apÉndice xii. la entropÍa y la evoluciÓn del universo … · 2019. 3. 29. · !757 apÉndice...
Post on 04-Feb-2021
3 Views
Preview:
TRANSCRIPT
-
! 757
APÉNDICE XII. LA ENTROPÍA Y LA EVOLUCIÓN DEL UNIVERSO por Juan Auping Birch con la asesoría de Erich Starke Fabres
!
XII.1. La primera ley de la termodinámica !
!!!"#! $%! &'()*+,#-),.%/! 0'! +,.'! 12'! 2#! 0,0&')%! *! 3*$2)'#! +'! .*#&(*$! ('%$,4%! &(%5%6*! /! 0,!
'78*(&%! '#'(9:%! 12'! #*! 0'%! .%$*(! /! ;%.,'#+*! (*&%(! 2#! '6'/! *! 9'#'(%#+*! 2#%! +,!E*(!$*!&%#&*/!'$!&(%5%6*!@!'$!.%$*(!0*#!FD!!)*5$)*"&'2#%*&32"#3"&/!
GD! !.*43"*)&' ()' 2#%6)42"#3%! A@! #*! !"#!'$!0,92,'#&'!+,%9(%)%!3')*0!
+*0!.,.$*0/!%!0%5'(!FMJMGMKMF!@!FMJMGMLMFC!
!"#$%&$'$()!*+,!-#-.+,!/)0)1)2)/!!3!!/)0)1)4)/!!56!76!,#,85'$!-+6!9+,!5,8$9+,!/!3!1!
!!!!"$!
-
!758
"#$! !
!!!!%&'!(&!)*+)&,!
"-$!! !
!!!.+/0')01+2&!(*!20'13304+!21(!303(&!"56()07(03*+2&!3&+!89$,!
":$!! !
!!!;!(&!50>5&,!
"?$!! !
!!!!@>A!>1!3&57'61B*!=61!(*>!)'*C13)&'0*>!D!C!E!>&+!36*+)0)*)0/*51+)1!0F6*(1>!C!7&'!(&!)*+)&! !"#$%&!"'()*$'+"*,(,",(-"#$&*,%&$'"!)%$.$,%"/"0)$1 2$#)*$(*3&4&*3(&*,$3&$!"$,%".&',)%("!C!2171+21+! G+03*51+)1! 21! (&>! 1>)*2&>! 0+030*(! C! H0+*(! 21! 6+! >0>)15*! &! /&(651+! 21! 3&+)'&()0)6C1+0>)15*! 1>! 3&+>)*+)1! 2130'0>)15*!&!3&+!>6>!*('1212&'1>!" $J!...$!M1!20>)0+F61+!1+!)1'31'!(6F*'J!!!!!Q*! 1+1'FA*! 1>)R! 3&5761>)*! 21! )'1>! 3&57&+1+)1>*B1'! 1+1'FA*! 30+S)03*!
!!!!%&'!"I$!C!"T$,!"U$! !
-
! 759
!!!"#$%&%'()!*+!#,-.+!/%&01%/+!2!*+!-,+3%1+/%(&+*4!
5678! !5#&!9(&9#! !#)!*+!3#*(/%9+98!
5668! !!5:!#)!/(&)1+&1#!-,+3%1+/%(&+*8!
!
!!!;
-
!760
"#$%&'(&)%!#&!("*+)%!("*+,'%&+-'%!.!$-%$'()+)("!,%&"*+&*("!(&!(/!0-(+!)(! /+!1&',+!(&*-+)+!.! /+!
1&',+!"+/')+2!
3456! !
!
!""#$#%&'%()*+,-'%.)/%-)%.'%0)123-4,5246'%
%
!!!7!,%&*'+,'8&9!"(!+&+/':+!/+!"(;#&)+!/(.!)(!/+!*(-!?(,%-)(! ! @#$%&;+
-
! 761
!
"#$%&'(!)'!*&+*,%&*$-.*!
!
!
/&-,.!$#0,&'1&!2.'!
1&*$14*$! !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !
5&+*,%&*$-.* !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !
/&-,.!$#0,&'1&!2.'!
1&*$14*$! !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!!!"#!$#!%&'%()&%*+,%-!
./01! !2!
./31! !
!
!!!4&!./01!2!./31-!
.561! !
!
!!!!!"7!8,&'(8(&!+&!%+(:(,! !!+&!$#!%&'%()&%*+,%!;&!+&'(#&!8,:,-!
.5/1! !
!
!!!!!;(! !
!
!!!!?,! 9,+,! 8(87,! %&@&%;(A7&! &;! $#! 8(87,! +&! B*%#,9>! C&%,! !"#"$ %&%'"$ #($ )*+,"!$ (-$ .,$ %&%'"$
+(/(+-&0'(=!"#!&7!8*;,!+&!$#!8(87,!+&!B*%#,9!DE$&!%&C%&;*!$#!8*;,!(+&*7!E$&!#,!&F(;9&!!7*!
%&*7(+*+>! 8,:,! $#! 7G:(9&! *7! E$&! $#! ;(;9&:*! *A(&%9,! ,! @,7$:! +&! 8,#9%,7! C$&+&! 9+&%D>! 7*!
&'(8((*!+&!$#*!:HE$(#*!9I%:(8*!&;!:HF(:*>!*$#E$&!#$#8*!/66J=!!
!
!!!KL,%*!A(!!&7!8(87,!+&!$#*!:HE$(#*!9I%:(8*-!
.5M1! !
!
!!!4(@(+(:,;!%&!7*!9&:C&%*9$%*! -!
.5N1! !!
6&!,#3.*1$!!!
!!!!!1*$0$7.! !
-
!762
!!!"#$%!&'(! !)! !*%+!,%+*-#+-(*.!*(!%/-0(+(!1#!2#30#,04+!$(!1#!(+-3%56#! (+!'+!,0,1%!$(!'+#!
78&'0+#!-9370,#!
:;+!(1!,#*%!$(!'+!3(?30@(3#$%3.!1#!2#30#,04+!$(!1#!(+-3%56#! (+!'+!,0,1%!(*A!
:;B=! !
!
!!!C!,%+-0+'#,04+!*(!#+#10D#+!!"!#$%&%"'(#)%&*+)&!$,%"%-),&.)&.$%&(/$!)%$%.!#!*#/(3.!'+!53%,(*%!
&'(!2#!$(!'+!(*-#$%!E!#!%-3%!(*-#$%!;!)!1'(@%!%-3%!53%,(*%!&'(!3(@3(*#!$(1!(*-#$%!;!#1!(*-#$%!EF!>1!
,0,1%! !5'($(!*(3!!"#"!$%&'"(%!%!!"#"!$%&'")!!
"#$%&'(!)'!*+*,-!.&/&.0+1,&!2!3'!*+*,-!+..&/&.0+1,&!
!!!!"#$#*!1#*!-3(*!$0*-0+,0%+(*!#330/#!7(+,0%+#$#*.!(G0*-(+.!(+!-(%36#.!2#30#*!,%7/0+#,0%+(*!$(!-3(*!
53%50($#$(*.!$(!1#*!,'#1(*!2(3(7%*!1#*!*0@'0(+-(*A!
01! H#!'2*+",3& -4/'"!3& :'+! *0*-(7#! ,(33#$%.! +%I#$0#/8-0,%=5!J(3(7%*! (1! ,#*%! 0$(#1! $(!
'+#!78&'0+#!-9370,#!,%+&!"!#$&/)6)/%"7#).!)!(1!,#*%!3(#1!$(!'+!!"!#$&,$&/)6)/%"7#)5&
KK=! >1! /)8/"9)/3.$/& :'+! *0*-(7#! ,(33#$%.! +%I#$0#/8-0,%=5! J(3(7%*! (1! ,#*%! 0$(#1! $(! '+!
3(?30@(3#$%3!,%+!!"!#$&/)6)/%"7#).!)!(1!,#*%!3(#1!$(!'+!!"!#$&,$&/)6)/%"7#)F!
KKK=! >1!L+02(3*%.! (+! -(%36#.! 5%$36#! *(3!+,& %"%-)'3& !)//3.$& :& 3."372-"!$;& &'(.! (+! -(%36#.!
5'($(!-(+(3!'+!!"!#$&/)6)/%"7#)!M5307(3%!*(!(G5#+$(!)!1'(@%!,%1#5*#.!,%+!@(%7(-36#!
,(33#$#N.! #'+&'(! (+! 1%*! O(,O%*.! *(! -3#-#! $(! +,& (/$!)%$! "//)6)/%"7#).! #! *#/(3.! 1#!
(G5#+*04+!#$0#/8-0,#!(+!'+#!@(%7(-36#!51#+#!%!#/0(3-#F!
!
$4!)'$!#563+'$!78.#+*$9!*-'!3'!*+*,-!.&/&.0+1,&!
:;B=! !
:;P=! !
:QR=! !
-
! 763
!!!"#$%&! !"#$%&$'()*"#+(#,&%+#-(!./0'!()#!*#!+,!-.//.0./,1,!#&! 2.*!+#-+.*'! 2,!/,34&!1#!1#! 2.*!
52)6.*!1#!-,2./!7!2,!/,34&!1#!2,!8#9:#/,8)/,!,28,! !7!0,6,! !#&!)&!-;-2.!1#!!7!=DE>!*#!.08;#!',(#,!%,0%1*(-"(',("*/!+23,("*(4*(0%0'+(!"#"!$%&'"5!
=DG>! !
!
!!!A.*!1.*!8J/9;&.*!1#2!2,1.!;3();#/1.!/#:/#*#&8,&!6)&8.*!#2!-;-2.!-.9:2#8.!7!:)#1#&!,&.8,/*#!#&!
5./9,!0/#?#!-.9.! '!1#!9.1.!()#!
=DD>! !
!
!!F,1.! ()#! 2,! ?,/;,-;4&! 1#! 2,! #&8/.:K,! #&! 2.*! ,2/#1#1./#*! 8;#! ()#! ?#/! -.&! 2,! ?,/;,-;4&! 1#! 2,!
#&8/.:K,!#&!#2!*;*8#9,!&.!,1;,0L8;-.'!:./!=DD>!*#!*;$)#!()#C!
=DM>! !
!
!!!F,1.!()#!2,!?,/;,-;4&!1#!2,!#&8/.:K,!8.8,2!#*!2,!*)9,!1#!2,!?,/;,-;4&!1#!2,!#&8/.:K,!#&!#2!*;*8#9,!
7!2,!?,/;,-;4&!1#!2,!#&8/.:K,!#&!2.*!,2/#1#1./#*'!*#!*;$)#'!:./!=DD>!7!=DM>C!
=DN>! !
!
!"#$%'()*+%,-.'+/&0#/1%#*%#/+/21#+..343.5+!236#
#
=DO>! !!!!7!
=DP>! !
!
!!!F,1.!()#'!-.9:,/,&1.!:/.-#*.*!/#?#/*;02#*!#!;//#?#/*;02#*C!
=DQ>! !
!
!!!7!1,1.!()#!=?J,*#!,//;0,>C!
=DH>! !
!
!!*#!*;$)#!()#C!
=MI> !
-
!764
!!"#$%&!'()*+!
,-./! !!!!!0!
,-1/! !!!!
!
!!!23!4$%!5)6(*(7(8*+!
,-9/! !
!
!!!:$%!,-;/3!,-./3!,-1/!0!,-9/3!$'+!
,--/! !
!
"#!$%!&'(&)*'&+,-&.!"-%!/%!")"0-!&'1'&2)30'!
!
,-?/! !
!
!!!:$%!@&!4%$4A)>4%)*5)!!"#$%&'()"!$"$#$%#*!")&')&3!&!>&')%!!"#$#%$&'('$)*)+'$
(#$)",+!"*#-$.*./,0$+,$#%&-'12,$3$(*./*%"4#$3$.*5"#$*5",+0$1#-'$%"%),$,"/#%&,6$
,?D/! !
-
! 765
!
!!!"#$!%&'()*+,!-%! .+/!/&+/!(0()1(-+/!/%!-%/0)%$-%! !"#$%&'()"# !%*#)%# !"# +%,-.)/(0-/1",! .(!
23(.!(4#)&(!53%,!%$!3$!0)+2%/+,!.(!%$1)+06(!1+1(.!-%!3$!/#/1%&(!!"#$#%$&'()*')!/#%&0)%!(3&%$1(!+!
53%-(!#*3(.,!0%)+!$3$2(!-#/$37%8!+),-!&'(&$&'$%'$#.#(&!-$/)'$/./,)$*&0&*#.1,&$2$-3.-1"(./)$,-$
&'(*)45-$()(-,$$/&*)6!
9:;
!
!!!=('%!(2.()()!53%!%.!%$3$2#(-+!53%!(4#)&(!53%! .(!>()#(2#?$!-%! .(!%$1)+06(! 1+1(.!-%!%'$#.#(&!-!
!"#$#%$&'()*')!/#%&0)%!(3&%$1(!+!53%-(!#*3(.,!%/!%.!%$3$2#(-+!(@#+&A1#2+8!B$(!2+$/%23%$2#(!
-%! %/1%! (@#+&(!%/! %.! %$3$2#(-+!53%! .(! %$1)+06(!-%.! %$1+)$+!%/!&(7+)!+! #*3(.! (! .(! %$1)+06(!-%.!
/#/1%&(!9 ()6(! 0+2+! 2+$! %.!
1#%&0+! 9
!
!!!HE+)(! 1+2(! ($(.#D()! !"# $%&'()"# !%*! -%! .(! 1%)&+-#$A(! %$! %.! 2(/+! -%.! B$#>%)/+,! %$! -+/!
>()#($1%/I!
J%)/+!2%))(-+!9
7!2+.(0/+!
K%)/+! 0.($+
-
!766
!
!!!"#!$%&%'!(%'!)*'%'+!',!$-*$*!&,!.#!/#01,-'%!)%2%!'0'$,2*!),--*&%!3!*&0*45$0)%+!&,!2%&%!6.,!
7!!8-02,-%!1,-,2%'!,(!)*'%!.#%!&,!.#*!,9:*#'0;#!-,1,-'04(,7!
!
!""#$#%#'()'*+,-./01'2131'0,04.35'2.//5617'21+'.895+0,:+'56,5;
-
! 767
"#$%! !!!
!
!!!&'!"#(%!)!"#$%!*+,'-'.*/0!!
!
"#1%! !!!!
!
!!!&23*!45'!62!'-,7*892!'/!5-2!:5-;
-
!768
"#$% !
!
!!!&'()! *)+,-)+.! /)! 01! 2134154,+! +)61(421! /)! 01! )+(3.781! )+! 9+! '9:'4'()-1! +.! 1/41:;(45.! /)0!
!10!
/4'4713! )0! C.0! )+.3-)'! 51+(4/1/)'! /)! )+)3681! /)! 510.3! H1541! )0! *38.! 5.'-.'>! 01! )+(3.781! 21! )+!
19-)+(.M!
"#N%! !
!
!!!O:241-)+()>!)+!(B3-4+.'!1:'.09(.'>!)0!4+53)-)+(.!/)!01!)+(3.781!/)0!5.'-.'!)'!-95H.!-1@.3!
=9)!01!/4'-4+954,+!/)!01!)+(3.781!)+!01!L4)331P!
"##%! !
!!!!!
!!!Q>!7.3!0.!(1+(.>!01!)+(3.781!(.(10!/)!01!L4)331!-;'!01!/)0!5.'-.'!21!)+!19-)+(.P!
"#R%! !
!
!!!S)-.'! 5.-73.:1/.! =9)! !"# $"%&"'&()# *+# !"# +),%-./"# +)# 0120&0,+3"0# *+!#4)&$+%0-5# '-3-# !"#
6&+%%"5#'-3."%"2!+0#'-)#3781&)"0#,9%3&'"0#&%%+$+%0&2!+05#.1+*+#0+%#)+:",&$"#*1%"),+#3&!+0#*+#
3&!!-)+0# *+# ";-05#
top related