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"amojsbguamrpbysjes.jo" =

EB@AJU^XZ

^B@XALNZOMAJEUJotrlnuetjlo 4

^b`ralnyomajes 4 ^b` hrmoeblc sej oe` wbjeb n`mis wjtb njcc`r ot clras lc `o`rky & tb`jr jot relov`rsjlo.

^B@XALNZOMAJEU

Cjrst imw lc^b`ralnyomajes

^b`raleb`ajstry(mppijemtjlo lc J imw jo

eb`ajemi r`metjlos)

U`elon imw lc^b`ralnyomajes

Mppijemtjlo lc tb`ralnyomajes 4

Jo eb`ajstry usjok tb`ralnyomajes

[` emo pr`njet c`msjhjijty lc tb` r`metjlo tbmt js jc twl suhstmoe`s mr` ajx`n tb`o tb` r`metjloh`tw``o tb`a wjii tmg`s pime` lr olt.

Jc r`metjlo nl`s tmg` pime` tb`o wbmt mr` tb` `o rky ebmok`s jovliv`n nurjok tb` r`metjlo. Jc jo m eb`ajemi r`metjlo, `qujijhrjua js kljok tl k`t mttmjo`n tb`o wbmt wjii h` tb` `qujijhrjua

eloe`otrmtjlos lc njcc`r`ot r`metmots & prlnuets, emo h` emieuimt`n wjtb tb ralnyomajes.

Ijajtmtjlos lc ^b`ralnyomajes 4

Imws lc tb`ralnyomajes mr` mppijemhi` tl amtt`r jo huig lr lo syst a ms m wbli , tb`s` emo olt h`mppij`n lo jonjvjnumi pmrtjei`s(t`ap`rmtur`, pr`ssur`, `otbmipy `te bmv` a`mojoks loiy clr syst`a

ms m wbli`). Psjok tb`ralnyomajes w`emooltemieuimt` tb`tja` tmg o clrelapi tjlo lc m r`metjlolr clrmttmjoa`ot

lc eb`ajemi `qujijhrjua.

@xmapi -= 4 M + H E+ N G=, `q

1 =65

@ + C K + B G8, `q

1 =65

[bjeb lc tb`s` r`metjlo wjii mttmjo qujijhrjua `mrij`r

EB@AJU^XZ

^b`rami `qujijhrjua 4^b`r sbluin olt h` moy t`ap`rmtur krmnj`ot (njcc`r oe`).^ ap rmtur` amy bmv njcc r`ot vmiu`s mt njcc r`ot pime s/ilemtjlos jo m syst`a hut jt sbluin r`amjoelostmot wjtb tja`.

Eb`ajemi `qujijhrjua 4^b`r` sbluin olt h` moy eloe`otrmtjlo krmnj`ot lc moy lc tb` sp`ej`s jotb` syst a.

^yp`s lc tb`ralnyomaje prle`ss lo hmsjs lc stmt`/elonjtjlos^b`ralnyomaje prle`ss 4Moy a`tbln/prle`ss hy wbjeb syst`a emo ebmok` jts stmt` crla lo` stmt` lctb`ralnyomaje `qujijhrjua tl moltb`r stmt` lc tb`ralnyomaje `qujijhrjua.^b`r emo h` jocjojt` typ` lc tb ralnyomaje prle`ss`s, lut lc tb`s` tb` cliilwjok mr` japlrtmot lo`s4

=. Jsltb`rami prle`ss 4 ^ 1 elostmotn^ 1 6^ 1 6

8. Jsleblrje prle`ss 4 S 1 elostmotnS 1 6S 1 6

5. Jslhmrje prle`ss 4 V 1 elostmotnV 1 6V 1 6

>. Mnjmhmtje prle`ss 4 q 1 elostmotlr b`mt `xebmok` wjtb tb` surrluonjok 1 6(z rl)

^yp`s lc tb`ralnyomajes prle`ss`s lo hmsjs lc tb` wmy tb` prle`ss`s mr` emrrj`n lut 4 X`v`rsjhi` prle`ss 4

^b` prle`ss tbmt emo h` r`v`rs`n hy m v`ry samii ebmok` js golwo ms r`v`rsjhi prle`ss. Jc m prle`ss js emrrj n lut jo sueb m amoo`r sl tbmt tb` syst a js miwmys jo tb`ralnyomaje `qujijhrjua

mt `v`ry stmk` lc tb` prle`ss.

Jc tb`prle`ss js emrrj`n lutsueb tbmt tb`njcc`r oe` jo nrjvjok clre` monlpplsjok clre js jocjojt sjamiiysamii sl tbmt prle`ss tmg`s pime` mt jocjojt`sjamiiy silw rmt`.

Cnrjvjok

Clpplsjok

1 nC mon nC6

Mo jn`mi r`v`rsjhi` prle`ss wjii tmg` jocjojt` tja` tl k`t elapi`t`n.

Jt js emrrj`n lut jocjojt`sjamiiy silwiy.

Utrjetiy sp`mgjok tb`r` js ol jn`mi r`v`rsjhi` prle`ss jo uojv`rs`.

l k`t mo jn`m lc m r`v`rsjhi prle`ss w` emo elosjn`r tb` cliilwjok syst`a.Mo jn`mi kms js `oeils`n jo m elotmjo`r mon m amssi`ss pjstlo js put lo tb` kms lo wbjeb m pji` lc smon jspime`n bmvjok pmrtjei`s lc o`kijkjhi` amss. l emrry lut m r`v`rsjhi `xpmosjlo w` wjii silwjok n`er`ms` tb`amss lc tb` smon i ts smy hy r`alvjok tb` pmrtjei s lo` hy lo`, sl tb` `xpmosjlo lc tb` kms wjii tmg` pime`mt jocjojt sjamiiysamii rmt mon w` emo miwmys mssua` tb` syst`a tl jo tb ralnyomaje `qujijhrjua. Ul, tb`

`xpmosjlo wjii h` lc r`v`rsjhi typ`.

CHN lc pjstlo

Clr pjstlo tl h` jo `qujijhrjua 4V

kms1 V

mta+ Ak/M

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Jrr`v`rsjhi` prle`ss4 ^b` prle`ss emo olt h` r`v`rs`n hy m samii ebmok` js golwo ms jrr`v`rsjhi . Jc m prle`ss js emrrj`n lut jo sueb m amoo`r sl tbmt tb` syst`a js jo tb`ralnyomaje `qujijhrjua (J)

Loiy mt jojtjmi & cjomi stmt` lc tb` prle`ss hut olt mt tb` jot`ra`njmt` stmk`s.

(JJ) Uyst a amy h` jo tb`ralnyomaje `qujijhrjua stmt` mt sla` cjojt` ouah`r lc jot`ra`njmt`

stmk`s loiy - clr `xmapi - o st`p jrr`v`rsjhi` `xpmosjlo lc m kms

Jc nurjok tb` prle`ss tb`r` js m cjojt` njcc`r`oe` jo nrjvjok clre` mon lpplsjok clre` sl tbmt prle`ss

tmg`s pime` wjtb m cjojt` rmt`.

Jrr`v`rsjhi` prle`ss`s wjii k`t elapi`t n jo cjojt` tja . Mt jot`ra`njmt stmk`s lc tb` jrr`v`rsjhi` prle`ss, njcc`r`ot stmt` cuoetjlo sueb ms Vr`ssur`,

t`ap`rmtur `te. mr` olt n`cjo`n.

Mii r`mi prle`ss mr` jrr v`rsjhi .

Elosjn`r tb` mhlv` syst`a. Jc tb` stlpp`r pime`n lv`r tb` pjstlo js r`alv n, tb`o tb` pjstlo wjii alv` wjtb

mialst jocjojt` mee i rmtjlo mon wjii g``p alvjok tl m plsjtjlo wb`r tb` pr`ssur` lc tb` kms h`ela`s `qumi

tl tb` `xt romi pr ssur . Ujoe` tb` prle`ss wjii k t elapi t`n jo cjojt` tja` mon tb`r` wms m cjojt` njcc r`oe`

h`tw``o tb` nrjvjok clre` mon tb` lpplsjok clre` sl, prle`ss js jrr`v rsjhi`.Nurjok tb` prle ss, tb` pr ssur`

lc tb` kms emo olt h` n cjo`n ms jt wjii h` bmvjok njcc r`ot vmiu`s mt njcc r`ot ilemtjlos.

Aln`s lc `o`rky `xebmok` 4^b`s` mr` twl wmys hy wbjeb m syst`a emo jot`rmet lr emo `xebmok` `o`rky wjtb jts surrluonjoks.

(j) B`mt & (jj) [lrg

B`mt & [lrg hltb mr` clras lc `o`rky.

B`mt 4 [b`o tb` `o`rky trmosc`r tmg`s pime` h`emus` lc t`ap`rmtur` njcc`r`oe` h`tw``o syst`a &

surrluonjoks. Jt js golwo ms b`mt.

[lrg 4@o`rky trmosc`r wbjeb js olt b`mt lr wbjeb js olt h`emus` lc t`ap`rmtur` njcc`r`oe` js emii`n wlrg.

[lrg emo h` lc amoy typ`s 4A`ebmojemi wlrg, @i`etrjemi wlrg, Amko`tje wlrg, Krmvjtmtjlomi wlrg `te.

^b` sma` `o`rky trmosc`r emo h` emii`n wlrg lr emo misl h` emii`n b`mt n`p`onjok lo eblje`

lc tb` syst a.

^l uon`rstmon tbjs, elosjn`r m syst`a sblwo h`ilw jo wbjeb wmt`r js tmg`o jo m eils`n elotmjo`r mt 80E,

tb` surrluonjoks js misl mt t`ap`rmtur` lc 80E mon tb`r` js m b`mt r elji jo tb` njpp`n jo tb` wmt r wbjeb js

eloo`et`n tl m hmtt`ry tbrlukb m swjteb U.B`mt`r elji js misl mt 80E jojtjmiiy.

Olw, tb`r` mr` twl wmys jo wbjeb syst`a emo h` ebls`o

Uyst`a 4Mii elot`ots lc tb` elotmjo`r (wmt`r + B`mt`r elji).[b`o swjteb js turo`n lo tb`r` wjii h` joer`a`ot jo tb` t`ap`rmtur` lc tb` syst a. Ujoe` tb` t`ap`rmtur`

lc tb` surrluonjoks wms `qumi tl t`ap rmtur` lc tb` syst`a sl, b`mt emo olt cilw hut stjii tb`r js joer`a`ot

jo tb` `o`rky lc tb` syst`a mon b`oe`, tb`r` js t`ap`rmtur` joer`a`ot. ^bjs aust h` h`emus` lc `i`etrjemi

wlrg nlo` hy tb` hmtt`ry lo tb` syst`a olt h`emus` lc tb` b`mt trmosc r ms jojtjmiiy t`ap`rmtur`s w r` `qumi.

Uyst`a 4 [mt`r loiy js lur syst`a. B`mt`r elji wjii h` pmrt lc tb` surrluonjoks.Jo tbjs ems` wb`o swjteb js turo`n lo tb` t`ap`rmtur` lc tb` b`mt`r elji wjii joer`ms` cjrst sl tb`r` wjii h` mt`ap`rmtur njcc`r`oe` h`tw``o syst`a & surrluonjoks. B`oe`, tbjs o`rky trmosc r wjii h` emii`n b`mt.

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JPVME Ujko elov`otjlo mhlut B`mt mon [lrgMoy `o`rky kjv`o tl syst`a js tmg`o plsjtjv` sl b`mt kjv`o tl syst`a 1 plsjtjv`b`mt kjv`o lut crla syst`a / tmg`o lut crla syst`a 1 O`kmtjv`[lrg nlo` lo tb` syst`a 1 Vlsjtjv`[lrg nlo` hy tb` syst`a 1 O`kmtjv`^b` sjko elov`otjlo js njcc`r`ot crla pbysjes, hut tb` a`mojok miwmys ela`s lut tlh` sma` loiy jo `qumtjlo w` bmv` tl us` m njcc r`ot sjko elov`otjlo clr wlrg.Ul jc jo moy prlhi`a, w 1 =6 D

Jt a`mos syst`a bms nlo` wlrg lc =6 Dlui lo surrluonjoks.Meelrnjok tl Eb`ajstry 4

w

]

w

]

Jo Vbysjes

P 1] +[ P 1] [

JPVME elov otjlo lc B`mt=. B`mt kjv`o tl tb` syst`a 1 +v`8. B`mt elajok lut lc tb` syst`a 1 v`5. [lrg nlo` lo tb` syst`a 1 +v`

>. [lrg nlo` hy tb` syst`a 1 v`

Cjrst Imw lc ^b`ralnyomajes (CIL^) 4Imw lc `o`rky elos`rvmtjlo 4@o`rky lc tltmi uojv`rs` js miwmys elos`rv`n.

lrltmi `o`rky lc mo jslimt`n syst`a js miwmys elos`rv`n.

lrB`oe` mhsliut`vmiu` lc @ emo o`v r h` emieuimt`n loiy ebmok` jo vmiu` lc @ emo h` emieuimt n clr m pmrtjeuimrprle`ss.

Amtb`amtjemi clra lc Cjrst Imw lc tb`ralnyomajes.

Jc m syst`a js jotjmiiy jo m pmrtjeuimr stmt jo wbjeb jts tltmi jot`romi `o`rky js @=. Olw q maluot lc b`mt js kjv`o

tl jt mon w maluot lc wlrg js nlo` lo jt sl tbmt jo o`w stmt` jts tltmi jot`romi `o`rky h`ela`s @ 8. ^b`omeelrnjok tl =st Imw lc tb`ralnyomajes.

@81 @

=+ q + w

sl @ 1 (@8 @

=) 1 q + w

Mppijemtjlo lc Cjrst Imw

P 1 ] + [ Ujoe` [ 1 V S P 1 ] VS

Emieuimtjlo lc njcc`r`ot qumotjtj`s jo Cjrst Imw lc ^b`ralnyomajes (CIL ) 4

Emieuimtjlo lc @ 4^b`ralnyomaje n`cjojtjlo lc mo jn`mi kms 4

Jc clr m kms tb` jot`romi `o`rky js njr`etiy prlplrtjlomi tl jts mhsliut` t`ap`rmtur` tb`o tb` kms jst`ra`n ms mo jn`mi kms.

sl^S

@

1 6 ,^V

@

1 6

Jot`romi @o`rky (@, misl n`olt`n hy P) 4

@v`ry syst`a bmvjok sla` qumotjty lc amtt`r js msslejmt`n wjtb m n`cjojt` maluot lc `o`rky,emii`n jot`romi `o`rky .

Jt js tb` sua lc mii clras lc `o`rkj`s pr`s`ot jo tb` syst`a.

@ 1 @^rmosimtjlomi+ @Xltmtjlomi+ @Sjhrmtjlomi+ @hlonjok+ .....@ 1 @

Cjomi @

Jojtjmi .

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@ 1 qv, b`mt suppij`n tl m kms mt elostmot vliua`, sjoe` mii tb` b`mt suppij`n kl`s tl joer`ms` tb`

jot`romi `o`rky lc tb` kms .

Jt js mo `xt osjv` prlp`rty & m stmt` cuoetjlo . Jt js `xeiusjv iy m cuoetjlo lc t`ap`rmtur .

Jc ^ 1 6 7 @ 1 6 ms w`ii.

[jtb ebmok` jo t`ap`rmtur` loiy gjo`tje `o`rky ebmok s.

N`kr`` lc cr``nla

^b` tltmi ol lc aln`s lo wbjeb m ali eui lc mo jn`mi kms emo `xebmok` `o`rkynurjok eliijslos js golwo ms jts n`kr``s lc cr``nla.

^rmosimtjlomi n`kr`` lc cr``nla 1 5 - clr mii typ` lc kms`s.Xltmtjlomi n`kr`` lc cr``nla

1 6 alolmtlaje kms`s

1 8 njmtlaje lr ijo`mr pliymtlaje kms`s1 5 olo-ijo`mr pliymtlaje kms`s.

Jc c js jojtjmi n`kr`` lc cr``nla clr tbmt kms.

c 1 5 clr alolmtlaje1 0 clr njmtlaje lr ijo`mr pliymtlaje

1 3 clr olo - ijo`mr pliymtlaje

Imw lc `qujpmrtjlo lc `o`rky 4@o rky `qumi tl

8

=g^ js msslejmt`n wjtb `meb n`kr`` lc cr``nla p r jn`mi kms ali`eui

[b`r` g js Hlitzamoo elostmot

P/ali`eui` 1 c x8

=g^

P/ali` 18

cX^ (g O

M1 X)

Clr o ali`s,

P 1 8

c

oX^ loiy clr jn`mi kms.

P 18

coX^

Emieuimtjlo lc B`mt (q) B`mt js m pmtb cuoetjlo mon js k`o`rmiiy emieuimt`n jonjr etiy usjok Jst Imw lc tb`ralnyomajes

Cjrst emieuimt`@ mon [ & tb`o q lr b`mt emo h` emieuimt`n jc b`mt empmejty lc moy prle`ss jskjv`o tl us.

B`mt empmejty js m pmtb cuoetjlo mon njcc`r`ot typ` lc b`mt empmejtj`s mr` n`cjo`n

X`a`ah`r b`mt empmejty lc m suhstmoe` js olt cjx`n jt js n`p`on`ot lo typ` lc prle`ss wbjeb js h`jok

p`rclra`n lo tbmt suhstmoe`

^ltmi B`mt Empmejty (E^)

B`mt r`qujr`n tl rmjs` tb` t ap`rmtur` lc syst`a hy =E uon`r tb` kjv`o prle`ss js golwo ms tltmi

b`mt empmejty.

Amtb`amtjemiiy, E^1

n^

nq

^

q

D/E

Jt js `xt osjv` prlp`rtj`s mon pmtb cuoetjlo.

Ul, nq 1 E^n^

lo jot`krmtjok q 1 n^E^

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Alimr b`mt empmejty (E)

B`mt r`qujr n tl rmjs` t`ap`rmtur` lc = ali lc m suhtmoe` hy =E

Amtb`amtjemiiy, E 1on^

nq

^o

q

D ali`= G=

Ul, nq 1 oEn^

q 1 ^oEoEn^

E js jot`osjv` pmtb cuoetjlo.E

pjs alimr b`mt empmejty mt elostmot pr`ssur`

ESjs alimr b`mt empmejty mt elostmot vliua`

Ep

mon ES

mr` jot osjv` hut olt m pmtb cuoetjlo

Up`ejcje b`mt empmejty (s) 4

B`mt r`qujr`n tl rmjs` t`ap`rmtur` lc uojt amss (k`o`rmiiy = k) lc m suhstmoe` hy =E.

U 1an^

nq

^a

q

Dk= G=

Ul, nq 1 asn^

q 1 ^asn^asnq U js jot`osjv` pmtb cuoetjlo

UV

js sp`ejcje b`mt empmejty mt elostmot pr`ssur`

US

js sp`ejcje b`mt empmejty mt elostmot vliua`

UV

& US

mr` jot`osjv` hut olt m pmtb cuoetjlo

ltmi b`mt empmejty, alimr b`mt empmejty & sp`ejcje b`mt empmejty lc m prle`ss lo m suhstmoe` mr` r imt`n ms

E^1 oE 1 as & E 1 As

[b`r` a w`jkbt lc suhstmoe`

A alimr amss lc suhstmoe`

o ol. lc ali`s lc tb` suhstmoe`

Clr jsltb`rami prle`ss E 1 Clr jslhmrje prle`ss E 1 Ep

Clr jsleblrje prle`ss E 1 Ev

Clr mnjmhmtje prle`ss E 1 6

B`mt empmejty emo bmv` vmiu` crla tl + n`p`onjok lo tb` prle`ss.

@xmapi -8 4 Nurjok mo `xpmosjlo lc jn`mi kms tb` wlrg nlo` hy kms js =66 D mon tb` b`mt empmejty lc prle`ss js

cluon tl h` + 8 D/E. Cjon@ lc kms jc tb` cjomi t`ap`rmtur` lc kms js 80E bjkb`r tbmo jts jojtjmi

t`ap`rmtur`.

Uliutjlo 4 @ 1 q + [

q 1 8 80 1 06 D & [ 1 =66 D

@ 1 06 =66 1 06 D

[LXG NLO@ (w) 4

@o`rky tbmt js trmosajtt`n crla lo` syst`a tl moltb`r jo sueb m wmy tbmt njcc`r`oe` lc t`ap`rmtur` js

olt njr`etiy jovliv`n js golwo ms wlrg. Jt js mpmtb cuoetjlo.

^bjs n`cjojtjlo js elosjst`ot wjtb lur uon`rstmonjok lc wlrg ms nw 1 Cnx. ^b` clre` C emo mrjs` crla

`i`etrjemi, amko`tje, krmvjtmtjlomi & ltb`r slure`s.

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Pojts 4

B`mt & wlrg hltb mr` clras lc `o`rky . B`oe`, tb`jr uojts mr` uojts lc `o`rky. j.`.U syst`a4 Dlui`s (D).Aueb nmtm js mvmjimhi` jo tb` lin uojts lc emilrj`s (emi) ms w`ii.V S 1 (ijtr`. mtalspb`r`) t`ra wbjeb bms uojt lc `o`rky . Jt js us`cui tl r`a`ah`r tb` elov`rsjlo= ijtr`. mta 1 =6=.5 Dlui`s 1 8>.863 emi

Clr jrr`v`rsjhi` prle`ss`s, stmt` pmrma`t`rs sueb ms V,^ `te emoolt h` n`cjo`n. B`oe`, wlrgemoolt h` `stjamt`n usjok V

kms. Hut hy tb` wlrg `o`rky tb`lr`a

[kms

1 [`xt

+Gpjsstlo

[b`o tb` pjstlo ela`s tl r`st mkmjoGpjstlo

1 6

[kms1 [ `xt1 nvV`xtms tb` `xt`romi pr`ssur` js miwmys n`cjo`n b`oe`, clr mii prle`ss`s wlrg emo h` emieuimt`n usjok

[`xt

1 nv.V`xt[lrg 4 n[ 1 C

`xtnx

V-S [lrg 4

Mssuajok tbmt uon`r mo `xt`romi clre` Cx, tb` pjstlo alv`s nlwo hy m njstmoe` nx.C`xt

nx

)nxM(M

Cn[ `xt n[ 1 V

`xt(nS) [

`xt1 nSV`xt & [ kms1 [ `xt 1 nSV`xt

Ms tb` wlrg nlo` jo tb` mhlv` ems` hy tb` `xt`romi mk`ot js +v` mon ms tb` `xpr`ssjlo elov`ys ltb`rwjs`,b`oe` m -v` sjko js jotrlnue`n.

n[ 1 V`xt. nS

Emieuimtjlo lc wlrg clr njcc`r`ot typ` lc prle`ss lo mo jn`mi kms.(M) Jsltb`rami `xpmosjlo 4^b`r` mr` amoy wmys jo wbjeb m kms emo h` `xpmon`n jsltb`ramiiy.

(m) Jsltb`rami r`v`rsjhi` `xpmosjlo 4

V`xt

1 V6+

M

ak1 V

kms1 V (miwmys)

Jo r`v`rsjhi` prle`ss,

V`xt

1 Vkms

(tb`ralnyomaje `qujijhrjua miwmys)

Ujoe` prle`ss js jsltb`rami

V 1S

oX^

[ 1 c

j

S

S

`xt nSV 1 c

j

S

S

nSV [1 c

j

S

S

nSS

oX^

[ 1 oX^ io

j

c

S

S

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EB@AJU^XZ

VS njmkrma X`pr`s`otmtjlo

Jo `xpmosjlo wlrg js nlo` hy syst`a lo tb` surrluonjoks mon Sc? S

j

[ 1 v`[lrg 1 Mr`m uon`r tb` VS njmkrma

(h) Jrr`v`rsjhi` jsltb`rami `xpmosjlo 4

(j) Ujoki` st`p jsltb rami `xpmosjlo

[` mr` mssuajok `xpmosjlo mkmjost mtalspb`rje pr`ssur` wbjeb o``n olt h` tb` ems` jo m kjv`o prlhi`a.M amss `qumi tl a

6js pime`n lo pjstlo jojtjmiiy tl amjotmjo `qujijhrjua.

Jojtjmiiy, Vj1 V

kms 1 V

mta+ a

6k/M

VS njmkrma X`pr`s`otmtjlo

Clr `xpmosjlo tl tmg` pime`, a6amss js sunn`oiy r`alv`n sl kms `xpmons mkmjost elostmot `xt`romi

pr`ssur` lc Vmta

Jo tbjs ems`, tb` pr`ssur` lc tb` kms wjii olt h` n`cjo`n ms tb` sunn`o `xpmosjlo bms tmg`o pime` sl mii tb`ali`eui`s lc smapi` wjii olt k`t tb` joclramtjlo lc `xpmosjlo sjauitmo`lusiy, tb`r` wjii h` m tja` kmp monb`oe`, tb`r` wjii h` mstmt` lc turhui`oe`.Crla sla` jot`ra`njmt stmt` lc vliua` S, tb` wlrg nlo` js sijkbt `xpmosjlo crla

S (S + nS)nw 1 V

`xt. nS (JPVME sjko elov`otjlo)

Ul, [ 1 c

j

S

S

`xt nv.Vnw

[ 1 V`xt

(Sc S

j)

Loiy jojtjmi mon cjomi stmt`s emo h` ilemt`n (ms mt jot`ra`njmt` stmk`s pr`ssur` lc tb` kms js olt n`cjo`n)

(jj) ^wl st`p jsltb`rami `xpmosjlo 4

Amss A6js njvjn`n jotl twl amss (amy h` `qumi lr uo`qumi)

)aa(A 8=6 Olw, jc a

=loiy js r`alv`n, tb`o tb` `xpmosjlo lc kms wjii tmg` pime` mkmjost elostmot `xt`romi

pr`ssur`

8/12/2019 Thermodynamics Theory E

11/45

"amojsbguamrpbysjes.jo" ==

EB@AJU^XZ

=`xtV 1 (V

mta+ a

8k/M)

mon tbjs `xpmosjlo wjii tmg` pime` loiy uptl vliua` S=sueb tbmt

=`xtV . S

=1 V

jS

j(jsltb`rami)

Olw, jc s`elon amss a8

js misl r alv`n tb`o `xpmosjlo

S= Scwjii tmg` pime` mkmjost elostmot pr`ssur`

Ul, 8`xtV 1 Vmta

wlrg nlo` js `xpmosjlo Sj

S=

[=1 (V

mta+A

8k/M) (S

j S

=)

& wlrg nlo` js `xpmosjlo S= Sc

[81 V

mta(S

c S

j)

^ltmi wlrg 1 [=+ [

8

Vmta

SSc A6

Sj

A=

VS Njmkrma r`pr`s`otmtjlo

[lrg nlo` jo tbjs jrr`v`rsjhi` `xpmosjlo js kr`mt`r tbmo wlrg nlo` hy kms nurjok tb` sjoki` stmk``xpmosjlo lc kms mon sl lo clr tbr`` st`p `xpmosjlo w` njvjn` tb` amss a

6jotl tbr`` amss`s a

=, a

8 mon

a5

mon r`alv` tb`s` st`p hy st`p mon sl lo.

(jjj) Clr o st`p `xpmosjlo mon o Jrr`v`rsjhi` prle`ss h`ela`s

VS Njmkrma r`pr`s`otmtjlo

(H) jsltb`rami elapr`ssjlo lc mo jn`mi kms 4

(m) X`v`rsjhi jsltb`rami elapr`ssjlo lc mo jn`mi kms

^bjs emo h` mebj`v`n hy pimejok pmrtjei`s lc smon lo` hy lo` mt m v`ry silw tmg` jo tb` mss`ahiy wbjeb

g``ps tb` t`ap`rmtur lc kms elostmot jo tbjs ems` tb` `xpr`ssjlo lc wlrg nlo` wjii h` `xmetiy sjajimr tl ms

lhtmjo`n jo ems` lc r`v rsjhi` `xpmosjlo lc kms[ 1 oX^ io(Sc/S

j)

8/12/2019 Thermodynamics Theory E

12/45

"amojsbguamrpbysjes.jo" =8

EB@AJU^XZ

^bjs wjii mutlamtjemiiy ela` lut tl h` +v` ms Sc9 S

j

Vmta

Sj

Sj

(V + A k/M) 1 Vmta 6 c

SjSc

Vmta

(h) Jrr`v`rsjhi` jsltb`rami elapr`ssjlo lc mo jn`mi kms

(j) Ujoki` st`p elapr`ssjlo 4

^l elapr`ss kms m amss a6js sunn`oiy pime`n lo amssi`ss pjstlo

nw 1 V`xt

. nv1 (V

mta+ a

6k/M) nv

sl. tl emieuimt` tltmi wlrg nlo` lo tb` kms

[ 1 c

j

S

S `xt nv.Vnw 7 [ 1 V

`xt(S

c S

j)

(jj) wl st`p elapr`ssjlo 4

Vime` amss a6

jo twl crmka`ots (a=

+ a8) tb` krmpbjemi r`pr s`otmtjlo wjii amg` tb` emieuimtjlo lc

wlrg nlo` .

Jc a=

js pime`n cjrst, tb`o tb` cjrst elapr`ssjlo bms tmg`o pime` mkmojst `xt`romi pr`ssur` lc

(Vmta

+ a=k/M)

Ul, [=1 (V

mta+ a

=k/M) (S

= S

j)

Ujaimriy, [81 (V

mta+ a

6k/M) (S

c S

j)

Olt` 4Jc prle`ss tmg`s pime` jo o st`ps mon o tb`o prle`ss wjii h` ijg` r`v`rsjhi` elapr`ssjlo

8/12/2019 Thermodynamics Theory E

13/45

"amojsbguamrpbysjes.jo" =5

EB@AJU^XZ

Eloeiusjlo 4

[b`o`v`r wlrg js nlo` lo tb` kms tb`o jt wjii h` ajojaua jo ems` lc r`v`rsjhi` prle`ss.

^bmts wby njcc`r`ot amebjo`s/`okjo`s mr` n`sjkon tl wlrg r`v`rsjhiy sl amxjaua lutput emo h` lhtmjo`n

hut ajojaua joput js kjv`o tl jt

lutput wlrg nlo` hy `okjo`/amebjo`/syst`a

joput wlrg nlo` hy syst`a us m surrluonjok

Jc xpmosjlo/elap r`ssjlo tmg`s pime` mkmjost elos tmot `xt`romi pr`ssur` tb`o jt js jrr`v`rsjhi`. J c tb`r` js sunn `o ebmok` tb`o tb` prle`ss js jrr`v`rsjhi`.

X`v`rsjhi` mon jrr`v`rsjhi` jsltb`rami prle`ss.

@xe`pt tb` jocjojt` stmk` elapr`ssjlo/`xpmosjlo, mii mr` jrr`v`rsjhi`. [` emo r`n`cjo` r`v`rsjhi` mon jrr v`rsjhi` ms cliilws 4

X`v`rssjhi` prle`ss 4 Jc m prle`ss lp`rmt`s js sueb m cmsbjlo tbmt wb`o jt js r`v`rs`n

H

M

hmeg hltb tb` syst`a ms w`ii ms surrluonjoks mr` r`stlr`n tl tb`jr jojtjmi plsjtjlo w.r.t. hltb wlrg mon b`mt,

js golwo ms r`v`rsjhi` prle`ss.

Jc clr tb` prle`ss M H wlrg 1 w, b`mt 1 ] tb`o jc clr tb` prle`ss HM, wlrg 1 w, b`mt 1 ] tb`o tb`

prle`ss js r`v`rsjhi`.

Jc tb` `xt`romi pr`ssur` js elostmot jo jsltb`ramiiy prle`ss, prle`ss js jrr`v`rsjhi`

@xmapi -5 4 Emieuimt tb` wlrg p`rclra`n wb`o 8 ali s lc bynrlk`o `xpmon jsltb`ramiiy mon r`v`rsjhiy mt 80E

clra =0 tl 06 ijtr`s.

Uliutjlo 4 [` bmv ,

[ 1 8.565 o X^ ilk=

8

S

S1 8.565 8 8 8:2 ilk

=0

061 =>53 emilrj`s.

@xmapi -> 4 Jc m kms mt m pr ssur` lc =6 mta mt 566 g `xpmons mkmjost m elostmot `xt romipr`ssur lc 8 mta crlam vli. lc =6 ijtr`s tl 86 ijtr`s cjon wlrg nlo` < WJsltb`rami prle`ssQ

Uliutjlo 4 Vrle`ss js jrr`v rsjhi`

Q=686W8nv8w

86

=6

1 86 I.mta

= ijtr` mta 1 =6=.5 D

Emieuimtjlo lc Ep

mon ES

(m) Elostmot vliua` prle`ss (Jsleblrje)nP 1 nq + nw

nP 1 nq pnS

nP 1 (nq)v

B`mt kjv`o mt elostmot vliua` 1 ebmok` jo jot`romi `o`rky

nu 1 (nq)

nP 1 (oEn^)v

nP1oEvn^

Evjs Up`ejcje alimr b`mt empmejty mt elostmot vliua`.

Ev 1

n^

nP.

o

=

n^

8/)coX^(n

o

=1

8

cX

8/12/2019 Thermodynamics Theory E

14/45

"amojsbguamrpbysjes.jo" =>

EB@AJU^XZ

(h) Elostmot pr`ssur` prle`ss (Jslhmrje) 4

nP 1 n] + n[

nP 1 n] VnS

n] 1 nP + VnS ............... (j)

N`cjojok m o`w tb`ralnyomaje cuoetjlo

B @otbmipy Jt js m stmt` cuoetjlo mon `xt`osjv` prlp`rty

Jt js amtb`amtjemiiy n`cjo`n ms 4B 1 P + VS

ms nB 1 nP + n (Vv)ms V 1 elostmot

nB 1 nP + VnS .............. (jj)

crla qumtjlo (j) & (jj)nB 1 (nq)

ploiy mt elostmot pr`ssur`.

B`mt kjv o mt elostmot pr`ssur 1 Ebmok` jo `otbmipy

nB 1 (oEn^)p

nB 1oEp

n^

X`imtjlo h`tw``o Ep

mn Evclr mo jn`mi kms

B 1 P + VS nB 1 nP + n(VS)clr mo jn`mi kms

VS 1 oX^

n(VS) 1 n(oX^) 1 oXn^oE

pn^1oE

vn^ + oXn^

Ep

Ev1 Xloiy clr jn`mi kms Amy`rs X`imtjlosbjp

MNJMHM JE VXLE@UU 4

n] 1 6 (ol b`mt ebmok`n h/w syst`a mon surrluonjok

nP 1 n] + n[

oESn

^1 VnS nv.S

oX^n^oeS

8

=

^

^

v

^

n^.E1

8

=

S

S

n^.S

X E

vio

=

8

^

^1 V io

=

8

S

S

io=

8

^

^1 io

ve/X

=

8

S

S

=

8

=

=

8

S

S

^

^

^8

S8

= 1 ^=S

== lr ^ S= 1 elostmot

VS

1 elostmot

^bjs js loiy vmijn wb`o tb` qumotjty VS lr ^S= js elostmot loiy clr m qumsj-stmtje lr r`v`rsjhi`prle`ss.

Clr jrr v rsjhi` mnjmhmtje prle`ss tb`s` `qumtjlos mr` olt mppijemhi .

8/12/2019 Thermodynamics Theory E

15/45

"amojsbguamrpbysjes.jo" =0

EB@AJU^XZ

Lp`rmtjlo lc mnjmhmtje prle`ss

(m) X`v`rsjhi` Mnjmhmtje

Lp`rmtjlo wjs` mnjmhmtje prle`ss mon jsltb`rami prle`ss mr` sjajimr b`oe` mii tb` erjt`rjm tbmt jsus`n clr dunkjok mo jsltb rami jrr v`rsjhi` prle`ss`s mr` mppijemhi` tl mnjmhmtje prle`ss.

Misl, vliua` jo ems` lc jsltb`rami vliua` js alr` tbmo tbmt lc mnjmhmtje mt elostmot pr`ssur` mon ollc ali`s, S ^

w 1

nvV .`xt , hut V

`xt

1 Vjot

1S

G

w 1 nv.SG

, [ 1 G

=

SS ===

8 1=

S.SVS.SV =====

888

wlrg nlo` 1=

SVSV ==88

(ms G 1 V

8S

8 1 V

=S

= )

(h) Jrr`v`rsjhi` Mnjmhmtje

Mnjmhmtje jrr`v`rsjhi` `xpmosjlo

[ 1 nvV .`xt 1 V`xt(S8 S=) , mon nwnu

[ 1u

[ 1 oEv(^

8 ^

=) 1

=

)^^(oX =8

1

=

)SVSV ==88

Olt`4 Jc twl stmt s M mon H mr` eloo et`n hy m r`v`rsjhi pmtb tb`o tb`y emo o`v r h` eloo`et n hy mo

jrr`v rsjhi pmtb.

Jc tb` twl stmt`s mr` ijog`n hy mo mnjmhmtje r`v`rsjhi mon jrr v rsjhi` pmtb tb`ow

r`v.1 u

r`v.

8/12/2019 Thermodynamics Theory E

16/45

"amojsbguamrpbysjes.jo" =3

EB@AJU^XZ

Hut ms u js m stmt` cuoetjlo

ur`v.

1 ujrr`v.

wjrr`v.

1 wr`v.

ms wlrg js m pmtb cuoetjlo.

Jc w` mssua` tbmt

wjrr`v.

1 wr`v.

Jt japij`s tbmt

ur`v.

ujrr`v..

wbjeb mkmjo js m elotrmnjetjlo ms P js m stmt` cuoetjlo.

^wl stmt`s M mon H emo o`v`r ij` hltb lo m r`v`rsjhi` ms wjii ms jrr`v`rsjhi` mnjmhmtje pmtb.

^b`r` ij`s loiy lo` uojqu` mnjmhmtje pmtb ijogmk` h`tw``o twl stmt`s M mon H.

Elapmrjslo lc Mnjmhmtje @xpmosjlo (sjoki` stmk` Ss Jocjojt` stmk`)

Ujoki` stmk` a`mos jrr`v`rsjhi` prle ss

Jocjojt` stmk` a`mos r`v rsjhi` prle`ss

Jo mnjmhmtje `xpmosjlo prle`ss,

([kms

)r`v

? ([kms

)jrr`v

ur`v.

?ujrr`v.

(^8)

r`v.9 (^

8)

jrr`v

(V8)r`v.9 (V8) jrr`v (Jc vliua` ebmok` mr` sma`)(S

8)

r`v.9 (S

8)

jrr`v (Jc pr ssur` ebmok` mr` sma`)

Elapmrjslo lc Mnjmhmtje @xpmosjlo (sjoki` stmk` Ss Jocjojt` stmk`)

Ujoki` stmk` a`mos jrr`v`rsjhi` prle ss

Jocjojt` stmk` a`mos r`v rsjhi` prle`ss

Jo mnjmhmtje elapr`ssjlo prle`ss,

([kms

)r`v

9 ([kms

)jrr`v

ur`v.

9ujrr`v.

(^8)

r`v.9 (^

8)

jrr`v

(V8)

r`v.9 (V

8)

jrr`v (Jc vliua` ebmok` mr` sma`)

(S8)

r`v.9 (S

8)

jrr`v (Jc pr ssur` ebmok` mr` sma`)

8/12/2019 Thermodynamics Theory E

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"amojsbguamrpbysjes.jo" =;

EB@AJU^XZ

Elapmrjslo lc sjoki` stmk` Ss twl stmk` `xpmosjlo(mnjmhmtje).Jc tb` `xpmosjlo js emrrj n lut jo twl stmk`s tb`o wlrg nlo` jo twl stmk` hy tb` kms ? wlrg nlo` jolo` stmk` hy tb` kms. Ul,P

twl stmk`?P

sjoki` stmk`

^c jo twl stmk` 9 ^

c jo sjoki` stmk` h`emus` n`er`ms` jo jot`romi `o`rky jo twl stmk` js ?

n`er`ms` jo jot`romi `o`rky jo lo` stmk`.

Mnjmhmtje Jrr`v`rsjhi` prle`ss (emieuimtjlo lc stmt` pmrma`t`rs)

Utmt` M jrr`v Utmt` H

V=,S=,^= V8,S8,^8

[ 1=

SVSV

=

)^^(oX ==88=8

1 V

`xt.(S

8 S

=) ,

=

==

^

SV1

8

88

^

SV

Cr`` `xpmosjlo Miwmys kljok tl h` jrr`rv`rsjhi` mon sjoe` V

`xt1 6

Ul, n[ 1 V`xt

. nS1 6

Jc ol b`mt js suppij`n q 1 6tb`o@ 1 6 Ul, ^ 1 6.

Emieuimtjlo lc B, P, wlrg, b`mt `te.Ems` - J Clr mo jn`mi kms uon`rkljok m prle`ss.

tb` clrauim tl h` us`n mr

nP1oEvn^ 1

8

coXn^

nB 1 oEpn^ 1

=

8

coXn^

[ 1 nS.V xtnB 1 nP + n (VS)B 1 P + oX^nu 1 n] + nw

@xmapi -0 4 Emieuimt` tb` amxjaua wlrg nlo` wb`o pr`ssur` lo =6 k lc bynrlk`o js r`nue`n crla 86 mta tl= mta mt m elostmot t`ap`rmtur` lc 8;5 G. ^b` kms h`bmv`s jn`miiy. [jii tb`r` h` moy ebmok` jojot`romi `o`rky< Misl,emieuimt` q.

Uliutjlo 4 [` bmv ,

[ 1 8.565 oX^ ilk8

=

V

V

o 1 ouah`r lc ali`s lc bynrlk`o 1 .wt.ali

krmasjo.wt1

8

=61 0 ali`s.

^bus, [ 1 8.565 0 8 8;5 ilk

=

861 2=26 emilrj s.

curtb`r, tb` ebmok` jo stmt` lc tb` syst`a mt elostmot t`ap`rmtur` wjii olt ebmok` jot`romi `o`rkyj.`.,@ 1 6.

Mkmjo, q 1@ [ 1 6 ( 2=26 ) 1 2=26 emilrj`s.

Ems` - JJ Clr slijns mon ijqujn syst a 4

nP 1 oEvn^

8

coXn^ (ms jt js olt mo jn`mi kms)

nB 1 oEpn^

=

8

coX^ (ms jt js olt mo jn`mi kms)

[ 1

nS.V xt

B 1P + (V8S

8 V

=S

=)

nP 1 nq + nw

8/12/2019 Thermodynamics Theory E

18/45

"amojsbguamrpbysjes.jo" =2

EB@AJU^XZ

@xmapi -3 4 M ijqujn lc vliua` lc =66 I mon mt tb` `xt`romi pr`ssur` lc =6 mta. Jt tb` js elocjo`n josjn` momnjmhmtje hmtb. @xt`romi pr`ssur` lc tb` ijqujn js sunn`oiy joer`ms`n tl =66 mta mon tb` ijqujn k`tselapr`ss`n hy = I mkmjost tbjs pr`ssur` tb`o cjon,(j) wlrg (jj) P (jjj) B

Uliutjlo 4 [lrg nlo` 1 =66 = 1 =66 I. mtaq 1 6 w 1P

=66 1P

B 1P + (V=S8 V=S=)1 =66 + (=66 :: =66 =6)1 =66 + =66 2: 1 :666 ijt mta.

= I. mta 1 =6=.5 Dlui`.

Ems` - JJJ Clr eb`ajemi r`metjlos 4

mM (s) + hH() + eE(k) mM(s) + hH () + e E (k)

[ 1 nSV .`xt

1 jc.`xt SSV1 V

`xt.W(S

M(s) + (S

H() + (S

E(k) (S

M(s) + (S

H() + (S

E(k)Q

1[ 1 V`xt.

WSE

(k) SE(k)Q

1 V`xt.

`xt

e

`xt

e

V

X^o

V

X^'o1

.`xt

ee.`xt

V

X^)o'o(V

[ 1 (oe o

e)X^

[ 1 okX^

nP 1 nq + nw

jc mt elostmot pr`ssur`

nq 1 nB

nP 1 nB pnS

nP 1 nB ok X^

nB 1 nP +ok X^

@xmapi -; 4 Clr tb` elahustjlo lc = ali lc ijqujn h`oz o` mt 80E, tb` b`mt lc r`metjlo mt elostmot pr`ssur` js

kjv`o hy,

E3B3() + ; 8= L8(k) 3EL8(k) + 5B8L ()7B 1 ;26:26 emi.

[bmt wluin h` tb` b`mt lc r`metjlo mt elostmot vliua`

EB@AJU^XZ

@otrlpy Emieuimtjlo slijn lr ijqujn syst`as4

(m) Eu hileg g`pt jo lp`o mtalspb r`

Usyst`a

18

=

^

^ ^

asn^1 asio

=

8

^

^

Usurr

1 ^nqsurr

8

surr

^q

hut qsurr

1 qsyst`a

1 as (^8 ^

=) 1 as (^

= ^

8)

Uuojv`rs`

1 Usyst`a

+ Usurr

Uuojv`rs`

1 as o=

8

^

^+

8

8=

^

)^^(as ? 6

(h) ^wl elpp`r hileg g`pt jo elotmet jo tb`ralstmt

^wl hilegs mr` lc sma` amss

Eu (A)

^= 8

^b`ralstmrt

/////////////////////////////////////

///////////////////////////////////////////////////////////

//////////////////////

Usurr1 6 (sjoe` ol b`mt js ilst tl surrluonjok)U

syst`a1U

M+U

H

Uyst`a wjii r`meb m elaalo t`ap`rmtur` (^c) mon ^

=? ^

c? ^

8

Usyst`a

1c

=

^

^

M

^

nq+

c

8

^

^

H

^

nq

1c

=

^

^ ^

asn^+

c

8

^

^ ^

asn^1 as

8

c

=

c

^

^o

^

^o

Usyst`a

1 aso8=

8c

^^

^

Ujoe` ^c1

8

^^ 8=

Usyst`a

1 aso

8=

88=

^^>

^^

8/12/2019 Thermodynamics Theory E

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"amojsbguamrpbysjes.jo" 80

EB@AJU^XZ

@xmapi -: 4 (m) Lo` ali lc mo jnmi kms `xpmons jsltb ramiiymon r`v rsjhiymt 80E crla m vliua` lc =6 ijtr`s tlm vliua` lc 86 ijtr s.

(j) [bmt js tb` ebmok` jo `otrlky lc tb` kms D.

(K)585

1 8.565 2.5=> 585 ilk ( =.355 =6-0)

1 8:360 D.

K 1 B ^U

8;=:> 1B 8:2U8:360 1B 585U

B 1 =.00 gD/aliU 1 :3.>>D/ali.G

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"amojsbguamrpbysjes.jo" 8:

EB@AJU^XZ

^B@XALEB@AJU^XZ @otbmipy lc m suhstmoe` 4

@v ry suhstmoe` bms m cjx`n vmiu` lc otbmipy uon`r moypmrtjeuimr stmt`. ^blukb, jts `xmet vmiu` emoolt h`emieuimt`n hut jt bms sla` cjojt` cjx`n vmiu`.

^b` `otbmipy lc lo` ali` lc m suhstmoe` emii n alimr `otbmipy jo moy pmrtjeuimr stmt emo h` mssjko`n syahli

Ba(suhstmoe ) 4 Clr `xmapi alimr `otbmipy lc wmt r vmplurs mt 5:2 G mon = mtapr ssur`amyh` r`pr`s`ot`nms Ba

(B8L, k, 5:2 G, = mta). Jo v ry sjapi` wlrgs, `otbmipy emo h` elosjn`r`n ms b`mt elostmot (maluot)

lc suhstmoe`, mon nurjok r`metjlo tbjs b`mt js h jok r`i`ms`n lr mhslrh`n.

Alimr `otbmipy lc suhstmoe` uon`r stmonmrn elonjtjlos js emii`n stmonmrn alimr `otbmipy lc m suhstmoe`.Utmonmrn stmt` lc moy suhstmoe` a`mos.

Clr mKMUstmonmrn stmt` a`mos jn`mi kms mt = hmr pmrtjmi pr`ssur mt moy kjv` t`ap`rmtur`.

Clr m IJ]PJN pur` ijqujn mt lo` hmr pr`ssur` mt = hmr pr`ssur` mt moy kjv`o t`ap`rmtur`.

Clrm VPX@EXZU MIIJO@ ULIJN pur` erystmiijo slijn mt = hmr pr ssur`monmt moykjv`o t`ap`rmtur`

Clr moy UPHU MOE@ lr JLO JO ULIP^JLO tb` sp`ej`s sbluin h` jo uojt alimijty(emo misl h` tmg`o

ms =A eloe`otrmtjlo), mt lo` hmr pr`ssur` mon mt moy kjv`o t`ap rmtur`.

Alimr stmonmrn `otbmipy lc wmt`r vmplurs mt 5:2 G wjii h` r`pr`s`ot`n ms B(B8L, k , 5:2 G) mon alimr

stmonmrn `otbmipy lc ijqujn wmt`r mt 5:2 G wjii h` r`pr`s`ot`n ms Ba

(B8L, i, 5:2 G)

(Jt js bypltb`tjemi hut emo h` emieuimt`n).

[` emoolt `xmetiy emieuimt` `otbmipy elot`ot lc m suhstmoe` loiy tb` ebmok` jo `otbmipy emo h` emieuimt`nwb`o suhstmoe` js tmg`o crla lo` stmt` tl ltb`r.

Clr `xmapi` 4

I`t `otbmipy elotmot jojtjmiiy h` 6 =,aB & cjomiiy `otbmipy elot`ot h` 6

8,aB

^b`o,B 1 6 8,aB 6

=,aB

1 b`mt mnn`n mt elostmot pr`ssur` tl ebmok` t`ap`rmtur` crla 80E tl 06E.

1 EV^ 1 (=2 emi/ali` E) (80E) 1 >06 emi

@xmapi`-== 4 [by nl s b`mt k`t r`i ms`n/mhslrh`n nurjok eb`ajemi r`metjlos gemi r`sp`etjv iy.

Uliutjlo 4 Kjv`o tbmt

(j) C8(k) +

8

=L

8(k) C8L (k)7B 1 0.0 gemi

(jj) B8(k) +

8

=L

8(k) B

8L (k)7B 1 0; gemi

(jjj)8

=B

8(k) +

8

=C

8(k) BC (k)7B 1 3> gemi

C8LmonB

8L jo `qos. (j) mon (jj) mon jo tb` `qo. kjv`o jo tb` prlhi`a mr lo tb` lpplsjt` sjn`s, wbji

BC jo `qo. (jjj) mon jo tb` `qo. kjv`o jo tb` prlhi`a js lo tb` sma` sjn`s.^bus mppiyjok,W @qo. (j) @qo. (jj) + 8 @qo. (jjj) Q, w` k t

C8(k)

8= L

8(k) B

8(k)

8= L

8(k) + B

8+ C

8(k) C

8L (k) B

8L(k) + 8BC(k)7

B 1 0.0 ( 0;) + 8 ( 3>) 1lr C

8L (k) + B

8L (k) L

8(k) + 8BC(k)7 B 1 ;3.0 gemi.

@otbmipy lc Elahustjlo 4 Jt js tb` `otbmipy ebmok` wb`o lo` ali` lc m elapluon elahjo`s wjtb tb` r`qujsjt` maluot lc lxyk`o tl

kjv` prlnuets jo tb`jr stmhi` clras.Clr `xmapi`, tb` stmonmrn `otbmipy lc elahustjlo lc a`tbmo` mt 8:2 G js 2:6 gD ali=. ^bjs japij`s tb`cliilwjok r`metjlo 4

EB>

(k)+8L8(k) EL

8(k)+8B

8L () B 1 2:6 gD ali=

^b` stmonmrn `otbmipy lc elahustjlo lc a`tbmo` mt 8:2 G amy h` wrjtt o msBe (EB>, k, 8:2 G) 1 2:6 gD ali=

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^b` nmtm lo tb` `otbmipy lc elahustjlo emo h` n`t rajo`n `xp`rja`otmiiy. [jtb tb` b`ip lc sueb nmtm, w` emo n`t`rajo` tb` `otbmipy lc clramtjlo lc m elapluon, wbjeb ltb`rwjs` js

njccjeuit lr japlssjhi` tl n`t rajo` `xp`rja`otmiiy. Elosjn`r clr `xmapi , tb` `otbmipy lc clramtjlo lc EB>(k)4

E(krmpbjt ) + 8B8(k) EB

>(k)

Cjrst lc mii, tb` elahjomtjlo lc emrhlo mon bynrlk`o nl`s olt leeur r`mnjiy. U`eloniy, jc tb` r`metjlo js `v`o

elapi t n, tb``on prlnuet wluin olt h` pur` a`tbmo . ^b r`clr , tb` `otbmipy lc clramtjlo lc a`tbmo` emo

h` n`t rajo`n jonjr`etiy tbrlukb tb` `otbmipy lc elahustjlo lc a tbmo` 4

EB>(k) + 8L8(k) EL8(k)+8B8L()BE(EB>, k) 1 Bc(EL8, k ) + 8Bc(B8L , ) Bc (EB>, k)

tb`r`clr`

Bc(EB>, k) 1 Bc(EL8, k ) + 8Bc(B8L , ) BE (EB>, k)

^b` `otbmipj s lc clramtjlo lc EL8

monB8L emo h` n`t rajo`n `xp`rja`otmiiy hy tb` elahustjlo lc emrhlo

(krmpbjt ) mon bynrlk`o. ^bus, golwjok tb` a`sur`n vmiu` lcBE

(EB>, k), tb` `otbmipy lc clramtjlo lc EB

>

emo h` emieuimt`n. ^b` vmiu` js

Bc(EB

>, k) 1B

c(EL

8, k) + 8B

c(B

8L , ) B

E (EB

>, k)

1 W 5:5 + 8 (820) (2:6)Q gD ali= 1 ;5 gD ali=

lr, `qujvmi`otiy, w` amy mnn tb` cliilwjok tbr ` eb`ajemi `qumtjlos.

E(krmpbjt ) + L8 (k) EL8 (k) EB 1 5:5 gD ali=

8 WB8(k) +

8

=L

8(k) B

8L()Q rB 1 8( 820) gD ali

=

WEB>(k)+8L

8(k) EL

8(k)+8B

8L()Q rB 1 ( 2:6) gD ali

=

E(krmpbjt`) + 8B8(k) EB

>(k)

cB 1 ;5 gD ali=

A`msur`a`ot lc @otbmipy lc Elahustjlo 4

@otbmipy lc elahustjlo mr` usumiiy a`msur`n hy pimejok m golwo amss lc tb` elapluon jo m eils`n st``i

elotmjo`r (golwo ms hlah emilrja`t`r) wbjeb js cjii`n wjtb lxyk`o mt mhlut 56 hmr pr`ssur`.^b` emilrja`t r js surrluon`n hy m golwo

amss lc wmt r. ^b` `otjr` mppmrmtus js g`pt jo mo

josuimt`n dmeg`t tl pr`v`ot b`mt `ot`rjok jotl lr

i`mvjok crla tb` elotmjo`r, ms sblwo jo cjkur`.

^b` smapi` js jkojt`n `i`etrjemiiy tl hrjok mhlut

tb`elahustjlo r`metjlo.^b`b`mt `vliv`n js us n

jo rmjsjok tb` t`ap`rmtur` lc wmt`r mon tb`

emilrja`t`r.

Jc tltmi b`mt empmejty lc emilrja`t`r mon mii lc jts

elot`ots 1 E, rjs` jo t`ap`rmtur` 1^tb`o b`mt r`i`ms`n 1 q 1 E^ lc tbjs b`mt jsh`emus`

lc amss a lc suhstmoe` tb`o

nu` tl = ali`, b`mt r`i`ms`n 1

a

Aq 1@E

(elostmot vliua` r`metjlo).

Olw,BE

emo h` emieuimt`n hy usjokBE 1@

E +o

kX .

[b`r`okjs tb` ebmok` jo stljebjla`trje ouah`r lc kms`lus sp`ej`s jo tb` hmimoe`n eb`ajemi `qumtjlor`pr`s`otjok tb` elahustjlo prle`ss.

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@xmapi`-=> 4 M kms ajxtur` lc > ijtr`s lc `tbyi`o` mon a`tbmo` lo elapi`t` elahustjlo mt 80E prlnue`s

3 ijtr s lc EL8

. Cjon lut tb` maluot lc b`mt `vliv`n lo hurojok lo` ijtr` lc tb` kms ajxtur . ^b` b`mts

lc elahustjlo lc `tbyi`o` mon a`tbmo` mr` =>3> mon :;3 gD ali-= mt 80E.

Uliutjlo 4E B +

8 > EB>

5.3; ijt.

+ L8

EL8+ B

8L

x ijt. (> x)ijt. 3 ijt.(smy)

lr x ali`s (> x) ali`s 3 ali`s

Mppiyjok VLME clr E mtlas,

8 x + = ( > x ) 1 = 3 7 x 1 8 ijt.

^bus, tb` vliua` lc E8B

>1 8 ijt., mon vliua` lc EB

81 8 ijt.

vliua` lc E8B> jo m = ijtr` ajxtur` 1 8/> 1 6.0 ijt.

mon vliua` lc EB>

jo m = ijtr` ajxtur` 1 = 6.0 1 6.0 ijt.

Olw, tb raleb`ajemi r`metjlos clr E8B

>mon EB

>mr`

E8B

>+ 5L

88EL

8+ 8B

8L7B 1 =>3> gD

EB>+ 8L8 EL8+ 8B8L7B 1 :;3 gDMsB vmiu`s kjv`o mr mt 80E, i t us cjrst emieuimt` tb` vliua` leeupj n hylo` ali` lc moy kms mt

80E (supplsjok pr`ssur` ms =mta)

Sliua` p`r ali` mt 80E 18;5

8:2 88.> 1 8>.> ijt.

^bus, b`mt `vliv`n jo tb` elahustjlo lc 6.330 ijt. lc E8B

>1

>.8>

=>3> 6.0 1 56 gD

mon b`mt `vliv`n jo tb` elahustjlo lc 6.550 ijt.lc EB>

1>.8>

:;3 6.0 1 86 gD.

tltmi b`mt `vliv`n jo tb` elahustjlo lc = ijtr` lc tb` ajxtur` 1 56 + ( 86) 1 06 gD.

Jot`krmi `otbmipy lc sliutjlo

^b` jot`krmi `otbmipy lc sliutjlo mt tb` kjv`o eloe`otrmtjlo js tb` `otbmipy ebmok` wb`o lo` ali lc

tb` sliut` js njssliv`n jo m n cjojt` qumotjty lc sliv`ot tl prlnue` m sliutjlo lc m n`sjr`n eloe`otrmtjlo.

[bji` r`elrnjok jot`krmi `otbmipj`s lc sliutjlo jt js m k`o`rmi prmetje` tl stmt` tb` maluot lc tb`

sliv`ot jo wbjeb = ali` lc sliut` js njssliv`n 7 ^bus

BEi(k) + =6B8L() BEi (=6B

8L) B

=1 3:.0 gD ali=

jonjemt`s tbmt wb`o = ali` lc bynrlk`o ebilrjn` kms js njssliv`n jo =6 ali lc wmt`r, tb`r` js mo

`vliutjlo lc 3:.0 gD lc b`mt. Ltb`r vmiu`s mr`

(j) BEi(k) + 80 B8L() BEi (80B

8L) B

81 ;8.5 gD ali=

(jj) BEi(k) + > 6 B8L() BEi (>6B

8L) B

51 ;5.6 gD ali=

(jjj) BEi(k) + 866 B8L() BEi (866B

8L) B

>1 ;>.8 gD ali=

(jv) BEi(k) + mq BEi (mq) B01 ;0.6 gD ali=

[b`o`v`r maluot lc sliv`ot js olt sp`ejcj`n tb`o tmg` jts maluot tl h` v`ry imrk` dust ijg`

jo `qumtjlo ol. (jv).

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@otbmipy lc Bynrmtjlo 4

@otbmipy lc bynrmtjlo js us`n jo cliilwjok tl wmys.

@otbmipy lc bynrmtjlo lc mobynrlus lr pmrtjmiiy bynrmt`n smits 4@otbmipy lc bynrmtjlo lc m kjv`o mobynrlus lr pmrtjmiiy bynrmt`n smit js tb` `otbmipy ebmok` wb`o jt elahjo`s

wjtb tb` r`qujsjt` maluot lc wmt`r tl clra m o`w bynrmt`n stmhi` smit.

Clr `xmapi`, tb` bynrmtjlo lc mobynrlus euprje suipbmt` js r`pr`s`ot`n hy

EuUL>(s) + 0B

8L ()EuUL>. 0 B8L(s)

^b`r` js m mialst jovmrjmhiy m ijh`rmtjlo lc b`mt jo sueb r`metjlos, j.`. tb` vmiu` lcB js o`kmtjv`.EuUL

>(s)+266B

8L () EuUL> (266 B8L) Br 1 32 gD ali

=

EuUL>. 0B

8L (s) + ;:0 B

8L () EuUL

>(266 B

8L) B

r 1 + =6 gD ali=

hy suhtrmetjlo, w` k`t EuUL>(s) + 0B

8L ()EuUL

>. 0 B

8L(s)B

r 1 ;2 gD ali=

@otbmipy lc bynrmtjlo lc kms`lus jlos.@otbmipy lc bynrmtjlo lc moy kms`lus jlo js tb` `otbmipy ebmok` wb`o = ali lc tb` kms`lus jlo js bynrmt n

jo imrk` maluot lc wmt r tl clra mq`lus jlo.

Hy elov`otjlo, tb` stmonmrn `otbmipy lc clramtjlo lc B+(mq) js tmg`o tl h` z`rl.

@otbmipy lc bynrmtjlo lc Ei kms`lus jlos wjii h` r`pr`s`ot`n hy 4

Ei (k) + mq. Ei(mq) Br 1B

c (Ei, mq)

@otbmipy lc O`utrmijzmtjlo 4 ^b` maluot lc b`mt r i`ms`n wb`o lo` krma `qujvmi`ot lc mo mejn js o`utrmijs`n hylo` krma `qujvmi`ot lc m

hms`.

lr

^b` maluot lc b`mt r`i ms`n jo clramtjlo lc lo` ali lc wmt`r wb`o mo mejn js o`utrmijs`n hy m hms`.lr

@otbmipy lc o`utrmijzmtjlo js n`cjo`n ms tb` `otbmipy ebmok` wb`o lo` ali lc B+ jo njiut` sliutjlo elahjo`swjtb lo` ali` lc LB tl kjv` rjs` tl uonjsslejmt`n wmt`r, j.`.

B+(mq) + LB(mq) B8L() B1 0;.= gD/ali` 1 =5.; gemi/ali

X`a`ah`r 4

ClrUtrlok Mejn + Utrlok Hms , b`mt lc o`utrmijsmtjlo js miwmys `qumi tl =5.; gemi/ali` lr 0;.= gD/ali . Clr moy ltb`r elahjomtjlo lcmejn mon hms`tbjs b`mt js i`ss tbmo =5.; gemi/ali` lr 0;.= gD/ali`.

@otbmipy lc Jlojzmtjlo 4

[b`o`v r m w`mg mejn (lr hms ) r`mets wjtb m strlok hms` (lr mejn), tb` r i`ms` lc b`mt js i`ss tbmo 0;.= gDali=.

Jt js h`emus` lc tb` cmet tbmt tb`s` mejns lr hms`s mr` olt elapi`t`iy jlojz n jo sliutjlo. Ula` lc tb` b`mt jselosua`n jo jlojzjok tb`r` mejns mon hms`s tbjs b`mt js golwo ms `otbmipy lc jlojzmtjlo. @xmapi`s mr` 4

BEO + Om+ LB Om+ + EO + B8L

rB 1 =8 gD ali=

EB5ELLB + Om+LB Om+ + EB5ELL

+ B8L rB 1 >: gD ali

=

^b` `otbmipy lc jlojzmtjlo emo h` emieuimt`n ms cliilws. ^b` o`utrmijzmtjlo lc m w`mg mejn, smy BEO, amyh`

r`pr`s`ot`n jo twl st`ps, oma`iy,Jlojzmtjlo BEO B+ + EO B

=1 x

O`utrmijzmtjlo B+ + LB B8L B

81 0;.= gD/ali`

^b` elapi`t r`metjlo js lhtmjo`n hy mnnjok tb` mhlv` twl st`ps. ^bus

BEO + LB B8L + EO B 1 =8 gD/ali`

Lhvjlusiy, B 1B=

+B8

B= 1 B B81 W=8 (0;.=)Q 1 >0.= gD/ali`

Kr`mt`r tb` `otbmipy lc jlojzmtjlo lc moy w`mg mejn lr w`mg hms`, w`mg`r wjii h` tb` mejn lr hms`.

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@xmapi`-=0 4 @otbmipy lc o`utrmijzmtjlo lc BEi hy OmLB js 0;.= gD/ali mon hy OB>LB js 0=.= gD/ali. Emieuimt`

tb` `otbmipy lc njsslejmtjlo lc OB>LB.

Uliutjlo 4 Kjv`o tbmt

B+(mq) + OB>LB(mq) OB

>+(mq)+B

8L() B 1 0=.= gD/ali`

[` amy elosjn`r o`utrmijzmtjlo jo twl st`ps.(j) Jlojzmtjlo

OB>LB(mq) OB

>+(mq) + LB(mq) B

=1 = gD ali=

Uuhtrmetjok, w` bmv , E(krmpbjt ) E(njmalon) Btrs

6 1 =.:6 gD ali=

@otbmipy lc Vr`ejpjtmtjlo 4

@otbmipy lc pr`ejpjtmtjlo js tb` `otbmipy ebmok` wb`o lo` ali` lc m pr`ejpjtmt` js clra`n.

Clr `xmapi 4 HmEi8(mq.) + Om

8UL

>(mq) HmUL

>(s) + 8OmEi(mq)

rB618>.8; gD ali=

@xmapi`-=3 4 Emieuimt`B clr tb` r`metjlo, Mk+(mq) + Ei(mq) MkEi(s)

mt 80E. Kjv`ocB (Mk+, mq) 1 =60 gD ali=,

cB (Ei, mq) 1 =3; gD ali=

moncB(MkEi, s) 1 =8; gD ali=

Uliutjlo 4 Clr tb` r`metjlo Mk+(mq) + Ei (mq) MkEi(s)

w`bmv B 1c

B (MkEi, s) c

B(Mk+, mq) c

B(Ei, mq)

1 W=8; =60 (=3; )Q gD ali=

1 30 gD ali=

@otbmipy lc Clramtjlo lc jlos 4

^b` `otbmipy ebmok` wb`o lo` ali` lc bynrmt`n jlos js lhtmjo`n crla `i`a`ot jo jts stmonmrn stmt` ms.

Ei8

(k) + mq Ei (mq) Br 1Bc (Ei, mq)

Hy elov`otjlo, tb` stmonmrn `otbipy lc clramtjlo lc B +(mq) js tmg`o tl h` z`rl.

[` bmv` s``o tbmt B+ (mq) + LB(mq) B8L(i) rB6 1 0;.= gD ali=

Clr tbjs r`metjlo, Br6 1B

c6 (B

8L,i) {B

c6 (B+, mq) +B

c6 (LB,mq)}

B`oe`, mt 80E, w` k`t Bc6 (B+, mq) +B

c6 (LB ,mq) 1B

c6 (B

8L, i) B

r6

sl Bc6 (LB ,mq) 1 { 823.= ( 0;.=)} gD ali= 1 88:.66 gD ali=

[jtb tb` `otbmipj`s lc clramtjlo lc tb`s` twl jlos, tb` `otbmipy lc clramtjlo lc moy ltb`r jlo emo h` cluoncrla tb` `otbmipj s lc clramtjlo mon sliutjlo lc jts pur` elapluon wjtb B+ lr LB. clr `xmapi , tb` `otbmipy

lc clramtjlo lc Om+ emo h` emieuimt`n crla tb` `otbmipy lc clramtjlo mon `otbmipy lc jocjojt` njiut` sliutjlo lc

OmLB. ^b` twl vmiu`s mr 4

^b` eb`ajemi `qumtjlo clr tb` clramtjlo lc jocjojt` njiut` sliutjlo lc OmLB(s) jsOmLB(s) + oB

8L() Om+(mq) + LB (mq)

mqB(OmLB, s) 1 >>.06 gD ali=

Ujoe` tb`r` mr` `qumi maluots lc wmt r lo hltb sjn`s lc tb` mhlv` `qumtjlo, tb` twl `otbmipj s kjv` ol o t

`cc`et mon tbus

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mq

B(OmLB, s) 1 cB(Om+,mq)+

cB(LB, mq)

cB(OmLB, s)

lr cB (Om+, mq) 1

mqB (OmLB, s)

cB(LB, mq) +

cB(OmLB, s)

1 W>>.06 (88:.::) + (>80.3=)Q gD ali= 1 8>6.=8 gD ali=

Ujajimriy, crla OmEi(mq) lr BEi(mq), tb` `otbmipy lc clramtjlo lc Ei (mq) emo h` n t rajo`n, mon sl lo. ^b`ebmok`s jo `otbmipy lc moy jloje r`metjlo emo tb`o h` cluon crla tb`s` jloje `otbmipj s lc clramtjlo mon tb`

usumi `otbmipj s lc clramtjlo lc elapluons.

@xmapi`-=; 4 ^b` `otbmipy lc clramtjlo lc B8L(i) js 820 gD ali= mon `otbmipy lc o`utrmijzmtjlo lc m strlok mejn

mon m strlok hms` js 00 gD ali=. [bmt js tb` `otbmipy lc clramtjlo lc LB jlos 85.52 gD ali=

^b` hlon otbmipy,LB, js n`cjo`n ms tb` mv`rmk` lc tb`s` twl vmiu`s, tbmt js 4

LB

18

gDali52.>85ali2;.06= == 1 >38.380 gD ali=

Jo tb` ems` lc njmtlaje ali`eui`s, sueb ms B8, tb` hlon `otbmipy mon hlon njsslejmtjlo `otbmipy mr`

jn`otjemi h`emus` `meb r`c`rs tl tb` r`metjlo.

B8(k) 8B(k)

B B1B

r6 1 >50.:5 gD ali=

^bus, tb` hlon `otbmipy kjv`o clr moy pmrtjeuimr pmjr lc mtlas js tb` mv`rmk` vmiu` lc tb` njsslejmtjlo

`otbmpij s lc tb` hlon clr m ouah`r lc ali`eui`s jo wbjeb tb` pmjr lc mtlas mpp`mrs.

@stjamtjlo lc @otbmipy lc m r`metjlo crla hlon @otbmipj`s 4

I`t tb` `otbmipy ebmok` clr tb` kms`lus r`metjlo

E8B

>(k) + BEi(k) E

8B

0Ei(k) (k)

h` r`qujr`n crla tb` hlon `otbmipy nmtm. ^bjs amy h` emieuimt`n ms cliilws 4

B 1

mtlaskms`slustb`crlaprlnuetsclratlr`i`ms`n@otbmipy

mtlaskms`slusjotlr`metmotshr`mgtlr`qujr`n@otbmipy

1 W>EB

+E1E

+ BEi

Q + W0EB

EE

EEi

Q1 (E1E+BEi) (EB+EE+EEi)

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@xmapi`-=: 4 Psjok tb` hlon `otbmipy nmtm kjv`o h`ilw, emieuimt` tb` otbmipy ebmok` clr tb` r`metjlo

E8B

>(k)+B

8(k) E

8B

3(k)

Nmtm 4 Hlon Hlon otbmipyE E 553 gD ali=

E 1 E 363 gD ali=

E B >=6 gD ali=

B B >5= gD ali=

Uliutjlo 4 Njmkrmaamtjemiiy, w` r`pr`s`ot tb` kjv`o r`metjlo ms cliilws 4

E 1 E

BB

BB

(k) + B B(k) B

Hr`mghlons

Hr`mghlons

amg` hlon

8E(k) + >B(k) + 8B(k)

B|

E|

B

B

B|

E|

B

B

B

E

B

B

B

E

B

B

B|

E|

B

B

B|

E|

B

B

B

E

B

B

B

E

B

B

B|

E|

B

B

B|

E|

B

B

B

E

B

B

B

E

B

B

B|

E|

B

B

B|

E|

B

B

B

E

B

B

B

E

B

B

B|

E|

B

B

B|

E|

B

B

B

E

B

B

B

E

B

B

B|

E|

B

B

B|

E|

B

B

B

E

B

B

B

E

B

B

B|

E|

B

B

B|

E|

B

B

B

E

B

B

B

E

B

B

B|

E|

B

B

B|

E|

B

B

B

E

B

B

B

E

B

B

^b` b`mt r`qujr`n tl njsslejmt` E8B

>(k) mon B

8(k) jotl tb` kms`lus mtlas js

Clr hr`mgjok = E 1 E 363 gD ali=

Clr hr`mgjok > E B > x >=6 gD ali=

Clr hr`mgjok = B B >5= gD ali=

ltmi 83;; gD ali=

^bus,B 1 8268 gD ali= + 83;; gD ali= 1 =80 gD ali=

@xmapi`-86 4 Psjok tb` hlon `otbmipy nmtm kjv o h`ilw, `stjamt` tb` `otbmipy lc clramtjlo lc kms`lus jslpr`o`

5

88

EB|

EBEBEEB

Nmtm Hlon otbmipy lc E B hlon 1 >=5.52 gD ali=

Hlon `otbmipy lc E E hlon 1 5>;.3: gD ali

=

Hlon `otbmipy lc E 1 E hlon 1 3=0.60 gD ali=

@otbmipy lc suhijamtjlo lc emrhlo (krmpbjt`) 1 ;=2.5: gD ali=

@otbmipy lc njsslejmtjlo lc B8(k) 1 >50.:; gD ali=

Uliutjlo 4 Clr jslpr`o , w` bmv` tl clra

8E E hlons 7 8E 1 E hlons mon 2E B hlons

Clr wbjeb `o`rky r i`ms`n jsW8(5>;.3:) + 8(3=0.60) + 2(>=5.52)Q gD ali= 1 0 858.08 gD ali=

tbmt js,B (crla kms`lus mtlas) 1 0 858.08 gD ali=

^b` r`metjlo elrr splonjok tl tbjs js

0E(k) + 2B(k) E0B

2(k)

cB

=1 0858.08 gD ali=

Hut w` wmot cB elrr splonjok tl tb` cliilwjok `qumtjlo0E(krmpbjt`) + >B

8(k) E

0B

2(k)

cB 1 B8(k) 2B(k)

rB

>1 > >50.:; gD ali=

Mnnjok, w` k`t0E(krmpbjt ) + >B

8(k) E

0B

2(k)

cB 1 =65.5= gD ali=

Njmkrmaamtjemiiy, tb` mhlv` emieuimtjlos amy h` r`pr s`ot`n ms cliilws.

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EB@AJU^XZ

X`slomoe` @o`rky 4 Njcc`r`oe` h`tw``o `o`rky lc r`slomoe` byhrjn mon r`slomtjok struetur` jo

wbjeb r`slomoe` byhrjn bmv` ilw`r `o rky h`emus` stmhjijs`n hy r`slomoe`.

Br`slomoe`

1Bc, `xp`rja`otmi

Bc, emieiuimt`n

1 Belahustjlo,emieiuimt`n

Belahustjlo,`xp`rja`otmi

@xmapi`-88 4 Emieuimt` tb` b`mt lc clramtjlo lc h`oz`o` crla tb` cliilwjok nmtm, mssuajok ol r`slomoe . Hlon`o rkj s 4

E E 1 25 gemi, E E 1 =>6 gemi, E B 1 :: gemiB`mt lc mtlajsmtjlo lc E 1 =;6 .: gemi

B`mt lc mtlajsmtjlo lc B 1 08.= gemi

Uliutjlo 4 [` bmv` tl emieuimt`B clr tb` r`metjlo3E (s) + 5B

8(k) E

3B

3(k)

Clr r`metmots 4

B`mt lc mtlajsmtjlo lc 3 ali`s lc E 1 3 =;6.: gemib`mt lc mtlajsmtjlo lc 3 ali`s lc B 1 3 08.= gemi

Clr prlnuets 4

B`mt lc clramtjlo lc 3 ali`s lc E B hlons 1 3 ::B`mt lc clramtjlo lc 5 ali`s lc EE 1 5 25

B`mt lc clramtjlo lc 5 ali`s lc E Ehlons 1 5 =>6lo mnnjok, w` k t b`mt lc clramtjlo lc E

3B

3,j.`.,

cB 1 3 =;6.: + 3 08.= 3 :: 5 25 1 ;0 gemi

X`imtjlo h`tw``o `o`rky mon `otbmipy lc m r`metjlo 4

rB 1

rP + ( v

k)X^

wb`r`vk js tb` ebmok` jo tb` stljebjlea`trje ouah`r lc kms`lus sp`ej`s jo kljok crla r`metmots tl

prlnuets.

Jt sbluin h` olt`n tbmt wbji` elaputjokvklc m r`metjlo, loiy tb` stljebjla`trje ouah`rs lc kms`lus jseluot`n mon tbls` lc ijqujns mon slijns mr` elapi`t`iy jkolr`n.

Gjreblccs `qumtjlo

(Smrjmtjlo lcB wjtb t`aprmtur )

Ujoe` tb` `otbmipy (lr stmonmrn `otbmipy) lc m suhstmoe` js n`p`on`ot lo stmt` lc tb` suhstmoe`, vmiu` lc

`otbmipy lc m suhstmoe` ebmok`s wjtb t`ap`rmtur` mon b`oe` tb` `otbmipy ebmok` lc r`metjlo js misl

n`p`on`ot lo t`ap`rmturt` mt wbjeb tb` r`metjlo js h`jok emrrj`n lut. ^bjs ebmok` js `otbmipy ebmok` (lr

@, lc r`metjlo js emrrj`n lut mt elostmot vliua`) js r`pr`s`ot`n hy Gjreblccs @qumtjlos.

V + ] X +U

mt t`ap`rmtur` ^=i`t tb` stmonmrn otbmipy lc r`metjlo h`B=, tb`oB

= 1B

a(X,^

=) +B

a(U, ^

=) B

a(V, ^

=) B

a(],^

=)

Jc tb` sma` r`metjlo js emrrj`n lut mt t`ap`rmtur` ^8, tb`o

B8 1B

a(X,^

8) +B

a(U, ^

8) B

a(V, ^

8) B

a(],^

8)

^b`o, tb` ebmok` jo `otbmipy (lr njcc r`oe` jo `otbmipy mt tb`s` twl t`ap rmtur`s)

B 1B8 B

= 1{B

a (X,^

8) B

a (X,^

=)} + {B

a (,^

8) B

a (,^

=)}

{Ba

(V,^8) B

a (V,^

=)} - {B

a (],^

8) B

a (],^

=)}

Ba

(X ,^8) B

a (X,^

=) 1 E

V, X(^

8 ^

=) 1 B`mt r`qujr`n mt elostmot pr`ssur` tl joer`ms` t`ap rmtur` lc lo`

ali` lc X crla =

tl ^8

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EB@AJU^XZ

Ujajimriy

Ba

(U,^8) B

a (U,

=) 1 E

V,U(^

8 ^

=)

Ba

(V,^8) B

a (V,^

=) 1 E

V,V(^

8 ^

=) mon

Ba

(],8) B

a (],^

=) 1 E

V,](^

8 ^

=)

sl B 1B8 B

= 1E

V,X(^

8 ^

=) +E

V,U(^

8 ^

=) E

V,V(^

8 ^

=)E

V,](^

8 ^

=)

1 WEV,X

+EV,U

EV,V

EV,]

Q (^8 ^

=)

1EV(^

8 ^

=)

EV

1EV, X

+EV,U

EV,V

EV,]

1 Njcc`r`oe` jo alimr b`mt empmejtj`s lc prlnuets mon r`metmots.

sl B8 1B

= + n^.EV

clr `xmapi clr tb` r`metjlo

O8

(k)+5B8

(k) 8OB5

(k)

B8 1B

= +E

V(^

8 ^

=)

wb`r` EV

1 885 B,VO,VOB,V E5EE8

* clr m elostmot vliua` r`metjlo

n^.E@@ S6=68

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EB@AJU^XZ

A J U E @ I I M O @ L P U U L I S @ N @ R M A V I @ U

=. Cjon (jo t`ras lc"m") tb` maluot lc `o`rky r`qujr`n tl rmjs` tb` t`ap`rmtur` lc m suhstmoe` crla 5 Gtl 0 G . Mt ilw t`ap`rmtur`s. E

V1 m^5 .

Uli. q 1 n^oEp 1 n^om^5

1 om

0

5

>

>

^

1

>

omW(0)> (5)>Q

1>

2=380om1 =53 om.

Mos.q 1 =53 om.

8. M tb`ramiiy jslimt`n v`ss`i elotmjos =66 k lc wmt`r mt 6E. [b`o mjr mhlv` tb` wmt`r js puap`n lut, sla`lc tb` wmt`r cr``z`s mon sla` `vmplrmt`s mt 6E jts`ic. Emieuimt` tb` amss lc tb` je` clra`n sueb tbmt olwmt`r js i`ct jo tb` v`ss`i. Imt`ot b`mt lc vmplrjzmtjlo lc wmt`r mt 6E 1 8.=6 x =63 D/gk mon imt`ot b`mt lccusjlo lc je` 1 5.53 x =60 D/gk.

Uli. ltmi amss lc tb` wmt`r 1 A 1 =66 kImt`ot b`mt lc vmplrjzmtjlo lc wmt`r mt 6E

1 I=1 8=.6 x =60 D/Gk

& Imt`ot b`mt lc cusjlo lc je` 1 I81 5.53 x =60 D/GkUuppls`, tb` amss lc tb` je` clra`n 1 a^b`o, tb` amss lc wmt`r `vmplrmt`n 1 A aB`mt ilst hy tb` wmt`r jo cr``zjok 1 B`mt tmg`o hy wmt r jo `vmplrmtjlo^bus, aI81 (A a) I=lr a 1 23 k Mos. 23.8 k

5. [lrg nlo` jo `xpmosjlo lc mo jn`mi kms crla > ijtr` tl 3 ijtr` mkmjost m elostmot `xt`romi pr`ssur` lc 8.=mta wms us`n tl b`mt up = ali` lc wmt`r mt 8:5 G. Jc sp`ejcje b`mt lc wmt`r js >.8 D k = G=, wbmt js tb`cjomi t`ap`rmtur` lc wmt`r Q1 8.= 81 >.8 mta ijt.1 >.8 =6=. 580 D

^bjs wlrg js us`n tl b`mt up tb` wmt`rUp`ejcje b`mt lc B

8L 1 >.8 .Gkrma

D

B`mt r qujr`n clr joer`msjok t`ap`rmtur hy =E lc = ali` 1 >.8 =2 1 ;0.3 D>.8 =6=.580 1 ;0.3 W^ 8:5Q0.35 1 ^ 8:5^ 1 8:2.35 G Mos. 8:2.35 G

>. = ali` lc je` mt 6E mon >.3 aa Bk pr`ssur` js elov`rt`n tl wmt r vmplur mt m elostmot t`ap`rmtur` monpr`ssur`. Cjon B mon @ jc tb` imt`ot b`mt lc cusjlo lc je` js 26 emi/k mon imt`ot b`mt lc vmplrjsmtjlo lc ijqujnwmt`r mt 6E js 0:3 emi/k mon tb` vliua` lc je` jo elapmrjslo tl tbmt lc wmt`r (vmplur) js o`ki`et`n.

Uli. Ol. lc ali` 1 = ali`^ 1 8;5 G.

Vv 1 oX .

;36

3.>v 1 = 6.628= 8;5

v 1 53:: ijt W5;66 ijtQimt`ot b`mt lc cusjlo 1 26 emi/krma Imt`ot b`mt lc vmplrjsmtjlo 1 0:3 emi/krma

B 1 26 =2 + 0:3 =2 1 W26 + 0:3Q =2B 1 =8=32 emiB 1@ + V WS

8 S

=Q

=8=32 1@ +;36

3.>W53::Q

@ 1 =8=32 ;36

3.> 53:: 8>.8>

1 =8=32 0>8.;81 ==380.82 emi. Mos. =8=32 emi, ==380.82 emi

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EB@AJU^XZ

0. Clr Mk, VE (DG= ali=) js kjv`o hy 8> + 6.663 ^. Emieuimt`B jc 5 ali lc sjiv`r mr` rmjs`n crla 8;E tl jtss

a`itjok pljot :8;E uon`r = mta pr`ssur`.

Uli. B 1 8

=

^

^

Vn^E 1 8

=

^

^

n^)^663.68>(

B 1 8> (^8 ^=) + 8=

6.663 ( 88^ 8

= ) Dali-= 1 80306 D/ali

Clr 5 ali,B 1 5 80306 1 ;3:06 D Mos. ;3:06 D

3. Emieuimt` tb` maluot lc b`mt `vliv`n nurjok tb` elapi`t elahustjlo lc =66 ai lc ijqujn h`oz`o` crla tb`cliilwjok nmtm.(j) =2 ka lc krmpbjt` lo elapi t` elahustjlo `vliv` 0:6 GD b`mt(jj) =022: GD b`mt js r`qujr n tl njsslejmt` mii tb` ali`eui s lc = ijtr` wmt`r jotl B

8mon L

8.

(jjj) ^b` b`mt lc clramtjlo lc ijqujn h`oz o` js 06 gD/ali(jv) N`osjty lc E

3B

3() 1 6.2; ka/a

Uli. (j) E(s) + L8(k)EL

8(k) 7 cB 1 5:5.55 GD/ali

(jj) B8(k) +

8

=L

8(k)B

8L () 7 cB 1 823 GD/ali

(jjj) E3B

3() +

8=0

L8(k) 3EL

8(k)+5B

8L ()

B 1 W3(5:5.55) + 5 (823)Q 06 1 5832 GD B`mt vliv`n crla 2; ka h`oz`o` 1 53>0 GD Mos. 53>0 GD

2. ^b` stmonmrn alimr `otbmipj s lc clramtjlo lc eyeilb`xmo` (i) mon h`oz o` (i) mt 80 E mr -=03 mon + >: GDali= r`sp`etjv`iy. ^b` stmonmrn `otbmipy lc bynrlk`omtjlo lc eyeilb`x`o` (i) mt 80 js ==: gD ali=. Ps`tb`s` nmtm tl `stjamt` tb` amkojtun` lc tb` r`slomoe` `o`rky lc h`oz`o`.

Uli. @otbmipy lc clramtjlo lc 5 emrhlo-emrhlo nluhi hlons

1BC

( ) Bc( )

1 =03 (+ >:) gD 1 860 gD.

Kjv`o tbmt, + B8 B 1 ==: gD^b`lr`tjemi `otbmipy lc clramtjlo lc 5 nluhi` hlons jo h`oz`o` rjok

1 5 (==:) gD 1 50; gD.r`slomoe` `o rky lc h`oz`o` 1 50; (860) gD 1 =08 gD ali = Mos. =08 gD ali`=

:. Cliilwjok krmpb sblws m sjoki` stmok` `xpmosjlo prle`ss, tb`o wlrgnlo` hy tb` syst`a js

=

8 >

0

S(itr)

V(mta)

(M) :=6> D (H) 868.3 D (E) 063 D (N) =6=.5 D

Uli.

6 8 > S (Ijt)

=

0

Mos. (H)

[ 1 V`xt (S8 S

=) 1 = 8 =6=.580 D 1 868.3 D

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EB@AJU^XZ

=6. M smapi lc 8 gk lc b ijua (mssua`n jn`mi) js tmg`o tbrlukb tb` prle`ss MHE mon moltb`r smapi` lc 8 gk lctb` sma` kms js tmg`o tbrlukb tb` prle`ss MNE. ^b`o tb` t`ap rmtur` lc tb` stmt`sM mon H mr` (Kjv`o X 12.5 dlui`s/ali G) 4(M) M1 =86.0 G, ^H1 =86. 0G (H) M1 8>= G, ^H1 8>= G EH

NM

=6 86S(a )5

V(=6O/a

)

>

8

=6

0

(E) M1 =86.0 G, ^H1 8>= G (N) M1 8>= G, ^H1 >28 GUli. ^

81 >^

=

VM

SM

1oXM

0 =6 1 8=6668

6.628 ^M

0

0

=66=.=

=60.6

=6 =65 1

8

=6668 6.628 ^

M

6=.=

=1 6.628 ^

M

M1=86.0G

mt elostmot vliua`

H

H

M

M

^

V

^

V

^H1

M

MH

V

.V1

0

=6 =86.0 1 8>= G. Mos. (E)

==. Jo mo jsltb`rami `xpmosjlo lc m kms`lus smapi tb` elrr`et r imtjlo js (elosjn r w (wlrg) wjtb sjko meelrnjoktl o`w JPVME elov otjlo)W^b` r`v`rsjhi` mon jrr v rsjhi prle`ss`s mr` emrrj`n lut h`tw``o sma` jojtjmi mon cjomi stmt`s.Q(M) w

r`v? w

jrr`v (H) w

jrr`v? w

r`v (E) q

r`v9 q

jrr`v (N) emo olt h` pr`njet`n

Mos. (H)

=8. Lo` ali` lc mo jn`mi alolmtlaje kms js emus`n tl kl tbrlukb tb` eyei`sblwo jo cjkur . ^b`o, tb` ebmok` jo tb` jot`romi `o`rky jo `xp`onjok tb`

kms crla m tl e milok tb` pmtb mhe js 4(M) 5 V6S6 (H)3X^6

e

hm

S6

^6

>S6

8V6

V6

Sliua`

Vr`ssur`

(E) >.0 X 6 (N) =6.0 X 6

Uli.

v6 >v6

^6

E

Sliua`

V6

8V6

Vr`ssur`

m h

Vv 1 oX^ mt pljot E8V

6 >v

61 = X^

E

^E

1

X

SV2 66

mt pljot mV

6S

61 = X^

6

^61 XSV 66

7 ^E1 2 ^6

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=;. JcBc clr Mk+ (jocjojt`iy njiut`n), OL5 (jocjojt`iy njiut`n), Ei (jocjojt`iy njiut`n) mon MkEi(s) mr` =60.0;:,

86;.53, =3;.=0: mon =8;.632 r`sp`etjv`iy. Emieuimt` tb` `otbmipy ebmok` clr tb` r`metjlo

MkOL5(mq.) + BEi(mq.) MkEi(s) + BOL5 (mq.)

(M) 8=.>;= GD/ali (H) =>0.322 GD/ali (E) 30.>22 GD/ali (N) Olo`

Uli. Br`metjlo1 WBc(MkEi) +Bc(B+) +Bc(OL5)Q

WBc(Mk+)Q +Bc(OL5) +Bc(Ei) +Bc(B

+)Q

1 =8;.632 W=60.0;: =3;.=0:Q 1 30.>22 GD / ali. Mos. (E)=2. [bmt js tb` wlrg nlo` mkmjost tb` mtalspb`r` wb`o 80 krmas lc wmt`r vmplrjz s mt 5;5 G mkmjost m

elostmot `xt`romi pr`ssur` lc = mta < Mssua` tbmt st`ma lh`ys p`rc`et kms imws. Kjv`o tbmt tb` alimr

`otbmipy lc vmplrjzmtjlo js :.;8 gemi/ali`, wbmt js tb` ebmok` lc jot`romi `o`rky jo tb` mhlv` prle`ss .6 emi, ==8>; emi (H) :8=.> emi, ==6;> emi

(E) =68>.2 emi, =8>;6.3 emi (N) ==8:.5 e mi, =686; emi

Uli. Ali` lc B8L 1 =.5:

Vv 1 oX^

= v 1 =.5: 6.628 5;5

v 1 >8.26.

w 1 V`xt. nv 1 = W>8.26Q mta ijt. 1 >8.26 =6=.580 D 1 8.>

580.=6=26.>8 1 =68>.2 emi.

B 1@ + WVvQ. 1 =8>;6.3 emi. Mos. (E)

=:. Clr tb` `qumtjlos

E(njmalon) + 8B8(k) EB>(k) B= 7 E(k) + >B(k) EB>(k) B8

Vr`njet wb tb`r

(M)B=1B

8 (H)B

=?B

8

(E)B=9B

8 (N)B

=1B

8+

vmpB(E) +

njssB(B

8)

Mos. (H)