CONTENIDO INTRODUCCIÓN...........................................................................................................3 AGRADECIMIENTO:................. AGRADECIMIENTO:................. ............................ .............. ............................ ............................ ..................... ............ .......... .......... .......... ....... 4 OBJETIVOS...................................................................................................................5 CAPITULO 1: GASES IDEALES.......... IDEALES..................... ..................... ..................... ..................... ..................... ...................... ....................6 .........6 1.1
Conce Concepto pto.... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........... ............... ..............6 ......6
1.2
C!c C!cte! te!"#t "#t$c $c## &e 'n (# (# $&e). $&e)..... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ......... .......6 ..6
1.3
V!$*)e !$*)e## +'e ,ec ,ectn tn e) co-p co-po!t o!t-$ -$ent ento o &e )o# (#e# (#e#.... ........ ........ ........... .............. .............. ......... ..
1.4
/e0e# /e0e# o)'-t o)'-t!$c !$c# # &e) e#t&o e#t&o (#eo# (#eo#o... o....... ........ ........ ........ ........ ........ ........ ........ ........... .............. ............... ......... .
1.4.1. /e0 &e Bo0)e................................................................................................. 1.4.2 /e0 &e C!)e#.............................................................................................14 1.4.3 /e0 &e G0 /'##c......................................................................................15 1.4.4 /e0 Gene!) &e )o# (#e# $&e)e#................................................................1 1.4.5 Ec'c$n &e) (# $&e).................................................................................1 1.4.6 CONSTAN CONSTANTE TE UNIVERSA/ DE /OS /OS GASES IDEA/ES:....................... IDEA/ES:.................. ........... .......27 .27 CAPITULO 2: MEZCLAS DE GASES IDEALES........................................................27 IDEALES ........................................................27 2.1 Concepto............................................................................................................27 2.2 /e0 &e D)ton.... D)ton.............. ..................... ..................... ..................... ..................... ..................... ..................... .................................. ........................ 21 2.3 /e0 &e A-(t A-(t.......... ..................... ..................... ..................... ..................... ..................... ............................................... .................................... 22 CAPITULO 3: GASES REALES..................................................................................23 REALES..................................................................................23 3.1. Concepto...........................................................................................................23 3.2. D$,e!enc$# ent!e (#e# !e)e# 0 (#e# $&e)e#.................................................23 3.3 Mo&e)o#..............................................................................................................24 3.3.1 Mo&e)o &e Vn &e! 8)#............................................................................24 3.3.2 Mo&e)o &e Re&)$c 9 ;on(........................................................................25 3.3.3 Mo&e)o &e Be!te)ot 0 &e Be!te)ot -o&$,$c&o............................................26 3.3.4 Mo&e)o &e D$ete!$.......................................................................................26 3.3.5 Mo&e)o &e C)'#$'#.....................................................................................26 3.3.6 Mo&e)o V$!$)................................................................................................2 3.3. Mo&e)o &e
EJERCICIOS RESUE/TOS:........................................................................................31 EJERCICIOS =ICAS.............................................................................41
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INTRODUCCIÓN To&o en e) Un$e!#o e#t? ,o!-&o po! -te!$. / -te!$ #e p'e&e encont!! en 3 e#t&o# &e (!e(c$n o e#t&o# ,"#$co#: #)$&o@ )"+'$&o 0 (#eo#o. En ,"#$c ,"#$c 0 +'"-$ +'"-$c@ c@ 'n 'n ec'c$ ec'c$n n &e e#t&o e#t&o e# 'n ec'c$ ec'c$n n con#t$ con#t$t't t't$ $ p! p! #$#te-# $&!o#t?t$co# +'e &e#c!$*e e) e#t&o &e (!e(c$n &e ) -te!$ co-o 'n !e)c$n -te-?t$c ent!e ) te-pe!t'!@ ) p!e#$n@ e) o)'-en@ ) &en#$&&@ ) ene!(" $nte!n 0 po#$*)e-ente ot!# ,'nc$one# &e e#t&o #oc$&# con ) -te!$. <! enten&e! )o# &$,e!ente# e#t&o# en )o# +'e ) -te!$ e$#te@ e# nece#!$o enten&e! )(o ))-&o Teo!" Mo)ec')! c$nt$c &e ) Mte!$. / Teo!" Mo)ec')! c$nt$c t$ene -'c# p!te#@ pe!o +'" $nt!o&'c$!e-o# #)o )('n#. Uno &e )o# concepto# *?#$co# &e ) teo!" !('-ent +'e )o# ?to-o# 0 -o)c')# po#een 'n ene!(" &e -o$-$ento@ +'e pe!c$*$-o# co-o te-pe!t'!. En ot!# p)*!#@ )o# ?to-o# 0 -o)c')# e#t?n en -o$-$ento con#tnte 0 -e&$-o# ) ene!(" &e e#to# -o$-$ento# co-o ) te-pe!t'! &e 'n #'#tnc$. M$ent!# -?# ene!(" 0 en 'n #'#tnc$@ -0o! -o$-$ento -o)ec')! 0 -0o! ) te-pe!t'! pe!c$*$&. /o# (#e# #e ,o!-n c'n&o ) ene!(" &e 'n #$#te- ece&e to&# )# ,'e!# &e t!cc$n ent!e -o)c')#. A#"@ )# -o)c')# -o)c')# &e (# $nte!ctn poco@ oc#$on)-ente oc#$on)-ente coc?n&o#e. coc?n&o#e. En e) e#t&o (#eo#o@ )# -o)c')# #e -'een !?p$&-ente 0 #on )$*!e# &e c$!c')! en c')+'$e! &$!ecc$n@ eten&$n&o#e en )!(# &$#tnc$#. A -e&$& +'e ) te-pe te-pe!t !t'! '! '-en '-ent@ t@ ) cnt$& cnt$&& & &e -o$-$ -o$-$en ento to &e )# -o)c' -o)c') )## $n&$ $n&$$& $&') ')e# e# '-ent. /o# (#e# #e epn&en p! ))en! #'# contene&o!e# 0 t$enen 'n &en#$&& *. De*$&o +'e )# -o)c')# $n&$$&')e $n&$$&')e## e#t?n -p)$-ente -p)$-ente #ep!&# 0 p'e&en c$!c c$!c') ')! ! )$*! )$*!ee-en ente te en e) e#t e#t&o &o (#e (#eo# o#o@ o@ )o# )o# (#e (#e## p'e& p'e&en en #e! #e! ,?c$ ,?c$))-en ente te co-p!$-$&o# 0 p'e&en tene! 'n ,o!- $n&e,$n$& E) co-po!t-$ento &e to&o# )o# (#e# #e '#t t!e# )e0e#@ )# c')e# !e)c$onn e) o)'-en &e 'n (# con #' te-pe!t'! 0 p!e#$n. /o# (#e# +'e o*e&ecen e#t# )e0e# #on ))-&o# (#e# $&e)e# o pe!,ecto#. A p!t$! p!t$! &e e#t -ono(!,"@ -ono(!,"@ #e p!opone $n&'c$! ) )'-no )'-no 0 )'-n ) ) conoc$-$ento conoc$-$ento &e) co-po!t-$ento co-po!t-$ento &e )o# (#e#@ #'# )e0e# 0 #'# p)$cc$one#.
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AGRADECIMIENTO: E#te p!e#ente t!*o (!&eco -$# p&!e#@ -$# co-pe!o# 0 -$(o# po! to&o e) po0o $nco ncon&$ n&$c$on c$on ) +'e #t #t o! o! -e n *!$n&&o@ e# e))o# +'$ene# &$!$($&o con 'n ep!e#$n &e (!t$t'&. De $(') -ne! ) Un$e!#$&& Nc$on) &e <$'! 0 )o# p!o,e#o!e#@ +'e -e co($&o 0 &&o &&o ) opo! opo!t' t'n$ n$& && & &e #'pe #'pe! !c$ c$n n 0 po! po! ,o!-!-e p! en 'n ,'t'!o po&e! )o(!! -$ -et p!op'e#t 0 #" #e! 'n *'en p!o,e#$on).
4
OBJETIVOS •
Ep)$c! )# p!op$e&&e# &e )o# (#e# $&e)e# 0 )# &$,e!ente# )e0e# +'e !$(en #' co-po!t-$ento.
•
Reconoce! )# c!cte!"#t$c# +'e po#een )o# (#e#.
•
Ap)$c! )# &$,e!ente# )e0e# en en p!o*)e-# cot$&$no#.
•
•
•
D$,e!enc$! ent!e (#e# !e)e# 0 )o# (#e# $&e)e#. Ap!en&e! c')e# #on )# !$*)e# +'e ,ectn 'n (#. I&ent$,$c! )# &$,e!ente# -(n$t'&e# !e)c$on&# con )o# (#e#@ #" co-o $&ent$,$c! #'# 'n$&&e# &e -e&$c$n
5
CAPITULO 1: GASES IDEALES 1.1 Concep Concepo o Se &e,$ne co-o (# $&e)@ +'e) &on&e to&# )# co)$#$one# ent!e ?to-o# o -o)c')# #on pe!,ect-ente e)?#t$c#@ 0 en e) +'e no 0 ,'e!# t!ct$# $nte $nte!!-o) o)ec ec') ')! !e# e#.. Se p'e& p'e&e e $#' $#') )$ $! ! co-o co-o 'n 'n co)e co)ecc cc$ $n n &e e#,e e#,e! !## pe!,ect-ente !"($&# +'e cocn 'n# con ot!# pe!o #$n $nte!cc$n ent!e e))#. En t)e# (#e# to& ) ene!(" $nte!n e#t? en ,o!- &e ene!(" c$nt$c 0 c')+'$e! c-*$o en ) ene!(" $nte!n co-p& &e 'n c-*$o en ) te-pe!t'!. Un (# $&e) #e c!cte!$ po! t!e# !$*)e# &e e#t&o: ) p!e#$n *#o)'t F<@ e) o)'-en FV@ 0 ) te-pe!t'! *#o)'t FT. / !e)c$n ent!e e))# #e p'e&e &e&'c$! &e ) teo!" c$nt$c 0 con#t$t'0e: PV =nRT = NkT
Don&e n H n-e!o &e -o)e# R H con#tnte 'n$e!#) &e (# H .3145 J-o) N H con#tnte &e Bo)t-nN Bo)t-nN H 1.3766 1723 J H .6135 .6135 175 eV k H R / N A N A
H n-e!o &e Ao(&!o H 6.7221 17 23-o)
/ )e0 &e) (# $&e) p'e&e #e! $#t co-o e) !e#')t&o &e ) p!e#$n c$nt$c &e )# -o)c')# &e) (# co)$#$onn&o con )# p!e&e# &e) contene&o! &e c'e!&o con )# )# )e0 )e0e# &e Ne; Ne;ton. ton.
1.2 C!"!ce"#$ C!"!ce"#$%c!$ %c!$ &e 'n (!$ %&e!) %&e!) /o# #$#te #$#te-# -# -te! -te!$) $)e# e# (#eo (#eo#o# #o# #e c!c c!cte! te!$ $n n &e#&e &e#&e 'n p'nto p'nto &e $#t $#t MACROSCÓ
/ e#t!'c e#t!'ct'! t'! &e )o# )o# (#e# (#e# e# $nte!p $nte!p!e !et& t& po! ) teo!" teo!" c$nt$ c$nt$co co-o) -o)ec' ec')! )! FMICROSCÓ
6
•
•
/# -o)c')# e#t?n n$-&# &e pe!pet'o -o$-$ento@ t!#)&?n&o#e en )"ne )"ne !ect !ect en to& to&## )# )# &$!e &$!ecc cc$o $one ne## 0 #ent #ent$& $&o# o# &ent &ent!o !o &e) &e) o)' o)'-e -en n oc'p&o. L0 co+'e# &e )# -o)c')# cont! )# p!e&e# &e) !ec$p$ente 0 t-*$n ent!e #$ Fco+'e# $nte!-o)ec')!e#. $nte!-o)ec')!e#.
1.3 V!"%!*)e$ V!"%!*)e$ +'e !,ec!n !,ec!n e) co-po"!-%eno co-po"!-%eno &e )o$ (!$e$ (!$e$ PRESIÓN E# ) ,'e! ee!c$& po! 'n$&& &e ?!e. En )o# (#e# e#t ,'e! ct en ,o!- 'n$,o!-e #o*!e to&# )# p!te# &e) !ec$p$ente. / p!e#$n t-o#,!$c e# ) ,'e! ee!c$& po! ) t-#,e! #o*!e )o# c'e!po# +'e e#t?n en ) #'pe!,$c$e te!!e#t!e. Se o!$($n &e) pe#o &e) $!e +'e ) ,o!-. M$ent!# -?# )to #e ))e 'n c'e!po -eno# $!e 0 po! enc$- &e )@ po! con#$('$ente ) p!e#$n #o*!e ) #e!? -eno!.
%('"! 1/1 / p!e#$n &e 'n (# #e o!$($n po! +'e cocn #'# -o)c')# con )# p!e&e#
&e) !ec$p$ente &on&e #e enc'ent!
TEMPERATURA E# 'n -e&$& &e ) $nten#$&& &e) c)o!@ 0 e) c)o! #' e e# 'n ,o!- &e ene!(" +'e po&e-o# -e&$! en 'n$&&e# &e c)o!"#. C'n&o 'n c'e!po c)$ente #e co)oc en contcto con 'no ,!"o@ e) c)o! ,)'0e &e) c'e!po c)$ente ) c'e!po ,!"o. / te-pe!t'! &e 'n (# e# p!opo!c$on) ) ene!(" c$nt$c -e&$ &e )# -o)c')# &e) (#. A -0o! ene!(" c$nt$c -0o! te-pe!t'! 0 $cee!#. / te-pe!t'! &e )o# (#e# #e ep!e# en (!&o# e)$n.
7
%('"! 1/2 Epn#$n $&e) &e 'n (# p!e#$n con#tnte
CANTIDAD / cnt$&& &e 'n (# #e p'e&e -e&$! en 'n$&&e# &e -#@ '#')-ente en (!-o#. De c'e!&o con e) #$#te- &e 'n$&&e# SI@ ) cnt$&& t-*$n #e ep!e# ep!e# -e&$ -e&$nte nte e) n-e! n-e!o o &e -o)e# -o)e# &e #'#tn #'#tnc$ c$@@ e#t e#t p'e&e p'e&e c)c') c)c')!# !#e e &$$&$en&o e) pe#o &e) (# po! #' pe#o -o)ec')!. %('"! 1/3 / cnt$&& &e (# -e&$& po! n-e!o &e -o)e#
VOLUMEN E# e) e#pc$o oc'p&o po! 'n c'e!po.
%('"! 1/0 E) o)'-en e# &$!ect-ente p!opo!c$on) ) cnt$&& &e (#
DENSIDAD E# ) !e)c$n +'e #e e#t*)ece ent!e e) pe#o -o)ec')! en (!-o# &e 'n (# 0 #' o)'-en -o)! en )$t!o#. %('"! 1/ Den#$&& &e )o# (#e#
1.0 Lee$ o)'-4"%c!$ o)'-4"%c!$ &e) &e) e$!&o (!$eo$o: 8
/# )e0e# o)'-t!$c# -?# #enc$))# !e)c$onn &o# &e )# c't!o -(n$t'&e# &e) e#t&o (#eo#o. /# &o# !e#tnte# #e -nt$enen con#tnte#. M(n$t'&e# MASA 5-6
Un$&&e# / 'n$&& &e -# en e) #$#te- CGS e# e) (!-o F( / 'n$&& &e -# en e) SIME/A e# e) $)o(!-o F(
VOLUMEN 5V6 5C!p!c%&!&6
En e) SIME/A ) 'n$&& &e o)'-en e# e) -et!o c*$co F- 3 /o# o)-ene# (#eo#o# #e ep!e#n en 'n$&&e# &e cpc$&& )$t!o# F/ o F-/
PRESIÓN 5P6
/ e+'$)enc$ ent!e )# 'n$&&e# &e p!e#$n -?# co-n e#: 1 !- 7 89 -- ;( 7 89 To"" 7113<2 =P!
TEMPERATURA 5T6
En c'nto ) te-pe!t'!@ ) e#c) Ce)#$'# no enc'ent! p)$cc$n en )o# c?)c')o#@ &e*$n&o#e e-p)e! ) e#c) *#o)'t o E/VIN. A-*# te-pe!t'!# +'e&n !e)c$on&# po! ) $(')&&: t C 23 H T
1.0.1. Le &e Bo)e / )e0 &e Bo0)e $nc') e) o)'-en 0 ) p!e#$n@ &e 'n -# con#tnte &e (# te-pe!t'! con#tnte. E) o)'-en &e 'n! -!$! &e,%n%&! &e (!$< ! e-pe"!'"! con$!ne< e$ %ne"$!-ene p"opo"c%on!) ! )! p"e$%>n. %('"! 1/ M# 0 te-pe!t'! e# con#tnte
En ot!# p)*!#@ ) p!e#$n !" en p!opo!c$n $ne!# con e) o)'-en:
9
P=
1 V
0 &e p'e&e !ep!e#ent! (!?,$c-ente co-o: %('"! 1/9 / p!e#$n !$ en p!opo!c$n $ne!# ) o)'-en
/ $nte!p!etc$n -te-?t$c &e) co-po!t-$ento e#: P .V = K ( Ley de Boyle )
&on& &on&e e
k e# con#tnte #$ ) te-pe!t'! 0 ) -# &e) (# pe!-necen
con#tnte#. Se p'e&e !ep!e#ent! (!?,$c-ente co-o:
10
%('"! 1/8 / p!e#$n 0 e) o)'-en #on con#tnte#
/ ,o!- +'e -?# 't$)$-o# p! !ep!e#ent! ) /e0 &e Bo0)e co!!e#pon&e ) =$(.12@ &on&e #e -'e#t! 'n !- &e 'n $p!*o) e+'$)?te! 0 po&e-o# '#! ) #$('$ente ep!e#$n p! &ete!-$n! )o# )o!e# &e &o# p'nto# &e ) (!?,$c: P1 . V 1= P2 .V 2
&on&e: P1
H
P2
H
V 1
H Vo)'-en $n$c$)
V 2
H Vo)'-en ,$n)
<! <! +'e +'e p! p! +'e +'e #e c'-p c'-p) ) ) /e0 /e0 &e Bo0) Bo0)e e e# $-po $-po!t !tn nte te +'e +'e pe"-!ne?c!n con$!ne$ e) con$!ne$ e) n-e!o &e -o)e# &e) (#@ n@ 0 ) te-pe!t'! &e t!*o@ T.
E@pe"%enc%! &e Bo)e E) e#t'&$o &e )o# (#e#@ 0 en p!t$c')! &e) $!e@ t!o ) tenc$n &e )o# ,"#$co# &e) #$()o PVII 0 -?# conc!et-ente ) &e) $!)n&# Ro*e!t Bo0)e F162161. F162161. /# epe!$enc$# epe!$enc$# +'e )e pe!-$t$e!on e#t*)ece! e#t*)ece! #' conoc$& )e0 con# con#$# $#t$t$e! e!on on@@ *?#$ *?#$c c-e -ent nte@ e@ en & &$! $! -e!c -e!c'! '!$o $o 'n t'*o t'*o co& co&& &o o #',$c$ente-ente )!(o *$e!to po! 'n et!e-o 0 p!o$#to &e 'n ))e en e) ot!o. Con ) ))e *$e!t e!t" -e!c'!$o 0 #' n$e) en )# &o# !-# &e) t'*o 11
#e $(')* Fp!$nc$p$o &e )o# #o# co-'n$c co-'n$cnte# nte#. . A cont$n'c cont$n'c$n $n ce!!* ce!!* ) ))e 0 &" #'ce#$-ente cnt$&&e# &e -e!c'!$o $(')e#@ con )o c')@ ) p!e#$n ) +'e e#t* #o-et$&o e) (# ence!!&o en e) ot!o et!e-o &e) t'*o@ '-ent* en $(') p!opo!c$n. Me&$nte #'ce#$# -e&$&# &e ) &$#tnc$ ent!e )o# &o# n$e)e# )c )cn n& &o# o# po! po! e) -e!c -e!c'! '!$o $o en -* -*## Ro*e" Bo)e !-# &e) t'*o@ o*#e! +'e ) &$#-$n'c$n &e) o) o)'-en -en &e) (# ('!& !&* c$e c$e!t !t !e)c$n con e) '-ento &e p!e#$n. S$ &o*)* e) pe#o &e -e!c'!$o@ e) o)'-en #e !e&'c" ) -$t&@ #$ )o t!$p)$c* #e !e&'c" ) te!ce! p!te 0 #" #" #'ce #'ce#$ #$-en -ente te.. Un n?) n?)$#$# #$# c'$& c'$&& &o o#o &e t) t)e# !e#' !e#'))t& t&o# epe!$-ent)e# )e pe!-$t$@ ,$n)-ente@ en'nc$! #' )e0.
Ee-p)o# con !e#')t&o# epe!$-ent)e# %('"! 1/ Epe!$enc$ &e Bo0)e
%('"! 1/ S$t'c$n $pott$c
G!,$c &e ) !e#p'e#t epe!$-ent)
ISOTERMA
12
Re$p'e$! e@pe"%-en!) P"e$%>n Vo)'-en 1< <.V 5!-6 F-/ 1
60
1.00
60
2
30
0.50
60
3
20
0.33
60
4
15
0.25
60
5
12
0.20
60
6
10
0.17
60
%('"! 1/1 En !e)c$n )o# epe!$e-ento# #e o*t'o ) (!,$c epe!$-ent)
T= Constante
13
A te-pe!t'! con#tnte 0 p! 'n -$#- -# &e (#@ e) o)'-en e# $ne!#-ente p!opo!c$on) ) p!e# p!e#$ $n. n. / ene! ene!(" (" c$n c$nt$t$c c e# con# con#t tnt nte@ e@ co-o co-o con#ec'enc$ ) e)oc$&& -o)ec')! p!o-e&$o 0 )# ,'e!# &e co)$#$n e#t?n con#tnte#. S$ '-ent e) o)'-en@ entonce# &$#-$n'0e e) n-e!o &e -o)c')# po! po! 'n$& 'n$&& & &e o)' o)'-e -en n 0 t-* t-*$ $n n &$#&$#-$n $n'0 '0e e ) cnt$&& &e co)$#$one# po! 'n$&& &e ?!e &e ) p!e&. Co-o Co-o con#ec con#ec'en 'enc$ c$ &e to&# to&# e#t# e#t# #$t' #$t'c$o c$one ne## ) p!e# p!e#$ $n n &$#&$#-$$n'0 n'0e. E# ?)$ ?)$& & p!e#$ !e#$on one e# &e p!o$-&-ente 1 t- e $n,e!$o!e#@ pe!o no ,'nc$on *$en p!e#$one# )t# o te-pe!t'!# *#.
1.0.2 Le &e C=!")e$ C'n&o #e c)$ent e) $!e conten$&o en )o# ()o*o# e!o#t?t$co# #to# #e e)en@ po!+'e e) (# #e epn&e. E) $!e c)$ente +'e e#t? &ent!o &e) ()o*o e# -eno# &en#o +'e e) $!e ,!"o &e) ento!no@ ) -$#- p!e#$n@ ) &$,e!enc$ &e &en#$&& ce +'e e) ()o*o #c$en&. S$-$)!-ente@ #$ 'n ()o*o #e en,!"@ #te #e enco(e@ !e&'ce #' o)'-en. / !e)c$n ent!e ) te-pe!t'! 0 e) o)'-en ,'e en'nc$& po! e) c$ent",$co ,!nc# J. C!)e# F146 123@ 't$)$n&o -'co# &e )o# epe!$-ento# epe!$-ento# !e)$&o# po! J. G0 /'##c F1 123. / )e0 &e C!)e# $nc') e) o)'-en 0 ) te-pe!t'! &e 'n -# con#tnte &e (# p!e#$n con#tnte. E) o)' o)'-e -en n &e 'n! 'n! -!$! -!$! &e,% &e,%n% n%&! &! &e (!$< (!$< ! p"e$ p"e$%> %>n n con$ con$! !n ne< e< e$ &%"ec!-ene p"opo"c%on!) ! )! e-pe"!'"! !*$o)'!. En ot!# p)*!#@ e) o)'-en !" en p!opo!c$n &$!ect con ) te-pe!t'!: V =T
/ $nte!p!etc$n -te-?t$c &e) co-po!t-$ento e#:
V = k ( Ley de Charles) T
G!?,$c-ente #e !ep!e#ent co-o:
14
/ p)$cc$n &e ) )e0 &e C!)e# &o# e#t&o#@ F1 0 F2 pe!-$te #ee!! +'e V 1 T 1
=
V 2 T 2
Ee-p)o p!?ct$co: C'n&o #e $e!te n$t!(eno )"+'$&o F16C #o*!e 'n ()o*o@ e) (# t!p&o en #te #e en,!" 0 e) o)'-en &$#-$n'0e@ -$ent!# +'e ) p!e#$n pe!-nece con#tnte.
%('"! 1/11 /e0 &e C!)e#
/o# /o# p!oce# p!oce#o# o# +'e #e !e)$ !e)$n n p!e#$ p!e#$n n con#t con#tnte nte #e &eno&eno-$n $nn n p!oce# p!oce#o# o# $#o*?!$co#. An?)o(-ente@ An?)o(-ente@ ) p!e#$n &e 'n &ete!-$n& cnt$&& &e (# +'e #e -nt$ene o)'-en con#tnte@ e# &$!ect-ente p!opo!c$on) #' te-pe!t'! *#o)'t@ +'e #e ep!e# co-o: P =Constante T 15
/o# p!oce#o# +'e #e p!o&'cen o)'-en con#tnte #e &eno-$nn p!oce#o# $#oc!$co#. <! &ete!-$n! )o# )o!e# ent!e &o# e#t&o# po&e-o# '#!: P1 T 1
=
P2 T 2
<! 'n -$#- -# &e (# p!e#$n con#tnte e) o)'-en@ e# p!opo!c$on) #' te-pe!t'! *#o)'t. S$ '-ent ) te-pe!t'!: • •
A'-ent ) e)oc$&& -o)ec')! p!o-e&$o A'-ent ) ,'e!# ,'e!# &e )# co)$#$one# co)$#$one# <! <! +'e +'e ) p!e#$ p!e#$n n pe!- pe!-ne nec c con#t con#tnte nte e# nece# nece#!$o !$o +'e +'e '-en '-ente te e) o)'-en &e -o&o +'e e) n-e!o &e -o)c')# po! 'n$&& &e o)'-en &$#-$n'0e 0 ) ,!ec ,!ec'e 'enc nc$ $ &e )# )# co)$ co)$#$ #$on one# e# &$#&$#-$n $n'0 '0. . A#" c'n c'n&o &o #e '-e '-ent nt ) te-pe!t'! &e) (# < con#tnte 0 '-ent e) o)'-en.
1.0.3 Le &e G! L'$$!c / )e0 &e G0 /'##c $nc') ) p!e#$n 0 te-pe!t'! *#o)'t &e 'n -# con#tnte &e (# o)'-en con#tnte. L! p"e$ p"e$%> %>n n &e 'n! 'n! -!$! -!$! &e,% &e,%n% n%&! &! &e (!$< (!$< ! o)' o)'-e -en n con$ con$! !n ne< e< e$ &%"ec!-ene p"opo"c%on!) ! )! e-pe"!'"! !*$o)'!. En ot!# p)*!#@ ) p!e#$n !" en p!opo!c$n &$!ect con ) te-pe!t'!: P=T
/ $nte!p!etc$n -te-?t$c &e) co-po!t-$ento e#: P =T ( Ley de Gay Lussac ) T
/ p)$cc$n &e ) )e0 &e C!)e# &o# e#t&o#@ F1 0 F2 pe!-$te #ee!! +'e: %('"! 1/12 /e0 &e G0 /'##c
16
S'pon(-o# +'e tene-o# 'n (# +'e #e enc'ent! 'n p!e#$n <1 0 'n te-pe te-pe!t !t'! '! T1 ) co-$en co-$eno o &e) epe!$ epe!$-en -ento. to. S$ '-en '-entt-o# o# ) te-pe!t'! #t 'n n'eo )o! T2@ entonce# ) p!e#$n #e $nc!e-ent!? <2@ 0 #e c'-p)$!?: P1 T 1
=
P2 T 2
E#t )e0@ ) $(') +'e ) &e C!)e#@ e#t? ep!e#& en ,'nc$n &e ) te-pe!t'! *#o)'t ep!e#& en e)$n. / $#co! #e o*#e! en ) #$('$ente (!?,$c < V:
%('"! 1/13 G!,$c &e p!e#$n 9 o)'-en
E#te p!oce#o t-*$n # e p'e&e !ep!e#ent! en 'n (!?,$c < T:
%('"! 1/10 G!?,$c &e p!e#$n te-pe!t'!
1.0.0 Le Gene"!) &e )o$ (!$e$ %&e!)e$ /# )e0e# +'e e-o# e#t'&$&o #e c'-p)en c'n&o #e t!* *# p!e#$one# 0 te-pe!t'!# -o&e!&#. Tene-o# +'e: P"op%e& P"op %e&!&e !&e$$ +'e +'e $e -!n -!n% %en enen en con$!ne$ -o)e$ 5n6 Te-pe!t'! FT -o)e$ 5n6
Le
E@p"e$%>n
Bo0)e C!)e#
< . VH con#tnte V TH con#tnte 17
p"e$%>n 5P6
Te-pe!t'! FT
G0 /'##c
V TH con#tnte
Con#$&e!e-o# Con#$&e!e-o# 'n &ete!-$n& cnt$&& &e (# $&e) con,$n&o en 'n !ec$p$ente &on& &on&e e #e p'e& p'e&e e !$ !$! ! ) p!e# p!e#$ $n@ n@ e) o)' o)'-e -en n 0 ) te-p te-pe! e!t t'! '!@ @ pe!o pe!o -nten$en&o ) -# con#tnte@ o #e@ #$n )te!! e) n-e!o &e -o)e#. A p!t$! p!t$! &e ) ec'c$n ec'c$n &e C)pe0!on@ C)pe0!on@ po&e-o# e#t*)ece! e#t*)ece! ) #$('$ente #$('$ente !e)c$n: pV =nRT →
pV =nR T
Co-o ,'e &e#c!$to@ e) n-e!o &e -o)e# n 0 R #on con#tnte#. Se conc)'0e entonce#: pV =constante T
E#to e#@ #$ !$-o# ) p!e#$n@ e) o)'-en 0 ) te-pe!t'! &e) (# con -# con#tnte@ ) !e)c$n !ec$n ep!e#&@ &!? e) -$#-o !e#')t&o. <! enten&e! -eo! )o +'e e#to #$(n$,$c@ o*#e!e ) ,$('! cont$n'c$n:
%('"! 1/1 Se t$ene 'n (# $&e) en &$#t$nto# e#t&o#
Tene-o# e) (# $&e) en t!e# e#t&o# &$,e!ente#@ pe!o #$ e#t*)ece-o# ) !e)c$n &e p!e#$n@ o)'-en 0 te-pe!t'!@ &e#c!$to# en ) p!$-e! ec'c$n@ #e ))e( )o# #$('$ente# !e#')t&o#. P1 V 1 T 1
=nR
18
P2 V 2 T 2 P3 V 3 T 3
=nR
=nR
O*#e!-o# +'e )# t!e# ec'c$one# &n e) -$#-o !e#')t&o@ )o c') #$(n$,$c +'e e))# #on $(')e#. Entonce# po&e-o# o*tene! ) #$('$ente ec'c$n ,$n): P1 V 1 P2 V 2 P3 V 3 T 1
=
T 2
=
T 3
E#t !e)c$n e# conoc$& co-o ) ec'c$n (ene!) &e )o# (#e# $&e)e#.
1.0. Ec'!c%>n &e) (!$ %&e!) / con#tnte &e p!opo!c$on)$&& &epen&e &e ) cnt$&& &e #'#tnc$ (#eo# V =
con#$&e!&. C'n&o e#t c$!c'n#tnc$ #e $nt!o&'ce en ) ec'c$n
k ´ ´ P
@ e# &ec$! #e t!* con 'n n-e!o &e -o)e# F cnt$&& &e #'#tnc$ (#eo# &$#t$nto &e 'no !e#')t ) ep!e#$n &e ) Ec'c$n &e) (# $&e): PV =nRT ( Ecuacindel !as ideal )
&on&e n e# e) n-e!o &e -o)e# &e ) -'e#t! (#eo# con#$&e!& 0 e# ) ))-& con#tnte &e )o# (#e# pe!,ecto# $(') :
−1
0,082 at".k ."ol
R −1
C'n&o #e ope! con (#e# !e)e#@ )o# &to# ))&o# epe!$-ent)-ente no co$nc$&e co$nc$&en n con )o# c)c')& c)c')&o# o# '#n&o '#n&o )# )e0e# )e0e# o)'-t!$ o)'-t!$c#@ c#@ p!t$c') p!t$c')!-en !-ente te c'n&o )# p!e#$one# 0 te-pe!t'!# #e p!tn -'co &e )# *$t')e#. /o# (#e# !e)e# c'-p)en con p!o$-&-ente p!o$-&-ente )# )e0e# o)'-t!$c#. o)'-t!$c#. E) e#t'&$ e#t'&$o o &e) &e) co-po! co-po!tt-$en $ento to !e) !e) !e+'$e !e+'$e!e !e ec'c$ ec'c$on one# e# ,"#$co ,"#$co-t -te-? e-?t$c t$c co-p)$c&#. n &e e-pe"!'"!. Con$!ne (ene"!) &e )o$ (!$e$ E) o)'-en &e 'n (# !" not*)e-ente c'n&o #e -o&$,$cn ) p!e#$n 0 ) te-p te-pe! e!t t'! '! &e) &e) #$#t #$#tee-. . En )# )# co-' co-'n$ n$c cc$ c$on one# e# c$en c$ent" t",$,$c c#@ #@ ) !?p$ !?p$& & co-p!c$n &e )# -e&$c$one# e# ,c$)$t& po! ) &opc$n &e )# con&$c$one# no!-)e# &e p!e#$n 0 &e te-pe!t'! t e-pe!t'!.. 19
Se conen$&o en &e,$n$! &o# con#tnte#: / p!e#$n no!-): / te-pe!t'! no!-): E) o)'-en no!-):
1t7QC 22@414 /
67 -- L( 23Q
Tnt# ece# #on c$t&# e#t# con&$c$one# no!-)e# no!-)e# +'e #e )# $n&$c *!e$&-ente con ) #$() CN
P0 V 0 n T 0
1 22,414 L = at". = 0.082 at".L 1 "ol 273 K
"ol K
D%-en$%one$ &e )! con$!ne (ene"!) &e )o$ (!$e$ An)$n&o c& 'n &e )# -(n$t'&e# +'e $nte!$enen en ) ep!e#$n &e ) con#tnte (ene!) &e )o# (#e# R ten&!e-o#:
[ ] $
R=
P0 V 0 n T 0
#
[ L L ] 3
L [ $ [ Ener!ia $ ] [ L L ] Ener!ia ] = = [ "ol ] [ T ] [ "ol ] [ T ] [ "ol ] [ T ] 2
V)o!e# &e R en ot!# 'n$&&e#: 1,01325. 10 P=1,01325.
5
K
−3
3
22,414. 10 " V 0=22,414.
K
T 0 =273 K
K
1 cal= 4,184 %
Ec'!c%one$ %nc')!&!$ ! )! ec'!c%>n &e) (!$ %&e!) E) n-e!o &e -o)e# &e 'n #'#tnc$ #e c)c') p!t$! &e) coc$ente &e ) -# &$$&$&o #' -# -o)!@ po! )o +'e #e o*t$ene ) #$('$ente ep!e#$n &e!$& &e ) ec'c$n &e e#t&o: " PV = RT &
A ) e@ #$ !eco!&-o# +'e ) &en#$&& e# ) -# &e ) 'n$&& &e o)'-en@ 0 +'e #e c)c') &$$&$en&o ) -# po! #' o)'-en@ ten&!e-o#: P& =
" RT ='RT V
20
T-*$n e# po#$*)e c)c')! ) -# -o)! &e 'n #'#tnc$ p!t$! &e: & =
"RT PV
E$'&%!n&o 'n $%$e-! (!$eo$o c'!)+'%e"! &e -!$! con$!ne: Ten&!? Ten&!? 'n e#t&o $n$c$) c')+'$e!@ c')+'$e!@ con 'n o)'-en V en )# con&$c$one# ,$&# &e p!e#$n 0 &e te-pe!t'!: < 0 T. p'e&e #'pone!#e +'e e) e#t&o ,$n) e# no!-)K )'e(o@ #' o)'-en #e!? en )# CN
E#t E#t e!#$ e!#$n n &e ) ep!e# ep!e#$n $n 'n$,$ 'n$,$c& c& enc'e enc'ent! nt! ent ento# o### p)$c p)$cc$o c$one ne## p!?ct$c#.
1.0.9 CONSTANTE UNIVERSAL DE LOS GASES IDEALES: / con#t con#tnte nte 'n$e! 'n$e!#) #) &e )o# (#e# (#e# $&e) $&e)e# e# e# 'n 'n con#t con#tnte nte ,"#$c ,"#$c +'e !e)c$on ent!e #" &$e!## ,'nc$one# &e e#t&o te!-o&$n?-$c#@ e#t*)ec$en&o e#enc$)-ente 'n !e)c$n ent!e ) ene!("@ ) te-pe!t'! 0 ) cnt$&& &e -te!$. En #' ,o!- -?# p!t$c')! ) con#tnte #e e-p)e en ) !e)c$n &e ) cnt$&& &e -te!$ en 'n (# $&e)@ -e&$& en n-e!o &e -o)e#Fn@ con ) p!e#$nF<@e) o)'-enFV 0 ) te-pe!t'!FT@ t!# &e ) ec'c$n &e e#t&o &e )o# (#e# $&e)e#. PV =nRT
E) -o&e)o &e) (# $&e) #'-e +'e e) o)'-en &e ) -o)c') e# ce!o 0 )# p!t"c')# no $nte!ctn ent!e #". / -0o! p!te &e )o# (#e# !e)e# #e ce!cn e#t con#tnte &ent!o &e &o# c$,!# #$(n$,$ct$#@ en con&$c$one# &e p!e#$n 0 te-pe!t'! #',$c$ente-ente )e&# &e) p'nto &e )$c'e,cc$n o #'*)$-c$n. /# ec'c$one# &e e#t&o &e (#e# !e)e# #on@ en -'co c#o#@ co!!ecc$one# &e ) nte!$o!.
CAPITULO 2: MEZCLAS DE GASES IDEALES 2.1 Concepo / -ec) $&e) e# 'n -o&e)o &e -ec) en e) c') e) o)'-en@ ) ene!(" $nte!n 0 ) ent)p" &e ) -ec) e# $(') ) &e )o# co-ponente# p'!o# po! #ep!&o@ e# &ec$! e) o)'-en@ ) ene!(" 0 ) ent)p" &e -ec) e# n'). C'nto -?# #e ce!+'en e#to# )o!e# )o# &e 'n -ec) !e) -?# $&e) #e!? ) -ec). A)te!nt$-ente A)te!nt$-ente 'n -ec) e# $&e) #$ #' coe,$c$ente &e ct$$&& e# 1. E#te
21
coe,$c$ente e# e) +'e -$&e ) $&e)$&& &e )# #o)'c$one#. S$-p)$,$c eno!-e-ente )o# c?)c')o# 0 #e '# &e !e,e!enc$ p! )# -ec)# !e)e#
2.2 Le &e D!)on En 'n -ec) &e (#e# +'e no !ecc$onn ent!e #"@ c& -o)c') #e -'ee $n&ep $n&epen en&$e &$ente nte-en -ente@ te@ &e 'n 'n ,o!- ,o!- n?)o( n?)o( co-o co-o #$ e#t'$ e#t'$e! e! tot)-e tot)-ente nte $#)&. En e# -ec) -ec)@@ c& c& (# #e &$#t!$ &$#t!$*'0 *'0e e 'n$,o! 'n$,o!-e -e-en -ente te po! to&o to&o e) e#pc$ e#pc$o o &$#pon$*)e@ co-o #$ n$n(n ot!o (# e#t'$e#e p!e#ente. /# -o)c')# ee!cen ) -$#- p!e#$n #o*!e )# p!e&e# &e) !ec$p$ente +'e )o cont$ene +'e ) +'e ee!ce!"n #$ no '*$e! n$n(n ot!o (# p!e#ente. "!cc%>n -o)!" En #$#te #$#te-# -# con !$o !$o## co-po co-ponen nente# te# F-ec) F-ec)# #@@ e# nece# nece#!$o !$o conoce conoce!! #' co-po#$c$n +'"-$c@ &e-?# &e &o# !$*)e# $n&epen&$ente#@ p! &e,$n$! #' e#t&o te!-o&$n?-$co Fpo#t')&o &e e#t&o. / co-po#$c$n +'"-$c #e p'e&e &! co-o ,!cc$n -o)!. ( i=
ni
=
∑n
i
ni nT
&on&e n$ e# e) n-e!o &e -o)e# &e) co-ponente $@ 0 nT e# e) n-e!o &e -o)e# tot)e# &e ) -ec) (#eo#. <! 'n -ec) &e (# n$t!(enoFA 0 (# o"(enoFB &e ) p)$cc$n &e ) ep!e#$n nte!$o! !e#')t: ( A=
n A
∑n
i
=
n A n A + nB
0
( B=
nB
∑n
= i
n A n A + nB
Se &e&'ce #" +'e )# #'- &e )# ,!cc$one# -o)!e# )e# &!? #$e-p!e $(') 1.
∑ ( =1 i
P"e$%>n p!"c%!)
22
%('"! 2/1 Co-*$nc$n 0 !ecc$one# con (#e#
Ap)$cn&o ) ec'c$n &e) (# $&e) c& co-ponente@ ) p!e#$n p!c$) &e) i #e!?:
co-ponente Pi=
ni RT V
(1 )
n T RT V
( 2)
D$$&$en&o )# ec'c$one# F1 0 F2@ #e e ) !e)c$n ent!e p!e#$n p!c$)@ p!e#$n tot) 0 ,!cc$n -o)! e#: Pi PT
=
ni nT
= ( i
e# &ec$!
Pi= ( i PT
o )o +'e e# )o -$#-o
∑ P = P i
T
k
<! 'n -ec) (#eo# &e &o# co-ponente# A 0 B@ &e ) p)$cc$n &e )# ep!e#$one# nte!$o!e# p! e) co-ponente A !e#')t: P A PT
=
n A nT
=
n A n A + nB
( A
P A = ( A PT
∑ P = P i
A
+ PB
Un concepto p!)e)o ) p!e#$n p!c$) e# e) o)'-en p!c$) $: o)'-en +'e oc'p!" 'n co-ponente &e 'n -ec)@ #$ e#t'$e! ) #)o ) p!e#$n 0 te-pe!t'! &e ) -ec). En -ec)# &e (#e# $&e)e#@ ) #'- &e o)-ene# p!c$)e# e# e) o)'-en tot). #e c'-p)e: ) i = ( i V T
A)('n# ece# #e *) &e ,!cc$n en o)'-en en )'(! &e ,!cc$n -o)!@ 'n+'e po! ) ec'c$n #e e +'e #on #$nn$-o#.
23
2.3 Le &e A-!(! / )e0 &e A-(t o )e0 &e )o# o)-ene# p!c$)e# e#t*)ece +'e en 'n -ec) &e (#e#@ c& (# oc'p #' o)'-en co-o #$ )o# !e#tnte# (#e# no e#t'$e!n p!e#ente#. E) o)'-en e#pec",$co &e 'n &ete!-$n&o (# en 'n -ec) #e ))- o)'-e o)'-en n p!c$ p!c$) ) F. F. E) o)'o)'-en en tot) tot) &e ) -ec) -ec) #e c)c') c)c') #$-p)e #$-p)e-en -ente te #'-n&o )o# o)-ene# p!c$)e# &e to&o# )o# (#e# +'e ) co-ponen. k
V " ( T * p )=
V ( T * p ) ∑ = i
i 1
E#t e# ) ep!e#$n epe!$-ent) epe!$-ent) &e) o)'-en co-o 'n -(n$t'& eten#$. / )e0 on! ) ,"#$co ,!nc# E-$)e A-(t F141115@ +'e ,'e +'$n ) en'nc$ po! e p!$-e! en 17.
CAPITULO 3: GASES REALES 3.1. Concepo Un (# !e)@ en opo#$c$n 'n (# $&e) o pe!,ecto@ e# 'n (# +'e e$*e p!op$e&&e# +'e no p'e&en #e! ep)$c&# ente!-ente 't$)$n&o ) )e0 &e )o# (#e# $&e)e#. <! enten&e! e) co-po!t-$ento &e )o# (#e# !e)e#@ )o #$('$ente &e*e #e! to-&o en c'ent: • • • • •
E,ecto# &e co-p!e#$*$)$&& co-p!e#$*$)$&& Cpc$&& c)o!",$c e#pec",$c !$*)e ='e!# &e Vn &e! 8)# E,ecto# te!-o&$n?-$co# &e) noe+'$)$*!$o noe+'$)$*!$o c'e#t$ c'e#t$one one## con &$#oc &$#oc$ $c$ c$n n -o)ec' -o)ec')! )! 0 !ecc$ !ecc$one one## e)e-en e)e-ent) t)e# e# con co-po#$c$n !$*)e.
<! ) -0o!" &e p)$cc$one#@ 'n n?)$#$# tn &et))&o e# $nnece#!$o@ 0 ) p!o$-c$n &e (# $&e) p'e&e #e! 't$)$& con !on*)e p!ec$#$n.
3.2. D%,e"enc%!$ en"e (!$e$ "e!)e$ (!$e$ %&e!)e$ /o# /o# G#e# G#e# +'e #e '#te '#ten n e#t# e#t# #'po#$ #'po#$c$o c$one# ne# #e ))- ))-n n (#e# (#e# $&e)e $&e)e## 0 +'e))# +'e no@ #e )e# ))-n (#e# !e)e#@ o #e@ $&!(eno@ o"(eno@ n$t!(eno 0 ot!o# •
Un (!$ e$ ,o"-!&o po" p!"#c')!$ ))!-!&!$ -o)4c')!$: -o)4c')!$: Depen&$en&o &e) (#@ c& -o)c') e#t? ,o!-& po! 'n ?to-o o 'n (!'po &e ?to-o#. S$ e) (# e# 'n e)e-ento o 'n co-p'e#to en #' e#t&o e#t*)e@ con#$&e!-o# +'e to&# #'# -o)c')# #on $&nt$c#. 24
•
•
•
L!$ -o)4c')!$ $e enc'en"!n !n%-!&!$ &e -o%-%eno !)e!o"%o o*e&ecen )!$ )ee$ &e Neon &e) -o%-%eno: -o%-%eno: /# -o)c')# #e -'een en to&# &$!ecc$one# 0 e)oc$&&e# &$,e!ente#. A) c)c')! )# p!op$e&&e# p!op$e&&e# &e) -o$-$ento #'pone-o# +'e ) -ec?n$c ne;ton$n #e p'e&e p)$c! en e) n$e) -$c!o#cp$co. Co-o p! to&# n'e#t!# #'po#$c$one#@ e#t -nten&!? o &e#ec!@ &epen&$en&o &e #" )o# eco# epe!$-ent)e# $n&$cn o no +'e n'e#t!# p!e&$cc$one# #on co!!ect#. E) n-e"o o!) &e -o)4c')!$ e$ ("!n&e: ("!n&e: / &$!ecc$n 0 ) !p$&e &e) -o$-$ento &e c')+'$e! &e )# -o)c')# p'e&en c-*$! *!'#c-ente en )o# co+'e# con )# p!e&e# o con ot!# -o) -o)c' c') )#. #. C') C')+' +'$e $e! ! &e )# )# -o) -o)c' c') )## en p!t p!t$c $c') ')! !@@ #e(' #e('$! $!? ? 'n 'n t!0ecto!$ &e $((@ &e*$&o &$co# co+'e#. S$n e-*!(o@ co-o 0 -'c# -o)c')#@ #'pone-o# +'e e) (!n n-e!o &e co+'e# !e#')tnte -nt$ene 'n &$#t!$*'c$n tot) &e )# e)oc$&&e# -o)ec')!e# con 'n -o$-$ento p!o-e&$o )eto!$o. E) o)'-en o)'-en &e )!$ -o)4c' -o)4c')!$ )!$ e$ 'n! ,"!cc%> ,"!cc%>n n &e$p"ec &e$p"ec%!*) %!*)e-en e-ene e pe+'eF! &e) o)'-en oc'p!&o po" e) (!$: A'n+' 'n+'e e 0 0 -'c -'c# # -o) -o)c' c') )#@ #@ #on #on et! et!ee-& &-en ente te pe+' pe+'e e# #.. S*e-o# +'e e) o)'-en oc'p&o po! 'n (# #e p'e&e c-*$! en 'n -!( -!(en en -'0 -'0 -p) -p)$o $o@@ con con poc poc &$,$ &$,$c' c')t)t& & 0 +'e@ +'e@ c'n c'n&o &o 'n (# (# #e con&en#@ e) o)'-en oc'p&o po! e) (# co-p!$-$&o #t &e!)o en ,o!- )"+'$& p'e&e #e! -$)e# &e ece# -eno!.
•
Lo$ c=o+'e$ $on e)$%co$ &e &'"!c%>n &e$p"ec%!*)e: &e$p"ec%!*)e: En )o# co+'e# ent!e )# -o)c')# con )# p!e&e# &e) !ec$p$ente #e con#e! e) "-pet' 0 F#'pone-o# ) ene!(" c$nt$c. De*$&o +'e e) t$et$e-po po &e co+ co+'e 'e e# &e#p &e#p!e !ec$ c$* *)e )e co-p co-p! !& &o o con con e) t$et$e-po po +'e +'e t!n#c t!n#c'!! '!!e e ent!e ent!e e) co+' co+'e e &e -o)c' -o)c')# )#@@ ) ene!( ene!(" " c$nt$ c$nt$c c +'e +'e #e con$e!te en ene!(" potenc$) &'!nte e) co+'e@ +'e& &$#pon$*)e &e n'e n'eo o co-o co-o ene! ene!(" (" c$n c$nt$t$c c@@ &e#p &e#p' '## &e 'n t$et$e-po po tn tn co!t co!to@ o@ +'e +'e po&e-o# $(no!! e#te c-*$o po! co-p)eto.
25
3.3 Mo&e)o$ 3.3.1 Mo&e)o &e V!n &e" !!)$ / ec' ec'c$ c$n n &e Vn &e! &e! 8) 8)## e# 'n 'n ec' ec'c$ c$n n &e e#t e#t&o &o &e 'n ,)'$ ,)'$&o &o co-p co-p'e 'e#t #to o &e p!t p!t"c "c') ')# # con con 'n t- t-o o no &e#p &e#p!e !ec$ c$* *)e )e 0 con con ,'e! ,'e! ## $nte!-o)ec')!e#@ co-o )# ,'e!# &e Vn &e! 8)#. / ec'c$n@ c'0o o!$(en #e !e-ont 13@ &e*e #' no-*!e Jonne# D$&e!$ n &e! 8)#@ +'$en !ec$*$ e) p!e-$o No*e) en 117 po! #' t!*o en ) ec'c$n &e e#t&o p! (#e# 0 )"+'$&o#@ ) c') e#t? *#& en 'n -o&$,$cc$n &e ) )e0 &e )o# (#e# $&e)e# p! +'e #e p!o$-e &e -ne! -?# p!ec$# ) co-po!t-$ento &e )o# (#e# !e)e# ) tene! en c'ent #' t-o no n')o 0 ) t!cc$n ent!e #'# p!t"c')#. /o# (#e# !e)e# #on oc#$on)-ente -o&e)&o# to-n&o en c'ent #' -# 0 o)'-en -o)!e#.
(
RT = P +
a 2
V "
)(
V "−+ )
&on&e < e# ) p!e#$n@ T e# ) te-pe!t'!@ R e# ) con#tnte &e )o# (#e# $&e $&e)e )e#@ #@ 0 V- e# e) o)' o)'-e -en n -o) -o)!!. 0 * * #on #on p!? p!?-e -et! t!o# o# +'e +'e #on #on &ete!-$n&o# &ete!-$n&o# e-p"!$c-ente p! c& (#@ pe!o en oc#$one# #on e#t$-&o# p!t$! &e #' te-pe!t'! c!"t$c FTc 0 #' p!e#$n c!"t$c F
a=
2
27 R T c 64 PC
R T C += 8 P c
%('"! 3/1 I#ote!-# p!e&ec$&# po! ) Ec'c$n &e Vn &e! 8)
3.3.2 Mo&e)o &e Re&)%c= H on( / ec'c$n &e Re&)$c9;on( e# ot! ec'c$n &e &o# p!?-et!o# +'e e# 't$)$ 't$)$& & p! p! -o&e) -o&e)!! (#e# (#e# !e)e# !e)e#.. E# c#$ c#$ #$e-p! #$e-p!e e -?# -?# p!ec$# p!ec$# +'e +'e ) ec'c$n &e Vn &e! 8)#@ 0 en oc#$one# -?# p!ec$# +'e )('n# ec'c$one# &e -?# &e &o# p!?-et!o#. / ec'c$n e#:
26
RT = P ( V " −+ ) +
a
(V " −+ )
1 /2
V " ( V " + + ) T
&on& &on&e e 0 * * #on #on &o# &o# p!? p!?-e -et! t!o# o# e-p" e-p"!$ !$co co## +'e +'e no #on #on )o# )o# -$#-$#-o# o# p!?-et!o# +'e en ) ec'c$n &e Vn &e! 8)#. E#to# p!?-et!o# p'e&en #e! &ete!-$n&o#: 2
a =0.4275
+ =0.0867
2.5
R T C Pc
R T c P c
3.3.3 Mo&e)o &e Be"=e)o &e Be"=e)o -o&%,%c!&o / ec'c$n &e Be!te)ot e# )$(e!-ente -?# co-p)e +'e ) ec'c$n &e Vn &e! 8)#. E#t ec'c$n $nc)'0e 'n t!-$no &e t!cc$n $nte!-o)ec')! +'e &epen &epen&e &e tnto tnto &e ) te-pe te-pe!t !t'! '! co-o co-o &e) o)'-e o)'-en. n. / ec'c$ ec'c$n n t$ene t$ene ) #$('$ente ,o!- P=
RT a − 2 V "− + T V "
Ap)$cn&o )# con&$c$one# &e) p'nto c!"t$co #e &ete!-$nn &ete!-$nn )o# p!?-et!o# p!?-et!o# 0 *@ o*ten$n&o#e: 2
a=
3
27 R T 64 PC
R T C += 8 PC
E#t ec'c$n ) $(') +'e ) &e Vn &e! 8)# p!e&$ce 'n )o! p! C $(') 7@35 po! )o +'e no e# con#e*)e 't$)$! ce!c &e) p'nto c!"t$co. <! #'p)$! e#t &e,$c$enc$ p! 't$)$! ) ec'c$n &e Be!te)ot ce!c &e) p'nto c!"t$co@ #e e,ect'&o 'n -o&$,$cc$n@ ) c') #e p!e#ent cont$n'c$n: P=
[
(
9 P / P c 6 RT 1+ 1− 2 128 T / T c V " ( T / T C )
)
= / &on&e: T C T T C te-pe!t'! !e&'c$&
27
Pr= P / PC
p!e#$n !e&'c$&
<! e#t ec'c$n e) ,cto! &e co-p!e#$*$)$&& c!"t$co t$ene 'n )o! &e 7@2 e) c') #e ce!c *#tnte ) )o! p!o-e&$o epe!$-ent) &e C p! ) (!n -0o!" &e )o# (#e# no po)!e# 3.3.0 Mo&e)o &e D%e!e"% / ec'c$n &e D$ete!$c$ #e &e#!!o)) p!$-o!&$)-ente p! &! 'n -0o! co$nc$&enc$ con e) )o! &e C &ete!-$n&o epe!$-ent)-ente. / ep!e#$n p! e#t ec'c$n e#: exp
P= RT
(
−a V " RT
)
V "− +
E) )o! &e C p! e#t ec'c$n e# &e 7@2 0 po! )o tnto e#t ec'c$n #e p'e&e '#! ce!c &e) p'nto c!"t$co. S$n e-*!(o e# poco '#& &e*$&o ) ,'nc$n eponenc$) +'e p!e#ent. 3.3. Mo&e)o &e C)!'$%'$ E#t ec'c$n &e t!e# p!?-et!o# ,'e p!op'e#t poco &e#p'# +'e ) ec'c$n &e Vn &e! 8)#. / ep!e#$n p! e#t ec'c$n e#: P=
R T a − V −+ T ( ( V + c )2
&on&e )# con#tnte# * 0 c #on )# +'e &e#c!$*en e) t-o &e )# -o)c')# &e) ,)'$&o. Ap)$cn&o ) con&$c$n con&$c$n &e $n,)e$n en e) p'nto p'nto c!"t$co 0 e)'n&o ) ec'c$n ec'c$n en )# con&$c$one# c!"t$c# F
a=
64 PC
+ =V C −
c=
3
27 R T C
RT R T C 4 PC
3 R T C 8 PC
−V C
A) $(') +'e ) ec'c$n &e Vn &e! 8)#@ 8)#@ ) con#tnte * !ep!e#ent e) -"n$-o o)'-en -o)! &e )# -o)c')# 0 po! )o tnto &e*e #e! po#$t$o. A) e-$n! ) ep!e#$n p! *@ #e &$e!te +'e #t e# #o)o po#$t$ #$ CW7@25K p! -'co# ,)'$&o# e) )o! &e C !" ent!e 7@25 7@31@ pe!o p! 'no# poco# co-o ('@ 28
-etno)@ -etno)@ -on$o@ ceton@ etc.@ C e# -eno! +'e 7@25@ )o +'e t!e con#$(o 'n )o! &e * ne(t$o@ )o c') e# ,"#$c-ente $-po#$*)e E$#te 'n -o&$,$cc$n p! #'pe!! e#te p!o*)e- 0 con#$#te en !ee-p)! ) con#tnte c po! ) * en ) ep!e#$n o!$($n)@ &n&o: P=
R T a − V −+ T ( ( V + + )2
p)$cn&o )# con&$c$one# &e) p'nto c!"t$co #e o*t$ene: 2
a=
+=
27 T C V C 20
V C 5
E#t -o&$,$cc$n e$t +'e e) p!?-et!o * #e ne(t$o 0 p!e&$ce 'n )o! p! C $(') 7@3125.
en &on&e )o# coe,$c$ente# B@ C@ D@ ... #e ))-n coe,$c$ente# $!$)e# 0 &epen&en &e ) te-pe te-pe!t !t'! '! 0 &e) co-p'e co-p'e#to #to.. E#to# E#to# coe,$c coe,$c$e $ente nte## e#t?n e#t?n !e)c$ !e)c$on on&o &o## &$!ect-e &$!ect-ente nte con )# ,'e!# ,'e!# $nte!-o) $nte!-o)ec') ec')!e# !e# +'e e$#ten ent!e ent!e (!'po# (!'po# &e -o)c')#K po! ee-p)o e) coe,$c$ente B &e#c!$*e $nte!cc$one# ent!e p!e# &e -o)c' -o)c') )#@ #@ C ent!e ent!e (!'po (!'po## &e t!e# t!e# -o)c' -o)c') )## 0 #" #'ce#$ #'ce#$-en ente. te. E#t# E#t# $nte!cc$one# $nte!cc$one# #e &eno-$nn $!$)e# 0 p'e&en #e! ep!e#&# co-o co-p)$c&# $nte(!)e# &e )# ,'e!# $nte!-o)ec')!e#. A#"@ #$ #e conoc$e!n )# ,'e!# $nte!-o)ec')!e# $nte!-o)ec')!e# ent!e c')+'$e! co-*$nc$one# &e -o)c')# en ,'nc$n &e )# #ep!c$one# -o)ec')!e#@ #e!" po#$*)e e,ect'! )# $nte(!c$one# 0 o*tene! #" )# )# ep! ep!e# e#$o $one ne## p! p! )o# )o# coe, coe,$c $c$e $ent nte# e# #$n #$n nece nece#$ #$& && & &e oc'p oc'p! ! &to &to## epe!$-ent)e#K #$n e-*!(o e#to# c?)c')o# #on &e-#$&o# co-p)$c&o# 0 n no n #$&o co-p)et&o#@ ecepto p! potenc$)e# potenc$)e# &e ,'e!# #$-p)$,$c&o# Fn con e#t #$-p)$,$cc$n )o# c?)c')o# #)o n #$&o ,ct$*)e# p! e) #e('n&o 0 oc#$on)-ente oc#$on)-ente e) te!ce! coe,$c$ente $!$). 29
T-*$n T-*$n ) ec'c$n $!$) p'e&e #e! e#c!$t &e ) #$('$ente -ne! F-?# ,?c$) &e '#!: P V = 1 + B ´ P + C ´ P 3 + , = R T
Don&e )o# coe,$c$ente# BX@ CX@ DX@ t-*$n #on ))-&o# coe,$c$ente# $!$)e# 0 &epen&en &e ) te-pe!t'! 0 &e) co-p'e#to. /o# coe,$c$ente# &e -*# ep!e#$one# #e p'e&en !e)c$on! &e ) #$('$ente -ne!. B B ´ = R T
C ´ =
C − B
2
-´ - ´ =
( R T ) 2
-−3 B C + 2 B ´ 3 ( R R T )
/# &o# ,o!-# &e ) ec'c$n $!$) #on #e!$e# $n,$n$t#K #' '#o p!?ct$co en $n(en$e!" !e#')t c'n&o cone!(e !?p$&-ente@ !?p$&-ente@ e# &ec$! c'n&o no #e nece#$t -?# -?# &e &o# &o# o t!e# t!e# t!t!-$n $no# o# p! p! +'e +'e )# )# #e!$ #e!$e# e# p!op p!opo! o!c$ c$on onen en )o )o!e !e## !on*)e-ente !on*)e-ente p!o$-&o#. E#to e# po#$*)e p! (#e# 0 po!e# p!e#$one# *# *# o -o&e! -o&e!&# &#.. E# po#$* po#$*)e )e t!'nc t!'nc!! ) ec'c$ ec'c$n n $!$) $!$) con#e! con#e!n n&o &o &o# t!-$no#: P V = 1 + B ´ , = R T
P=1 +
BP R T
E#t ec'c$n !ep!e#ent #t$#,cto!$-ente e) co-po!t-$ento p! -'co# po!e# te-pe!t'! #'*c!$t$c 0 #t p!e#$one# &e 15 *!. A te-pe!t'!# -0o!e# e# p!op$& p! (#e# &ent!o &e 'n $nte!)o &e p!e#$one# c!ec$ente -e&$& +'e '-ent ) te-pe!t'!. <! p!e#$one# #o*!e )o# 15 *! pe!o *o )o# 57 *! ) ec'c$n t!'nc& ent!e# t!-$no# & ece)ente# !e#')t&o#: P V B C =1 + + 2 , = R T V V
E#t ec'c$n e# c*$c en o)'-en 0 ) #o)'c$n #e o*t$ene con ,!ec'enc$ po! $te!c$one# en 'n co-p't&o!. /# &e#ent# &e '#! ) ec'c$n $!$) e# ) &$,$c')t& p! c)c')! )o# coe,$c coe,$c$e $ente nte## #$n !ec'! !ec'!!$! !$! &to# &to# epe!$ epe!$-en -ent) t)e#. e#. A&e-? A&e-?## po! ) ,o!- ,o!- +'e +'e p!e#ent e) '#te &to# epe!$-ent)e# t-poco e# t!e #enc$))@ po! )o tnto ) ec'c$n $!$) e# poco '#& en $n(en$e!". S$n e-*!(o@ -'c# &e)# ot!# ec'c$one# co-n-ente 't$)$&# p'e&en #e! !e&'c$&# 'n ,o!- #$-$)! ) ec'c$n $!$)@ 0 +'e &e e#t ,o!- )# ec'c$one# #on -?# t$)e#.
30
3.3.8 Mo&e)o &e Pen( H Ro*%n$on E#t E#t ec' ec'c$ c$n n@@ ) $(' $(')) +'e +'e ) ec' ec'c$ c$n n &e Vn &e! &e! 8) 8)#@ #@ po#e po#ee e &o# &o# p!?-et!o#@ pe!o #' ,o!- e# -?# co-p)$c&. / ep!e#$n &e e#t ec'c$n e# ) #$('$ente: P=
R T a − V "− + V " ( V "+ + ) + + ( V "− + )
Ut$)$ Ut$)$n n&o &o )# )# con&$ con&$c$o c$one# ne# &e $n,)e $n,)e$ $n n en e) p'nto p'nto c!"t$c c!"t$co@ o@ #e o*t$en o*t$ene e )o# )o# p!?-et!o#: 2
a =0,45724
2
R T C P C
+ =0,077796
R T C PC
E#t ec'c$n p!e&$ce 'n )o! p! c $(') 7@374 po! )o +'e e#t ec'c$n e# po#$ po#$*) *)e e &e p)$ p)$c c!! ce!c ce!c &e) &e) p'nt p'nto o c!"t c!"t$c $co. o. A&e-? &e-?## pe!pe!-$t$te e p!e& p!e&ec ec$! $! &en#$&&e# &en#$&&e# &e )"+'$&o# )ee-ente ecto# p! &$#eo# !e)e#. 3.3. Mo&e)o &e o=) / ec'c$n &e 8o) Fno-*!& en ono! &e A. 8o) e#t? ,o!-')& en t!-$no# &e )o!e# c!"t$co#@ c$n&o) t$) c'n&o no e#t?n &$#pon$*)e# )# con#tnte# &e (#e# !e)e#.
(
RT = P +
)
a c − 2 3 ( V "− + ) T V " ( V "− + ) T V "
&on&e: 2
a =6 PC T C V C C
+=
V C 4 2
3
c = 4 PC T C V C
3.3. Mo&e)o &e Be!%eHB"%&(-!n E#t ec'c$n e#t? *#& en c$nco epe!$-ent)-ente. epe!$-ent)-ente. E#t? ep!e#& co-o: P=
RT )
2
(
1−
c 3
) T
)
con#tnte#
&ete!-$n&#
( ) + B )− A2 )
&on&e
31
( )
A = A 0 1−
a )
( )
B = B0 1−
+ )
Se #*e +'e e#t ec'c$n e# !on*)e-ente p!ec$# p! &en#$&&e# #t )!e&e&o! &e 7. Y c! @ &on&e Yc! e# e# ) &en#$&& &e ) #'#tnc$ en #' p'nto c!"t$co. /# /# con# con#t tnt nte# e# +'e +'e p! p!ec ecen en en ) ec' ec'c$ c$n n #'pe #'pe!$ !$o! o! e#t? e#t?n n && &&## en ) "
#$('$ #$('$ent ente e t*) t*) c'n&o c'n&o < e#t? e#t? en <@ e#t? e#t? en
3
K"ol
@ T e#t? en 0
3
RH.314
k Pa . " K "ol . K
G! $ A%"e A"(on< A" D%>@%&o &e C!"*ono< CO2 ;e)%o< ;e ;%&">(eno<;2 N%">(eno< N2 O@#(eno< O2
A 131.441 137.72 57.236
! 7.7131 7.7232 7.7132
B 7.74611 7.7331 7.1746
* 7.771171 7.7 7.7235
c 4.34174 5.17 4 6.67Z17 5
2.16 27.711 136.2315 151.75
7.754 7.77576 7.7261 7.72562
7.71477 7.7276 7.75746 7.74624
7.7 7.7435 7.7761 7.77427
47 574 4.27Z17 4 4.7 Z174
T!*)! 3/1 Con )# con#tnte# &&#
3.3.1 Mo&e)o &e Bene&%cHe**HR'*%n E#t ec'c$n p!e#ent oco con#tnte# 0 po! )o tnto !ep!e#ent -'co -eo! e) co-po!t-$ento &e )o# ,)'$&o# +'e )# ec'c$one# nte!$o!e#. / ep!e#$n p! e#t ec'c$n e#:
[
P= RTd + d RT ( ( B + +d )−( A + ad − a/ d 2
4
) − 12 ( C − cd ( 1 + 0 d 2 ) exp (−0 d 2 ) ) T
]
E#t ec'c$n #e p'e&e 't$)$! c'n&o ) &en#$&& #e $n,e!$o! 1@2 ece# ) &en#$&& c!"t$c. / ec'c$n &e Bene&$ct8e**R'*$n pe#! &e #' co-p)e$&& t$ene 'n (!n '#o p! &ete!-$n! p!op$e&&e# &e $&!oc!*'!o# $&!oc!*'!o# )$(e!o# 0 ot!o# co-ponente# (#eo#o# co-n-ente encont!&o# tnto en ) $n&'#t!$ &e) pet!)eo co-o en ) &e) (# nt'!).
32
EJERCICIOS RESUELTOS: 1. Un &$#po#$t$o &e c$)$n&!o-*o)o cont$ene 7.75- 3 &e 'n (# +'e #e )) $n$c$ $n$c$))-ent ente e 277 <. En e#te e#te e#t&o e#t&o@@ 'n !e#o! !e#o!te te )$ne )$ne)) +'e t$ene 'n con#tnte &e !e#o!te &e 157 N- e#t? en contcto con e) -*o)o #$n ee!ce! n$n('n n$n('n ,'e! ,'e! #o*!e ). De#p'# De#p'# #e t!n#,$e!e t!n#,$e!e c)o! c)o! ) (# &e -o&o +'e e) -*o)o #'*e 0 co-p!$-e e) !e#o!te #t +'e e) o)'-en &ent!o &e) c$)$n&!o #e &'p)$c. S$ e) ?!e &e #ecc$n t!n#e!#) &e) -*o)o e# &e 7.25- 2@ &ete!-$ne: !6 ) p!e#$n ,$n) &ent!o &e) c$)$n&!o. *6 e) t!*o tot) eco po! e) (# c6 ) ,!cc$n &e t!*o !e)$&o cont! e) !e#o!te p! co-p!$-$!)o. So)'c%>n En 'n &$#po#$t$o &e c$)$n&!o -*o)o e+'$p&o con 'n !e#o!te )$ne) #e epn&e 'n (# &e*$&o ) c)ent-$ento. Se &ete!-$n!?n ) p!e#$n ,$n) &e) (#@ e) t!*o tot) !e)$&o 0 ) ,!cc$n &e) t!*o eco p! co-p!$-$! e) !e#o!te. S'$pen$%one$ E) p!oce#o &e epn#$n e# &e c'#$ e+'$)$*!$o. E) !e#o!te e# )$ne) en e) $nte!)o &e $nte!#. An)%$%$ E) o)'o)'-en en ce!!&o ce!!&o en e) e) e#t&o e#t&o ,$n) ,$n) e#:
(
V 2=2 V 1= ( 2 ) 0.05 "
3
)=0.1 "
3
E) &e#p)-$ento &e) -*o)o F0 &e) !e#o!te e# 1 V ( 0.01 −0.05 ) " = =0.2 " ( = 2 A 0.25 " 3
/ ,'e! p)$c& po! e) !e#o!te )$ne) en e) e#t&o ,$n) e# $ =k( =
(
150 kN
"
)(
0.2 ") =30 kN
/ p!e#$n &$c$on) +'e e) !e#o!te p)$c #o*!e e) (# en e#te e#t&o e#
33
P=
$ 30 kN = =120 kPa A 0.25 "2
S$n e) !e#o!te@ ) p!e#$n &e) (# pe!-nece!" con#tnte en 277 < -$ent -$ent!# !# #'*e #'*e e) -*o)o -*o)o..
en e) e#t&o ,$n). * Un Un ,o!- ,?c$) ,?c$) &e )) ))!! e) t!*o t!*o !e)$ !e)$& &o o e# (!,$c (!,$c! ! e) p!oce# p!oce#o o en 'n &$(!- <V 0 encont!! e) ?!e *o ) c'! &e) p!oce#o. De ) =$(. 41 %('"! 0/1 E#+'e- &e) &$(!- <V
E) ?!e *o ) c'! &e) p!oce#o en 'n &$(!- <V 0 encont!! e) ?!e *o ) c'! &e) p!oce#o F 'n t!peo$&e #e &ete!-$n co-o: 2 = 3rea =
( 200 + 320 ) kPa 2
[ ( 0.1 −0.05 ) " ] 3
(
1 k% 3
1 kPa."
)=
13 k%
Note +'e e# #$#te- e# e) !e)$ e) t!*o c E) t!*o t!*o !ep!e#en !ep!e#ent&o t&o po! po! e) ?!e !ectn(') !ectn(')! ! F!e($n F!e($n I #e !e)$ !e)$ cont! e) -*o)o 0 ) ?t-o#,e!@ ?t-o#,e!@ -$ent!# +'e e) !ep!e#ent&o !ep!e#ent&o po! e) ?!e t!$n(')! F!e($n II #e ce cont! e) !e#o!te.
2 resorte =
3
(
1 k% 1 kPa."
3
)=
3 k%
1 [( 320 −200 ) kPa ] ¿ 2
2./ Se co-p!$-e (# e)$o -e&$nte 'n co-p!e#o! &$*?t$co &e#&e 'n e#t&o $n$c$) &e 14 p#$ 0 57 Q= #t 'n te-pe!t'! ,$n) &e 327Q= en ,o!- !ee!#$*)e. Dete!-$ne ) p!e#$n &e #)$& &e) e)$o. So)'c%>n Se So)'c%>n Se co-p!$-e e)$o $#ent!p$c-ente &e 'n e#t&o &&o #t 'n p!e#$n e#pec$,$c&. Se &ete!-$n!? ) p!e#$n &e #)$& &e) e)$o.
34
S'po$%c%one$ En )# con&$c$one# e#pec$,$c&#@ p'e&e t!t!#e ) e)$o co-o 'n (# $&e).
/ !e)c$n &e c)o!e# e#pec$,$co# &e) e)$o e# 1.66 0 e# $n&epen&$ente &e ) te-pe!t'! en ) !e($n &on&e #e co-po!t co-o 'n (# $&e). A#"@ ) p!e#$n ,$n) &e) e)$o p'e&e &ete!-$n!#e &e ) ec'c$n
( )
T 2 P2= P1 T 1
K K − 1
(
780 R =( 14 psia ) 510 R
)
1.667 0.667
=40.5 psia
3./ S*e-o# +'e 3.57/ &e 'n (# cont$ene 7.5 -o). S$ '-ent-o# #t 1.47 -o)@ [C'?) #e!? e) n'eo o)'-en &e) (#\ So)'c%>n: V 1 n 2=V 2 n1
( 3.50 L ) ( 1.40 "ol ) =(V 2 )( 0.875 "ol )
Co-p!'e* +'e #$ &e#pe-o# V 2 o*tene-o# 'n )o! &e 5.67 / 0./ / te-pe!t'! en 'n &" &e e!no ,'e 35C 0 ) &e 'n &" &e $n$e!no 5C. Ep!e#! )# te-pe!t'!# nte!$o!e# en (!&o# =!ene$t F= 0 en (!&o# e)$n F. So)'c%>n: S'*#t$t'0en&o en )# ,!-')# nte!$o!e# = H 5 P 35 32 H 5= = H5 P 5 32 H 41=
H 23 35 H 377 H 23 5 H 2
35
<! <! ) p!e# p!e#$ $n n F,'e! F,'e! ee! ee!c$ c$& & #o*! #o*!e e 'n 'n #'pe #'pe!, !,$c $c$e $e &e &$-e &$-en# n#$o $one ne## 'n$t!$#@ #e -$&e en -$)"-et!o# &e -e!c'!$o F-- &e L( o t-#,e!# Ft-.. Un t-#,e! e#t?n&! e# ) p!e#$n +'e@ 7 0 ) n$e) &e) -! ee!ce #o*!e 'n #'pe!,$c$e &e 'n cent"-et!o c'&!&o FCM2 'n co)'-n &e -e!c'!$o &e 67 -- &e )t'!.
So)'c%>n <! &ete!-$n! ) p!e#$n en )$*!#p')(2@ nece#$t-o# )# #$('$ente# e+'$)enc$#: 1734 (c-2 H 1 t- H 14. )*p')(2
=
2
c"
14.7 2 l+ / pul! 1034
&on&e: 976 !
c"
2
=979 4
14.7 l+ / pul! 1034 ! / c"
2
2
=13.9 l+ / pul! 2
* +'e 1734 (c- 2 H 1 t979 ! 2
c"
=
979 = 0.947 at" 1034
36
& /# 'n$&&e# en (!-o#c-2 #on &$!ect-ente &$!ect-ente p!opo!c$on)e# &$n#c-2 0 #e o*t$enen -')t$p)$cn&o )t'! po! &en#$&&. P=altura altura 4 densidad densidad
En e#te c#o: P=72 c"4 c" 4 13.6 ! / c"aP =979 ! / c" 2
U#')-ente #e 't$)$ e) )$t!o F)@ e) -$)$)$t!o F-) o e) cent"-et!o c*$co Fcc p! -e&$! e) o)'-en. En ) p!?ct$c e) -) #e con#$&e! $(') ) cc. 9./ Un -'e#t! &e 'n (# oc'p )$t!o# 25C 0 67 -- &e L(. C)c')! e) o)'-en : F 25C 0 1527 -- &e L( F* 25C 0 37 -- &e L( Re#p'e#t / te-pe!t'! &e) p!o*)e- e# con#tnte@ p'&$en&o p)$c!#e ) )e0 &e Bo0)e 0 M!$otte: <1V1 H <2V2 A#$(nn&o A#$(nn&o )o!e# <1 H 67 -- &K. L( V1 H )$t!o#: <2 H 1527 -- &e L(K V2H \
8 4 760 =16 litros 380
8./ Un -'e#t! &e (# t$ene 'n o)'-en &e 257 -) 57C. [C'?) #e!? e) o)'-en 7C@ #$ #' p!e#$n pe!-nece con#tnte\ con#tnte\ Re#p'e#t :
37
Co-o ) te-pe!t'! ,$n) e# -eno! +'e ) $n$c$)@ t-*$n &$#-$n'$!? e) o)'-en. /'e(o #'*#t$t'0en&o 250 "l V 2 "l = 348 5K 273 5K
0 &e#pen&o V2 250 "l 4 273 5K =V 2 "l =211 "l 348 5K
./ Un (# oc'p 577 -) 37C 0 27 -- L(. [C'?) #e!? #' o)'-en en )# con&$c$one# e#t?n&! F7C67 -- L(\ Re$p'e$!: C-*$n&o )# te-pe!t'!# &e C . 37C 23 C H 373 7C 23 C H 23 S'*#t$t'0en&o@ en ) ep!e#$n -te-?t$c &e ) co-*$nc$n &e )# )e0e# &e )o# (#e# $&e)e#. 720 ""de6!4 500 "l 760 "" de 6!4V "l = 303 5K 273 5K
De#pen&o: 720 ""de6!4 500 "l 4 273 5K =V "l = 427 "l 760 "" 6!4 303 5K
-- &e L( 577 -1 P 23 H V -) H 42 -). 67 -- L( P 373
on#$&e!n&o ) p!e#$n con#tnte F67 -- &e L( 0 #'*#t$t'0en&o en ) ,!-') &e ) )e0 &e C!)e#@ con e) n'eo o)'-en &e 43 -) 473 "l V "l = 303 5K 273 5K
De#pen&o: 38
473 "l 4 273 5K =V "l =427 "l 303 5K
/ co-*$nc$n -?# (ene!) &e )# )e0e# &e) e#t&o (#eo#o $nc)'0e ) )e0 &e Ao(&!o@ ep!e#n&o ) !e)c$n ent!e o)'-en@ te-pe!t'!@ p!e#$n 0 n-e!o &e -o)c')#: PV = k nT
E) )o! &e ) con#tnte &e p!opo!c$on)$&& #e p'e&e c)c')! '#n&o e) o)'-en &e 22.412 )t#. +'e oc'p 'n -o) &e (# en con&$c$one# e#t?n&! &e p!e#$n 0 te-pe!t'!. < H 1 t-K
V H 22.412 1K
n H 1 -o)K
T H 23
S'#t$t'0en&o: 1 at"4 22.412 litros = k 1 "ol4 273 5K −1
k =0.08205 < at""ol !rado
−1
−1
k =82.05 "l −at"4"ol !rado
−1
E#t con#tnte #e ))- con#tnte 'n$e!#) &e )o# (#e# 0 #e #$-*o)$ con 'n R. Ante!$o!-ente )o# +'"-$co# '#*n e) )o! &e 16.7777 #$(n&o 'n ?to-o &e o"(eno. /o# ,"#$co# e-p)e*n co-o 'n$&& e) pe#o &e 'no &e )o# $#topo# &e) o"(eno@ e) O16. E#to o!$($n* pe+'e# &$#c!epnc$# en -'co# &to# ,"#$co#.
/ )e0 &e )o# (#e# $&e)e# o pe!,ecto# +'e& ep!e#& -te-?t$c-ente po!: PV = R nT
en &on&e R H 7.7275 )$t!o#t- -o)1 (!&o1 ./ [C'?) e# ) p!e#$n &e 7.2 -o) &e 'n (# +'e oc'p 'n o)'-en &e 4 )$t!o# 54QC\ Re#p'e#t S'*#t$t'0en&o en ) ec'c$n
39
−1
−1
0.2 "ol4 0.08205 litro −at""ol "ol 327 5K P= 4 litros
P=1.34 at"
1./ Se !eco($ 'n (# po! &e#p)-$ento &e (' 2 QC. / p!e#$n *!o-t!$c &'!nte ) !eco)ecc$n ,'e 66. -- L(. Se !eco($e!on e#t te-pe!t'! 0 p!e#$n 257 -). [C'?) e# e) o)'-en &e) (# #eco en con&$c$one# e#t?n&!\ So)'c%>n U#n& U#n&o o ) ec'c$ ec'c$n n co-*$ co-*$n& n& p! p! )o# )o# (#e# (#e# $&e)e $&e)e## #e o*t$en o*t$ene e V2@ V2@ o)'-en en con&$c$one# e#t?n&!. V 2=
P1 V 1 T 2 P2 T 2
V1 H 257 -)
T1 H 377 Q
V2 H \
T2 H 23 Q
<2 H 67 --
<! o*tene! <1@ ) p!e#$n e!&&e! &e) (#@ '#-o# ) )e0 &e D)ton 0 *'#cn&o en ) T*) 41 ) p!e#$n &e po! &e) (' 2 QC@ tene-o#: <1 H
250 "l 4 740 ""de6!4 273 5K 760 ""de 6!4 300 5K
V 2=221 "l a condici condiciones ones est3nda est3ndarr
EJERCICIOS PROPUESTOS 1./ Un 1./ Un cnt$&& &e (# oc'p 'n o)'-en &e 7 c-3 'n p!e#$n &e 57 -- L(. []' o)'-en oc'p!? 'n p!e#$n &e 1@2 t-. #$ ) te-pe!t'! no c-*$\ 2./ C)c')! 2./ C)c')! e) pe#o -o)ec')! p!o-e&$o &e) $!e #t'!&o con po! &e ('@ 25QC 0 'n p!e#$n tot) &e 1 t-. / p!e#$n &e po! &e) (' e#t te-pe!t'! e# &e 40
23@ -- L(. Con#$&!e#e ) $!e co-o ,o!-&o po! 7^ &e n$t!(eno 0 27^ &e o"(eno en o)'-en.
3./ D$#po D$#ponene-o# o# &e 'n !ec$p !ec$p$en $ente te &e o)'-e o)'-en n !$ !$*)e *)e.. In$c$ In$c$))-ent ente e p!e#en p!e#ent t 'n o)'-en &e 577 c-3 0 cont$ene 34 ( &e -on"co. S$ -nten$en&o con#tnte ) < 0 ) T@ #e $nt!o&'cen 6 ( &e -on"co@ [+' o)'-en p!e#ent!? ,$n)-ente e) !ec$p$ente\ 0./ Un 0./ Un !ec$p$ente ce!!&o &e 2 ). cont$ene o"(eno 277QC 0 2 t-. C)c'): /o# (!-o# &e &e o"(eno conten$&o# conten$&o# en e) !ec$p$ente. !ec$p$ente. * /# -o)c')# &e o"(eno p!e#ente# en e) !ec$p$ente. ./ Ut$)$n&o ./ Ut$)$n&o ) ec'c$n &e Vn &e! 8)#@ c)c')! ) p!e#$n ee!c$& po! 'n -o) &e *$$&o &e c!*ono 7QC en 'n o)'-en &e F 1 )$t!o@ F* 7@75 )$t!o#@ Fc Repet$! )o# c?)c')o# 177QC@ en 7@75 )$t!o#
9./ E) 9./ E) $!e cont$ene p!o$-&-ente 'n 21 ^ &e o"(eno@ 'n ^ &e n$t!(eno 0 'n 7@ ^ &e !(n@ e#tn&o e#to# po!cente# ep!e#&o# en -#. [C'?nt# -o)c')# &e o"(eno *!? en 2 )$t!o# &e $!e\ [C'?) e# ) p!e#$n ee!c$& #$ #e -ete e) $!e nte!$o! en 'n !ec$p$ente &e 7@5 ) &e cpc$&& ) te-pe!t'! &e 25 QC\ / &en#$&& &e) $!e H 1@23 (). 8./ Ut$)$! 8./ Ut$)$! ) ec'c$n &e n &e! 8)# p! e)*o!! ) (!?,$c &e # e) CO 2 ent!e 7 0 1777 t- 377@ 577 0 2777. <! e) CO 2
41
2
−2
a = 3.64 at" L "ol
0
−1
+ =0.04267 L"ol L "ol
./ C)c')! e) o)'-en o)'-en +'e oc'p 'n -o) -o) &e $(eno 177 tt- 0 2 con#$&e!n&o con#$&e!n&o +'e #e co-po!t co-o 'n (# &e n &e! 8)#. 2
−2
a = 1.36 L at""ol
K
−1
+ =0.0318 L"ol
./ C)c')! ./ C)c')! e) o)'-en oc'p&o po! 27( &e *$$&o &e c!*ono 'n p!e#$n &e 47 -- L( 0 37QC@ to-n&o en c'ent +'e #e o*e&ece ) )e0 &e )o# (#e# $&e)e#
1./En 1./En 'n p!to &e V"cto! Me0e! ) epo!c$n &e 7@117 7@117 ( &e 'n $&!oc!*'!o p'!o@ LFCL2 nL@ &e#p) 2-) &e $!e -e&$&o# en 'n *'!et &e -e!c'!$o 26@1QC 0 43 -- L( [C'?) e# e) pe#o -o)ec')! &e) $&!oc!*'!o 0 e) )o! &e n\
CONCLUSIONES •
/# ec'c$one# &e e#t&o #e 't$)$n p! &ete!-$n! &to# &e e+'$)$*!$o#@ ent)p"# ent)p"#@@ p!e#$one p!e#$one#@ #@ o)-ene o)-ene#@ #@ 0 ot!# p!op$e& p!op$e&&e# &e# te!-o&$n? te!-o&$n?-$c# -$c#.. / 42
e)ecc$n &e ) ec'c$n 't$)$! &epen&e!? &e ) p!ec$#$n +'e #e !e+'$e! 0 &e )# con&$c$one# &e ope!c$n en )# +'e #e t!*e. •
•
•
•
/# ec'c$ ec'c$on one# e# &e e#t&o e#t&o## c*$c c*$c## no p'e&en p'e&en !ep!e# !ep!e#ent ent! ! ,$e)-e ,$e)-ente nte e) co-po!t-$ento co-po!t-$ento &e )o# (#e#@ e#pec",$c-ente en ) on &e &o# ,#e#@ 0 +'e #)o po#een &o# con#tnte#. / ec'c$n &e) $!$)@ *#& en ) -ec?n$c e#t&"#t$c@ p'e&e !ep!e#ent! ,$e)-ente e) co-po!t-$ento. S$n e-*!(o@ e# poco poco 't$)$ 't$)$& & en $n(en$ $n(en$e!" e!" &e*$& &e*$&o o ) co-p)$ co-p)$cc cc$n $n &e) &e) c?)c') c?)c')o o &e )o# coe,$c$ente#. De )# ec'c$one# c*$c#@ ) -?# 't$)$& e# ) &e Re&)$c ;on(@ ) c') co-*$n ) #$-p)$c$&& &e 'n ec'c$n &e 2 p!?-et!o# con 'n )t p!ec$#$n #$-$)! ) ec'c$n &e Bene&$ct8ee*R'*$n &e oco p!?-et!o#. Un (# $&e) e# 'n (# te!$co co-p'e#to &e 'n con'nto &e p!t"c')# p'nt' p'nt')e )e## con &e#p) &e#p) -$e -$ento nto )et )eto!$ o!$o o +'e no $nte! $nte!ct ctn n ent!e ent!e #". E) concepto &e (# $&e) e# t$) po!+'e e) -$#-o #e co-po!t #e(n ) )e0 &e )o# (#e# $&e)e#@ 'n ec'c$n &e e#t&o #$-p)$,$c&@ 0 +'e p'e&e #e! n)$& -e&$nte ) -ec?n$c e#t&"#t$c. / p!$nc$p) c!cte!"#t$c &e )o# (#e# !e#pecto &e )o# #)$&o# 0 )o# )"+'$&o#@ e# +'e no p'e&en e!#e n$ toc!#e@ pe!o t-*$n #e enc'ent!n co-p'e#to# &e ?to-o# 0 -o)c')#. De#p'# &e to&o# )o# e#t'&$o# !e)$&o# &e p'e&e conc)'$! +'e 'n p!e#$n con#tnte e) o)'-en &e 'n (# #e epn&e c'n&o #e c)$ent 0 #e cont!e c'n&o #e epn&e.
REERENCIAS BIBLIOGRICAS @ Bo)e#@ M. F277. Te!-o&$n?-$c Te!-o&$n?-$c F6t.e&.. M$co: Mc G!; / Cen(e)@ @ L$)) Inte!-e!$cn
43
=$!e# =$!e#@@ V @S$--n( @S$--n(@@ C. F13. F13. Te Te!-o&$n !-o&$n?-$ ?-$c c F6t. F6t. e&. e&. Me$co Me$co:: Un$n Un$n T$po(!?,$c T$po(!?,$c E&$to!$) L$#pno-e!$cn.
8!@ 8!@ . 0 R$c! R$c!&#@ &#@ D. F277 F2771. 1. Te Te!-o&$n !-o&$n?-$ ?-$c c F6t. F6t. e&.. e&.. E#p E#p:: Mc G!; L$)) Inte!-e!$cn
'ene$ E)ec">n%c!$:
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