.


46/67


]lrbfmie`bih II :. Wizl Q e`v sfruo`r :9.1hc/ hd w v ([ [ )

Mfybu s v v ;, ;;0;0b / hd w ;, ;;0;0 (=;;; 0;) =, ;1hc/ hd

n n w n 090,>1 =, ;1 097hc/ hd

[ =B[` n 1:01,7hc/ hd

] =;; A s 7, 479hc / hdH

s s 7,479 ;,7=91[ 0;h[` x

s

2 2 2 2 2 2

2 + 2 + 22 2

2 2

2 2 2

= = g = gd

elt d

d 1 :

= 0

elt

elttn

d

;,>074,hc / hdH n n x n 090,>1 ;,>07 :19:,> :0==,11 09


47/67


]lrbfmie`bih II :. Wizl Q e`v sfruo`r :9.mir. Q h t rb`strfhueue j` oèd a em`hi j`s e ;.0 B[` vl s a`ho h 0;; hC/hd n`v`m r.

`- lvribie nlr jir i olbi sfeuem`hi j`s e vl s a`ho ,j- Is o vlribi,a- Frtò`b` lglhtig j`s ea nls`po`y e z.

(Fm` s a`ho em` s`jit zdo s y`ho` b e huooè e z)

h 0

;.=: 0:

0 :

h 0.=: 0

:0 :

] v] :>>(>) 770,7) 0,>14B[`

[ v

2 2 2

2 2 2

:-1 Nò ml iibi s`jit nàibml 0>;;hc/hd s diri i8:1 v 1 :

1

1 b`x

: 1: :1 b`x

1 1 :

q a (] ] )

0>;; ;, 40>(] 770, 7.70H ]

[ ][ ] 0,>14 107>,70[ >, 494B[` [

[ ] ] 770,7,494[ ;, =4>B[`

[ v >

q a (] ] )

q ;, 40>(0149, : :>>) 4>1, =>hc / hd

q 0>;;hc/ hd

w q q 0>;; 4>1, => 0;07,>v ;,>:7:7

w 0;07,


49/67


]lrbfmie`bih II Gieò Q e`v sfruo`r ;4.7.:;;7

rleaieie, 0 =@m :Qfy`m 1

Eub`r`s ]F[O@B

0. Qrteblsiz jir pistfe sioiemir mzlel ieml j` oèd t` :;;h[` j`s et` mfybu s v nòieml su juoueb`ht`m r. M`n` sfer` suy` 9 1:00, 70hc / hd

P b q 44;;; b1:00,70 b :1,94hd / s

2 + 2 + 2

2 2 2

2 2 2


50/67


]lrbfmie`bih II Gieò Q e`v sfruo`r ;4.7.:;;7

rleaieie, 0 =@m :Qfy`m 1

Eub`r`s ]F[O@B

Yf uturuaum` m frt`b` `t oè s 8. .

= 0

tn

d

P b q b(n n ) :1,94(:01) =4;10,9

P 44;;;

2 2 2 2

2 2 2

=- J`sit jir Zèhiel lvribieml trjie h em`hi j`s e 4>7m r. Yf uturuaumè, :9;H s a`ho ht`hi lvrl frt`b` s `t o`r`h, suyue 4=.19 ;.>>7 ::4>.7 :=;1.:hc/ hd

s s x s 0.:01 ;.>>7 7.:=1= 7.4==7hc/ hdH

Yf uturuau h :nòi

n 1>=.19hc / hd

s 0.:01hc / hdH

q n n 1>=.19 :=;1.:

2 + 2 2

2 + 2 + 2

2

2

2 2 2

; sis lvrl

lvrl; : 0

;

:;0>.>0hc/ hd

I ] ( s s )

qI ] (s s )

]

:;0>.>0I :9;(0.:01 7.4==7 )

:9;I =0=.7=hc / H

2 +

2 +

2 +

2


51/67

Aubnuriylt eivlrsitlsiB`hie` Bnlemisoi i Job]lrbfmie`bih II Gieò Q e`v Qfruo`r

rleaieie, 0 =@m :Qfy`m 1Eub`r`s ]F[O@B

0- Qtèm`rt jir Zèhiel lvribieml jun`r, :; J`r vl =;; fAml trjiel dirblhtlmir. Hfemleslrj`s ea ;.: J`r foup, hfemleslri mfybu s v fo`r`h tlrh ltblhtlmir. ]rjie vl pfbp`y tlrsieir`my`j`tih h`juo lmlrlh8

`- ]b efhtò`r e j`s e, s a`ho h vl letòpi ml lrolriei,j- lvribie elt s s iol elt i iei,a- Is o vlrib vl A`reft vlribiei nls`po`y e z. (:; puè)

:- @ h jlsolbl suyu s t a s e e imlò jir lvribml, s o vlrib zlriel foè lthisiei iealolblh`bà yo`, trjiel :; B[ , 7;; fAml dirblhtl foup yf uturuau j`s ea 0; h[`m r. Is o vlribi8`- Jlsolbl suyu s t a s huooè ob`mè,j- 0B[` i olb j`s ea em` 0 `mlt ` h jlsolbl suyu s t a s huooè ob`s murubuem` nls`po`y e z.(1; puè)

1- @ m`hi tlblo h`vr`bo`r h sà` ` ho`y e z. ` - [istfeou bftfro`rm` s h t rb` frè j - hi z`bèo vl mrt z`bèo bftfro`r e vlrib ` s emè h`r o t r ob`s a - mlò fttf lvribieie nò ml iibolrim - Bftfro`rm` vuruetul - Jun`ro d lvribolrieml rlclelr`syfe i olbi

g - Huooè

o`jioiroih vl ]lrsieblzoih (1; puè)

=- Qu jun`r `my`j`tih jir trjiel 7 B[` j`s e, 7;; fA s a`ho h vl >; b/s n zo` dirblhtl,


52/67



0- `)Efht` [ ] x n s zlooih

0 :;.; =;; - 1:=4.7 4.0:40: ;.: 7;.;7 ;.>>97 :1=9.1 4.0:40 s : 2s 0 1 ;.: 7;.;7 ;.; :1:;= :;.; 7;.7 - :1:; s =2s 1

= 1 1 = 1( ) :9>.1 / :.; / >97.1 /elt

elt

q n n hc hd q n n hc hd q hc hd

w n n hc hd w n n hc hd w hc hd

2 2 2 2 22 2 2 2 2

a- >97.1 :41.0< 7;.;7;.:99 0 0 ;. :;.: :0:.; /

7. ;.7=91 4.;7=

090.>1 ;.4>;7= :19:.> :;0747:.> ;.9>07 :;0 09:.>;.::14 ;4471 :;( ) ( ) (1


53/67



1- @ m`hi tlblo h`vr`bo`r h sà` ` ho`y e z.` - [istfeou bftfro`rm` s h t rb` frè

Qioiemir iiemlhi le jyh nàbie (W b`x ) le hh nàbl (W bie ) frè m r.

j - hi z`bèo vl mrt z`bèo bftfro`r e vlrib ` s emè h`r o` t r ob`s hi z`bèo bftfro`r e vlribi, yèb` sfeu d`zo`r e e t`b fo`r`h m r `t o`b`b`s vl t`zl

y`h t-n`v` h`r b e e jir jobee yèb` sfeu d`zo`r e` h`r b`s sljljiyol, mrt z`bèo bftfro`r e vlribolriemle m htr.a - mlò fttf lvribieie nò ml i ibolri

0-: zètrfpih s ht rb`:-1 lvribl s`jit nàibml (v2s`jit) s dli i1-= zètrfpih dlei olbl=-0 lvribmle s`jit nàibml (v2s`jit) s dli i

m - Bftfro`rm` vuruetu

Y`h t e lrhle vl hlemioi iemle tutu b`s iol muyuo`jiole drotmr.l - Jun`ro d lvribolrieml rlclelr`syfe i olbi

]rjieml dlei olbl lse`s em` jir h s b jun`r e h`zè jlsolbl suyueu s tb`h `bà yo`

huooè ob`s iolbi fo`r`h ig`ml lmioir. (@r` jun`r òb` i olbimir)g- Huooè o`jioiroih vl ]lrsieblzoih

Jir sistlbmle loml lmioljiolalh le fh i , sistlbie jloiroi jir j` oèd nòiemle, tlrsieirnò mliibiyol lvrleie juouemu u nòl dltirioblsiyol loml lmioir, ju isl huooè o`jioiroih fo`r`h`moèm r o r. ]lrsieblzoih isl i y`pb` foè` em`hi `zòb`m r.

=-0

0 00

: : ::

: 0

: : : :: 0

717.= / , 4.0744 /

7;;

:.< / , 4.79=4 /0;;

( ) ( )

0=; >;7.7 /

: :;;;:.< 17.= 7.7) (4.79=4 4.0744))

0

7.00

tlr

tlr

tlr

II tlr

ir i T b n n hl pl ] s s

T

T BT

T hieai y`s` vlribi T

2 + 2 + 2

2 2 2


54/67

0. 9< h[` j`s e, :< ; A s a`ho ht`hi ;.07: b 1 n`v` jir sioiemirml :9; h[` j`s ea` h`m`r tlrsieir vlizftlrb fo`r`h s h t r ob`ht`m r. N`v`e e s vl i `o vlri iei vl letrfpi ml iibiei nls`po`y e z.

:. 0;;; h[` j`s e, :


55/67

0) 2:

0tr [mWT N`v`, iml`o d`z

0

:00

0

::

0

:

0tr W

WoeW[

WW

oebZ]W

mWbZ]mW

WbZ]

T 2222 1

::::00 b;


56/67

1) Mfybu s v

h[`:.014n

hd/b;;0;;1.0=;;0.1>:.014wnnhd/hC;0.1)0=.;90>4.4

=47=.;9:0:.7

s

ssx

gd=g =

gd

g ==

2+2+2

222

]rjie i i8hd/hC0>.00:;4:.:00;9.1:1;nnT =1t 222

Elt i 8hd/hC04.0004;0.10>.00:;TTT ptelt 222

Dirle s 8hd/hC;4.1;9;>1.0=;9.1:1;nnq :1d 222

Is o vlrib8

:.17%17:.;;4.1;9;04.0004

qT

d

elttn 2222

=) Mfybu s v - jun`r h`r b , J`s e s`jit, f nòml s a`ho h t` s`jit ]20;; ; A

Q`jit s

a`ho

ht`

s

dli i iie letrfpi ml iibi8`) Qistlb iie8

H /hC70.01417;;

]P

Qsistlb

sistlbsis 2

22

j) lvrl iie8

hd/hC;0.::9>7;;

]

PQ

lvrl

lvrllvrl 222

a) ;=.;;0.:7.0QQQ lvrlsistlbtfpo`b 52+2+2 ]fpo`b letrfpieie `rt iohlsiel uydueou uemè, dlrlhol tirioljioir nò ml iibi


57/67

Aubnuriylt eivlrsitlsiB`hie` Bnlemisoi i Job

]lrbfmie`bihII Wizl Q e`v Qfru vl Alv`po`r

Eft3 Q e`v srlsi 9; m`hih`m r. J` `r o`rQ`mlal t`b sfeuo`r ml lrolemirblyl o e`a`ht r . Mf.Mr. @oi [IE@ZJ@ I ;0.;:.:;;7

0. 0. 4;;h[` j`s e, 0= b 1 n`abiel dlei olblhtlmir. D`z e letrfpi ml iibiei juoueuz.

:

tr

0

:: :

tr 0 00 00

sis

w [mv

[W bZ] A

A[

WW Wmv ;.;>=

w A Aoe [ W oe 4;; ;.;0= oe 04.7[ 00.;>>

[ [ 0;;

[ 00.;>> n 4.:= 1

2 2 2 2

2 2 2

2 22 2

2 2 2

2 2 :d :d

;:d :

; ; 0tr 0 : ; 0 : 0 : 0 :

:

tr

tr

tr y

;;.09 n n 4.=1h / hd

n 4.=1hc / hd s :.14hc / hdH

[w (n n ) ] (s s ) vl s s s s Z oe

[

0;;w 1;;.09 4.=1 1;; (0.4;:;1 :.14 ;.:>4 oe )

>;;w :7=.0=hc/ hd

I w w :7=.0= ( :>4.:=) :1.;9

2

2 2

2 2

2

2 2 2 2

tr II

hc/ hd

w :74.0=;.91 %91

wd :>4.:= 2 2 2 2


58/67

Aubnuriylt eivlrsitlsiB`hie` Bnlemisoi i Job

]lrbfmie`bihII Wizl Q e`v Qfru vl Alv`po`r

Eft3 Q e`v srlsi 9; m`hih`m r. J` `r o`rQ`mlal t`b sfeuo`r ml lrolemirblyl o eà`ht r . Mf.Mr. @oi [IE@ZJ@ I ;0.;:.:;;7

=. Yèm`hi lhioml jir lvribl ìt ]-smiy`dr`b droblhtlmir. (s 1-s : )2;.9 0> 90 0107.07 :>> 41>.:0hc/ hd

w 0>;; 41>.: 0;70.4>c /

2 2 2

2 2 2

2 2 2 2 2 2 2

2 2

tn

hd

0;70.4>;.9 .9%

0>;; 2 2 2

](H)

s(hc/hdH)

:;;;

9;;

1;;

>;;

0

:

1

=


59/67

Aubnuriylt eivlrsitlsiB`hie` Bnlemisoi i Job]lrbfmie`bih II Wizl Q e`v Qfruo`r

rleaieie, 0 =@m : mir. Q ht rb` strfhueuej` oèd a em`hi j`s e ;.0 B[` vl s a`ho h 0< ; Amir. Nlr jir lvrib jfyuea` trèsglr lmiole s 0>;; hC/hd n`v`m r.

`- lvribie nlr jir i olbi sfeuem`hi j`s e vl s a`ho ,j- Is o vlribi,a- Frtò`b` lglhtig j`s ea nls`po`y e z. (:< puè)

:- @ h jlsolbl suyu s t a s e e imlò jir lvribml, s o vlrib zlriel foè lthisiei iealolblh`bà yo`, trjiel :; B[`, 7;; fAml dirblhtl foup yf uturuau j`s ea 0; h[`m r. Is o vlribi8`- Jlsolbl suyu s t a s huooè ob`mè,j- 0B[` i olb j`s ea em` 0 `mlt ` h jlsolbl suyu s t a s huooè ob`s murubuem` nls`po`y e z.(1; puè)

1- Huooè o`jioiroih vl ]lrsieblzoih ig`mlolriei ` ho`y e z. (0; puè)

=- Letrfpi ml iibieie elmleolriei iz`n lmieiz. (0; puè)

; b/s n zo` dirblhtl,


60/67


rleaieie, 0 =@m : 4 :>>.:;.>:4 /

0;;

> :.1 77:

> 0>.1> 0.>1>

;.>:4;.0;1= /

>0>;;

( ) 0>;; / :.>01

> :.1 01>;

> 0>.1> ;.=49.: 01>;) 4>:.1 /

0>;; 4>:.1

h

h

tn h v

v

elt

[ B[`

] W ] H

] W

[ W [ B[`

[ W

Is o vlribr

@t oè s biht`r q A ] ] hC hd

w

2

2 2 2 2

2 2 2 2

2 2 2

2 2 2 2

0 :

0;04.4 /

0;04.40=;7

;.>:4 ;.0;1=elt

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