2ok13 - IPBtakmicenja.ipb.ac.rs/zadaci/2013_2_okruzno.pdf · 2013. 3. 9. · !"#$%&'(' %) *%)%#'...

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!"#$%&'(' %) *%)%#' +&',%#" -.'/(%0 1#23" 1#23-#' 2012/2013. 42/%,'. II .").'/ /56789: ;<=<>?5? -5@<AB 2#.+C,% ,%D2 09.03.2013. $<E<F8?5F89: G5:F9B8B, E?6HB < 8BIE:J:7:K 5?=9:A? .BG6@J<HB -5@<AB )"/"L% 1. !"#$%& '()* +$,-*.&( /% 0%1" &"0(2*&( &*3%# -*)&%45(. 6$,-*.&" %71$3" '"83" 0%1(0.*)&$3" 1m R = $ /(9$&* 5m L = , 0%,-"'8*&" :* -"3% /" :%: ,* %," +$1$&/.$)&* ,$#*-.$:* 0%31"0" ," 0."'+*# 3.*-"2". ;%<") 3"#$%&" (%)$ 0.*0.*3( &" 0(-( $ 0%)&* &"=1% /" 3%)$. >%3%# 3%)*2" -*)&%,- <"(<#* 0%1%9":, =1*/"&% ( %/&%,( &" 0%0.*)&$ 0.*,*3 '"83" (0."'%(="%&$3), -"3% /" :* ,'" $,0%/ /$:"=%&"1* 0."'%(="%&$3" ('$/$ ,1$3(). !"#$%& :* (,0*% /" ,-"&* &*0%,.*/&% 0.* 0.*0.*3*. ?<.")(&"-$: ") 3%*@$+$:*&- -.*2" 31$<"2" $<#*A( -%)3%'" 3"#$%&" $ 0(-"; 7) 7.<$&( 3"#$%&" &*0%,.*/&% 0.* 3%)*2", "3% ,* 3"#$%& <"(,-"'$% <" 5s ; ') B/"8*&%,- 3"#$%&" %/ 0.*0.*3* ( -.*&(-3( 0%)*-3" 3%)*2". B<*-$ /" :* 2 10m s g = . (20G) 2. ?/*"1&$ =", ,* =.*:*, 0.'% $<%7".,3$ 0.$ )*#( 0%'*5" ,'%:( <"0.*#$&( -.$ 0(-", " <"-$# $<%C%.,3$ 0.$ )*#( ,* 0.$-$,"3 0%'*5" 0*- 0(-". D3% :* 0%)*-&" <"0.*#$&" ="," 3 1 1m V = $ 0%)*-&$ 0.$-$,"3 1 100kPa p = , 0.$3"<"-$ 0.%#*&( ,-"2" ="," =."@$)3$ ( p V ! /$:"=."#( $ &"5$: ") (3(0&( 0.%#*&( (&(-."42* *&*.=$:* =","; 7) $<'.4*&$ ."/ ; ') 3%1$)$&( -%01%-* 3%:( =", 0.$#$ ( -%3( 0.%+*,". E%1".&" #"," ="," :* 28,8g/mol M = , 2*=%'" ,0*+$@$)&" -%01%-&" 3"0"+$-"-$'&%,- :* 720J/kgK v c = " (&$'*.<"1&" =",&" 3%&,-"&-" 8,314J/mol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g/mol M = , 2 32g/mol M = , 3 4g/mol M = $ 4 2g/mol M = . J/.*/$-$ (=1%'* ! , ! , ! $ ! 3%:* #*A(,%7&% <"31"0":( 0.*=."/* ( ."'&%-*9$. B<*-$ /" :* <"0.*#$&" -%.(," 2 ! V rS = , =/* :* r ,.*/2$ 0%1(0.*)&$3, " S 0%'.4$&" &%.#"1&%= 0.*,*3" -%.(,". (20 G) 5. K$.%3" +$,-*.&" &"0(2*&" :* '%/%# /% '$,$&* 0 h . G" :*/&%# 2*&%# '*.-$3"1&%# <$/(, &" '$,$&"#" 1 h $ 2 h ( %/&%,( &" /&% +$,-*.&*, &"0."'8*&" ,( /'" $/*&-$)&" #"1" %-'%.". H%3"<"-$ /" #1"<*'$ '%/* $< %7" %-'%." (/".":( ( 0%/1%=( :*/&"3$# 7.<$&"#". (20 G) L"/"-3* 0.$0.*#$1$: !" #$%$ &'()*, ?&,-$-(- <" @$<$3(, M*%=."/ !" +',$- .)/'0)*, ?&,-$-(- <" @$<$3(, M*%=."/ N*+*&<*&-: !" 1"$2$- 1. 3$"/4(56, ?&,-$-(- <" @$<$3(, M*%=."/ H.*/,*/&$3 !%#$,$:* <" -"3#$)*2" ()*&$3" ,.*/2$C 43%1": !" 705/8$-!$" 9":;'<, ?&,-$-(- <" @$<$3(, M*%=."/

Transcript of 2ok13 - IPBtakmicenja.ipb.ac.rs/zadaci/2013_2_okruzno.pdf · 2013. 3. 9. · !"#$%&'(' %) *%)%#'...

Page 1: 2ok13 - IPBtakmicenja.ipb.ac.rs/zadaci/2013_2_okruzno.pdf · 2013. 3. 9. · !"#$%&'(' %) *%)%#' +&',%#" -.'/(%0 1#23" 1#23-#' 2012/2013.42/%,'. ii.").'/ /56789: ;

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.1. ") H%,#"-.":#% -*)&%,- $< &*$&*.+$:"1&%= ,$,-*#" '*<"&%= <" +$,-*.&(. B%)$#% &*3$ /*1$5 -*)&%,-$ #",* m! . G" 2*=" /*1(:* $&*.+$:"1&" ,$1" ma! ( C%.$<%&-"1&%# 0."'+( (1G) $ ,$1" L*#8$&* -*9* ( '*.-$3"1&%# 0."'+( mg! (1G), =/* :* a $&-*&<$-*- (,0%.*2" 3"#$%&". >% (,0%.*2* #%9* /" ,* %/.*/$ $< :*/&")$&* 3.*-"2" $ $<&%,$: µa g= (3G), =/* :* µ 3%*@$+$:*&- -.*2". ?< ,1$)&%,-$ -.%(=1%'" /%7$:"#%

/" :*: 22 / 4m/sa g R L= = (4G), 0" :* µ=2 / =0,4R L (3G). 7) ?< :*/&")$&* 0 -µ 0v v gt= = (2G), /%7$:"#% /" :*

&*0%,.*/&% 0.* 3%)*2" 7.<$&": 0 µ 20m/sv gt= = (2G). ') B/"8*&%,- 3"#$%&" %/ 0.*0.*3* &" 0%)*-3(

3%)*2" :*/&"3" :* <"(,-"'&%# 0(-( 3"#$%&" 20 / 2 50md v a= = (4G).

.2. p V! /$:"=."# 0.%#*&* ,-"2" =",". (3G) a) H.%#*&" (&(-."42* *&*.=$:* :*: 3 1( )vU mc T T! = " (2G) .

?< 1 1 1 /pV mRT M= (2G) ,1*/$ 1 1 1 /T pVM mR= (1G). ?< 3 3 3 /p V mRT M= (2G) $ 3 15p p= , -:. 2 3 13V V V= =

/%7$:"#%: 3 3 3 1 1/ 15 /T p V M mR p M mRV= = (1G). L"#*&%# ( $<."< <" (&(-."42(

*&*.=$:( /%7$:"#%: 61 114 / 3,5 10 JvU p c M RV! = = " (2G). 7) N"/ :*: 12 23A A A= +

(1G). H.%+*, 1 2! :* $<%7".,3$ 0" :*: 12 1 2 1( )A p V V= ! (1G), /%3 :* 0.%+*, 2 3!

$<%C%.,3$: 23 1 3 2( ) 0A p V V= ! = (1G). !%&")&% $#"#% /" :* 5

12 1 12 2 10 JA A pV= = = ! (2G); ') 63, 7 10 JQ U A! = ! + = " (2G).

.3. H%)*-&$ 0%1%9": $ 0%)*-&" 7.<$&" #*C(.$5" ,( :*/&"3$ 0" 5* /% 0%'.4$&* ,-$5$ ( $,-% '.*#* 0%/ (,1%'%# /" ,( $# (7.<"2" ( ,'"3%# -.*&(-3( :*/&"3". ?< :*/&")$&* 3.*-"2" #*C(.$5": ! fma gV mg= !

(3G) , =/* :* ! f gV ,$1" 0%-$,3", /%7$:"#% (7.<"2* #*C(.$5": (! / 1)fa g V m= ! (1G). I" /.(=* ,-."&*, $< :*/&")$&* ,-"2" /pV mRT M= (2G) $#"#% /" :* / /V m RT Mp= (2G) 0" <"#*&%# ( $<."< <" (7.<"2* /%7$:"#%: (! / 1)fa g RT Mp= ! (3G). ?< (,1%'" /" :* 0.$-$,"3 &" #*C(.$5 (C$/.%,-"-$)3$ 0.$-$,"3)

:*/&"3 0.$-$,3( ( 2*=%'%: ,.*/$&$, -:. ! fp gh= (3G) ( h :* /(7$&" &" 3%:%: ,* &"1"<$ ,.*/$&", -:. +*&-".

#*C(.$5") /%7$:"#% 3%&")"& $<."< <" (7.<"2*: [ ]( / ) 1RT Mgha g != (4G). ;$/$#% /" (7.<"2* &* <"'$,$

%/ =(,-$&* @1($/" ! f 4-% <&")$ /" 5* ,* $,-$# (7.<"2*# 3.*-"-$ #*C(.$5$ ( %7* 0%,(/*, -:. ( $,-% '.*#* 5* ,-$5$ /% 0%'.4$&* @1($/" (2G). .4. L"0.*#$&" ="," ( /*1( -%.(," %/.*A*&%# (=1%# ! :*: !V Sl Sr= = (1G). O*/&")$&" ,-"2" ="," <" -": /*% +*'$ :*: /!p mRT MSr = (2G). B ."'&%-*9$ ,'* -*#0*."-(.* ,( :*/&"3*, 0" <" +*% ,$,-*# '"9$:

/! mRT pM Sr const= = (2G), %/&%,&%: 1 2 3 4! " # $M M M M= = = (2G). ?< 0.*-C%/&* /'* :*/&")$&* $

(,1%'" o!+"+#+$=360 (1G) #%=( ,* %/.*/$-$ -."9*&$ (=1%'$: o

2 3 4 1 2 3 1 3 4 2 3 4 1 2 4! 360 / ( )M M M M M M M M M M M M M M M= + + + (2G), o

1 3 4 1 2 3 1 3 4 2 3 4 1 2 4! 360 / ( )M M M M M M M M M M M M M M M= + + + (2G), o

1 2 4 1 2 3 1 3 4 2 3 4 1 2 4! 360 / ( )M M M M M M M M M M M M M M M= + + + (2G), o

1 2 3 1 2 3 1 3 4 2 3 4 1 2 4! 360 / ( )M M M M M M M M M M M M M M M= + + + (2G).

B=1%'$ ,( .*/%#: o!=15,8 (1G), o!=13,8 (1G), o!=110,2 (1G) $ o!=220,2 (1G).

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0 0 2 2! / 2 ! ! / 2 !v gh v gh+ = + (2G) . H%4-% :* +$,-*.&" '*1$3" " %-'%.$ #"1$, 7.<$&" '%/* &" 0%'.4$&$ :* 0 0v ! (1G) 0" ,( %/=%'".":(5* 7.<$&* $,-$+"2":

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$,-$)* $< +$,-*.&* 3.%< 0.'$ %-'%.: 2 ,21 1 1/ 2 / 2mv mgh mv! +! = ! (3G) $ <"#*&%# $<."<" <" 1v /%7$:"#%

7.<$&( 3%:%# 0.'$ #1"< (/"." % 0%/1%=(: , 21 1 1 02 2v v gh gh= + = (2G). D&"1%=&%, <" /.(=$ #1"< $#"#%:

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