!"#$%&'(' %) *%)%#' +&',%#" -.'/(%0 1#23" 1#23-#' 2012/2013. 42/%,'. /56789: ;<=<>?5? -5@
%3%# 3%)*2" -*)&%,- <"(<#* 0%1%9":, =1*/"&% ( %/&%,( &" 0%0.*)&$ 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"#$%&" %/ 0.*0.*3* ( -.*&(-3( 0%)*-3" 3%)*2". B<*-$ /" :* g = 10 m s 2 . (20G)
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2. ?/*"1&$ =", ,* =.*:*, 0.'% $<%7".,3$ 0.$ )*#( 0%'*5" ,'%:( <"0.*#$&( -.$ 0(-", " <"-$# $<%C%.,3$ 0.$ )*#( ,* 0.$-$,"3 0%'*5" 0*- 0(-". D3% :* 0%)*-&" <"0.*#$&" ="," V1 = 1m3 $ 0%)*-&$ 0.$-$,"3 p1 = 100kPa , 0.$3"<"-$ 0.%#*&( ,-"2" ="," =."@$)3$ ( p ! V /$:"=."#( $ &"5$: ") (3(0&( 0.%#*&( (&(-."42* *&*.=$:* =","; 7) $<'.4*&$ ."/ ; ') 3%1$)$&( -%01%-* 3%:( =", 0.$#$ ( -%3( 0.%+*,". E%1".&" #"," ="," :* M = 28,8g/mol , 2*=%'" ,0*+$@$)&" -%01%-&" 3"0"+$-"-$'&%,- :* cv = 720J/kgK " (&$'*.<"1&" =",&" 3%&,-"&-" R = 8,314J/mol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g/mol , M 2 = 32g/mol , M 3 = 4g/mol $ M 4 = 2g/mol . J/.*/$-$ (=1%'* ! , ! , ! $ ! 3%:* #*A(,%7&% <"31"0":( 0.*=."/* ( ."'&%-*9$. B<*-$ /" :* <"0.*#$&" -%.(," V = 2r!S , =/* :* r ,.*/2$ 0%1(0.*)&$3, " S 0%'.4$&" &%.#"1&%= 0.*,*3" -%.(,". (20 G) 5. K$.%3" +$,-*.&" &"0(2*&" :* '%/%# /% '$,$&* h0 . G" :*/&%# 2*&%# '*.-$3"1&%# <$/(, &" '$,$&"#" h1 $ h2 ( %/&%,( &" /&% +$,-*.&*, &"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*%=."/
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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"#$%&". rel="nofollow">% (,0%.*2* #%9* /" ,* %/.*/$ $< :*/&")$&* 3.*-"2" $ $<&%,$: a = µg (3G), =/* :* µ 3%*@$+$:*&- -.*2". ?< ,1$)&%,-$ -.%(=1%'" /%7$:"#% /" :*: a = g 2 R / L = 4m/s 2 (4G), 0" :* µ=2R / L=0,4 (3G). 7) ?< :*/&")$&* v = v0 -µgt = 0 (2G), /%7$:"#% /" :* &*0%,.*/&% 0.* 3%)*2" 7.<$&": v0 = µgt = 20m/s (2G). ') B/"8*&%,- 3"#$%&" %/ 0.*0.*3* &" 0%)*-3( 3%)*2" :*/&"3" :* <"(,-"'&%# 0(-( 3"#$%&" d = v0 2 / 2a = 50m (4G).
p ! V /$:"=."# 0.%#*&* ,-"2" =",". (3G) a) H.%#*&" (&(-."42* *&*.=$:* :*: !U = mcv (T3 " T1 ) (2G) . ?< p1V1 = mRT1 / M (2G) ,1*/$ T1 = p1V1M / mR (1G). ?< p3V3 = mRT3 / M (2G) $ p3 = 5 p1 , -:. V2 = V3 = 3V1 /%7$:"#%: T3 = p3V3 M / mR = 15 p1V1M / mR (1G). L"#*&%# ( $<."< <" (&(-."42(
.2.
*&*.=$:( /%7$:"#%: !U = 14 p1V1cv M / R = 3, 5 " 106 J (2G). 7) N"/ :*: A = A12 + A23 (1G). H.%+*, 1 ! 2 :* $<%7".,3$ 0" :*: A12 = p1 (V2 ! V1 ) (1G), /%3 :* 0.%+*, 2 ! 3 $<%C%.,3$:
A23 = p1 (V3 ! V2 ) = 0 (1G).
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A = A12 = 2 p1V1 = 2 ! 105 J (2G); ') !Q = !U + A = 3, 7 " 106 J (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": ma = ! f gV ! mg (3G) , =/* :* ! f gV ,$1" 0%-$,3", /%7$:"#% (7.<"2* #*C(.$5": a = g (! f V / m ! 1) (1G). I" /.(=* ,-."&*, $< :*/&")$&* ,-"2" pV = mRT / M (2G) $#"#% /" :* V / m = RT / Mp (2G) 0" <"#*&%# ( $<."< <" (7.<"2* /%7$:"#%: a = g (! f RT / Mp ! 1) (3G). ?< (,1%'" /" :* 0.$-$,"3 &" #*C(.$5 (C$/.%,-"-$)3$ 0.$-$,"3) :*/&"3 0.$-$,3( ( 2*=%'%: ,.*/$&$, -:. p = ! f gh (3G) ( h :* /(7$&" &" 3%:%: ,* &"1"<$ ,.*/$&", -:. +*&-".
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#*C(.$5") /%7$:"#% 3%&")"& $<."< <" (7.<"2*: a = g ( RT / Mgh) ! 1 (4G). ;$/$#% /" (7.<"2* &* <"'$,$ %/ =(,-$&* @1($/" ! 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" ="," <" -": /*% +*'$ :*: pSr! = mRT / M (2G). B ."'&%-*9$ ,'* -*#0*."-(.* ,( :*/&"3*, 0" <" +*% ,$,-*# '"9$:
!M = mRT / pSr = const (2G), %/&%,&%: M1! = M 2" = M 3 # = M 4$ (2G). ?< 0.*-C%/&* /'* :*/&")$&* $ (,1%'" !+"+#+$=360o (1G) #%=( ,* %/.*/$-$ -."9*&$ (=1%'$: ! = 360o M 2 M 3 M 4 / ( M 1M 2 M 3 + M 1M 3 M 4 + M 2 M 3 M 4 + M 1M 2 M 4 ) (2G), ! = 360o M 1M 3 M 4 / ( M 1M 2 M 3 + M 1M 3 M 4 + M 2 M 3 M 4 + M 1M 2 M 4 ) (2G), ! = 360o M 1M 2 M 4 / ( M 1M 2 M 3 + M 1M 3 M 4 + M 2 M 3 M 4 + M 1M 2 M 4 ) (2G), ! = 360o M 1M 2 M 3 / ( M 1M 2 M 3 + M 1M 3 M 4 + M 2 M 3 M 4 + M 1M 2 M 4 ) (2G). B=1%'$ ,( .*/%#: !=15,8o (1G), !=13,8o (1G), !=110,2o (1G) $ !=220,2o (1G).
!"#$%&'(' %) *%)%#' +&',%#" -.'/(%0 1#23" 1#23-#' 2012/2013. 42/%,'. .5. M*.&(1$:*'* :*/&")$&* <" ,-.(:&* +*'$ 3%:* 0%'*<(:( =%.2( 0%'.4$&( '%/* $ %-'%.* 1 $ 2 $#":( %71$3: !v0 2 / 2 + !gh0 = !v12 / 2 + !gh1 (2G), -:. !v0 2 / 2 + !gh0 = !v2 2 / 2 + !gh2 (2G) . H%4-% :* +$,-*.&" '*1$3" " %-'%.$ #"1$, 7.<$&" '%/* &" 0%'.4$&$ :* v0 ! 0 (1G) 0" ,( %/=%'".":(5* 7.<$&* $,-$+"2":
v1 = 2 g (h0 ! h1 ) (2G), -:. v2 = 2 g (h0 ! h2 ) (2G). ?< <"3%&" %/.9"2" *&*.=$:* <" #",( '%/* !m 3%:" $,-$)* $< +$,-*.&* 3.%< 0.'$ %-'%.: !mv12 / 2 + !mgh1 = !mv1,2 / 2 (3G) $ <"#*&%# $<."<" <" v1 /%7$:"#% 7.<$&( 3%:%# 0.'$ #1"< (/"." % 0%/1%=(: v1, = v12 + 2 gh1 = 2 gh0 (2G). D&"1%=&%, <" /.(=$ #1"< $#"#%:
!mv2 2 / 2 + !mgh2 = !mv2, 2 / 2 (3G), %/&%,&% v2, = v2 2 + 2 gh2 = 2 gh0 (2G) . !%&")&%,
v1, = v2, = 2 gh0 (1G).
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