ESCUELA DE INGENIERÍA BIOQUÍMICA FACULTAD DE INGENIERÍA PONTIFICIA UNIVERSIDAD CATÓLICA DE VALPARAÍSO
ICB 590 LABORATORIO DE PROCESOS ALIMENTARIOS PRACTICO 1: ISOTERMAS DE SORCIÓN
Alumn!:
Cl"u#$" M"ll%" V%&'( Mu)* M"(&+l" P$n N","#+' R#(%-u+*
P(.+!(+!:
P"'($&$" A(/"l An#(+" Ru$*
M", 015
RESUMEN
El objetivo del siguiente estudio fue determinar isotermas de adsorción de humedad de la avena avena a una una temp tempera eratu tura ra de 37°C, 37°C, para para un rango rango de aw entre 0,11 0,111 0,!1 0,!11 1"
#as #as
isotermas fueron modeladas con dos ecuaciones, ecuación $E% ecuación &'$, ambas com(nmente com(nmente aplicadas en alimentos" #a calidad de ajuste se evaluó con el coeficiente de regresión r ) con el porcentaje de error medio relativo *+E, en base a esto se observó -ue -ue con modela modelació ción n por por &'$ &'$ emp.ricamente en laboratorio"
se ajustar ajustaron on de mejor mejor manera manera los datos datos obtenid obtenidos os
CAPITULO 1 RESULTADOS 2 DISCUSIÓN Un" $!'+(m" #+ !(&$3n +! l" (+l"&$3n +n'(+ l" &"n'$#"# #+ "-u" ''"l 4u+ (+!+n'" un !3l$# , l" "&'$$#"# '+(m#$n6m$&" #+l "-u" +n +!+ !3l$# " un" #+'+(m$n"#" '+m+("'u("7 En +!'+ &"! !+ '("8"3 " un" '+m+("'u(" #+ ;um+#"# +n 8"!+ !+&" ?@8! !+ +n&u+n'("n +n +l "n+= 71 , 7 "(" &"#" $!'+(m" #+ "#!(&$3n (+!+n'"#"! " &n'$nu"&$3n: T"8l" 1: D"'! +=+($m+n'"l+! "(" $!'+(m"! #+ "#!(&$3n7 Slu&$n S"l$n" L$Cl M-Cl CO N"B( N"NO ?NH SO NHHPO
" 0111 019 0 05; 01 0;91 0911
@8! 01900;1 015 0500; 00911; 0999 095;9 059091
Cn +!'! #"'! 8'+n$#! +! !$8l+ (+(+!+n'"( l" &u(" #+ $!'+(m" " ;
07 07 Xbs (g masa agua/g masa seca)
07 07 0 0
075
1
aw
F$-u(" 1: $!'+(m" #+ "#!(&$3n "(" "+n" " ;
171 C((+l"&$3n #+ l"! I!'+(m"! #+ S(&$3n &n M#+l! M"'+m6'$&! L! #"'! +=+($m+n'"l+! !+ &((+l"&$n"(n &n m#+l! #$!'$n'! ?BET , GAB7
•
M =
M#+l"&$3n #+ l" $!'+(m" #+ BET
M mon ∙ C ∙ aw
( 1−a ) ∙ ( 1+( C −1 )∙ a ) w
w
D3n#+: M:
Hum+#"# "l +4u$l$8($ #+l "l$m+n' +n 8"!+ !+&"7
Mmon: C:
Hum+#"# #+l "l$m+n' +n l" mn&""7
&n!'"n'+ 4u+ (+(+!+n'" l" #$.+(+n&$" #+ +n+(-%" +n'(+ l"! ml/&ul"!
"#!(8$#"! +n l" ($m+(" &"" , l" #+ l"! &""! !$-u$+n'+!7 aw:
A&'$$#"# #+ "-u"7
Lu+- #+ l$n+"l$*"( l" +&u"&$3n , (+"l$*"( (+-(+!$3n l$n+"l " l! #"'! ?+( "n+= !+ 8'$+n+ l" -u(" 4u+ (+(+!+n'" l" +&u"&$3n m#+l"#" ( +l m/'#! #+ BET7 0 15 Y
.?= J 19719= K 7 R J 07;
10 5 0 0
071
07
07
07
075
07
07;
07
079
1
X
F$-u(" : R+(+!+n'"&$3n #+ l" +&u"&$3n m#+l"#" ( +l m/'# #+ BET7 E! $m('"n'+ +"lu"( +l "u!'+ #+ +!'+ m/'# &n +l &+&$+n'+ #+ (+-(+!$3n ?R , +l (&+n'"+ #+ +((( +!'+ l'$m n #+8+ +=&+#+( +l 10 #+ +((( "(" "!% '+n+( un m#+l 4u+ !+ "u!'+ #+ m+( .(m" " l! #"'! +=+($m+n'"l+!7 D+ l" -u(" !+ u+#+ "(+&$"( 4u+ l" &((+l"&$3n &u"#(6'$&" &n l! #"'! +=+($m+n'"l+! +! 05 !$+n# un 8u+n $n#$&"#( #+ 4u+ l" m#+l"&$3n ( +l m/'# #+ BET +! &((+&'" ," 4u+ +l R #+8+ !+( m",( " 05 "(" #+( "l$&"( +l m/'# " l! #"'! +=+($m+n'"l+!7 En +l &"! #+l &6l&ul #+l (&+n'"+ #+ +((( #+m!'("# +n +l "n+= !+ #+'+(m$n" 4u+ +!'+ +! #+ un ; (++"n# 4u+ !+ "l+" #+l 3'$m7 G("n "('+ #+ +!'+ "l' (&+n'"+ !+ u+#+ #+8+( " 4u+ +l ($m+( #"' m!'("# +n l" '"8l" !+ "l+" 8"!'"n'+ #+l #"' +=+($m+n'"l (+!ul'"n# !+( un "l( n+-"'$7 Lu+- #+ "u!'"( l! #"'! " l" $!'+(m" #+ BET (+!+n'"#! +n +l "n+= !+ '$+n+ un M ?@8! (+&"l&ul"# &n !u (+!+&'$" "&'$$#"# #+ "-u" #+ l" !$-u$+n'+ m"n+(": T"8l" : D"'! 8'+n$#! "(" m#+l"&$3n #+ l" $!'+(m" #+ BET
" 0111 019 0 05; 01 0;91 0911
M ?@8! K 00;5; 00 ; 0195 01;;1 000900 010 0;55
D3n#+: M ?@8!: E! l" >um+#"# +n 8"!+ !+&" (+&"l&ul"#" "(" m#+l"&$3n #+ $!'+(m" #+ BET Cn l! "n'+&+#+n'+! 8'+n$#! #+ l" '"8l" !+ #+'+(m$n" -(6&"m+n'+ +l "u!'+ #+ l! #"'! +=+($m+n'"l+! ( +l m/'# #+ BET7
07 07 07 Xbs (g masa agua/g masa seca)
07 0
D"'! E=+($m+n'"l+! BET
075 K07 0 1 aw
F$-u(" : $!'+(m" #+ "#!(&$3n #+ BET "(" "+n" " ;
•
M =
M#+l"&$3n #+ l" $!'+(m" #+ GAB
M mon ∙ C ∙ k ∙ aw
( 1−k ∙ a w) ∙ ( 1 +( C −1) ∙ k ∙ a w)
D3n#+: C:
Cn!'"n'+ &"("&'+(%!'$&" #+l (#u&' #+l m#+l #+ GAB
k :
F"&'( #+ &((+&&$3n #+l M#+l #+ GAB
M:
>um+#"# #+ +4u$l$8($ +n +l "l$m+n' +n 8"!+ !+&"
Mmon:
Hum+#"# #+l (#u&' &((+!n#$+n'+ " l" mn&""7
Lu+- #+ l$n+"l$*"( l" +&u"&$3n , (+"l$*"( (+-(+!$3n &u"#(6'$&" " l! #"'! ?+( "n+= !+ 8'$+n+ l" -u(" 4u+ (+(+!+n'" l" +&u"&$3n m#+l"#" ( +l m/'#! #+ GAB7 75 .?= J K ;70;= 7= K 079 R J 079
175 Y
1 075 0 0
071 07 07 07 075 07 07; 07 079
1
X
F$-u(" : R+(+!+n'"&$3n #+ l" +&u"&$3n m#+l"#" ( +l m/'# #+ GAB7
Al $-u"l 4u+ +n +l m/'# #+ BET +! $m('"n'+ +"lu"( +l "u!'+ #+ +!'+ m/'# &n +l &+&$+n'+ #+ (+-(+!$3n ?R , +l (&+n'"+ #+ +((( "(" "!% '+n+( un m#+l 4u+ !+ "u!'+ #+ .(m" &((+&'" " l! #"'! +=+($m+n'"l+!7 En l" -u(" !+ u+#+ "(+&$"( 4u+ l" &((+l"&$3n &u"#(6'$&" &n l! #"'! +=+($m+n'"l+! +! 0901 !$+n# un 8u+n $n#$&"#( #+ 4u+ l" m#+l"&$3n ( +l m/'# #+ GAB +! &((+&'" ," 4u+ +l R #+8+ !+( m",( " 05 "(" #+( "l$&"( +l m/'# " l! #"'! +=+($m+n'"l+!7 En +l &"! #+l &6l&ul #+l (&+n'"+ #+ +((( #+m!'("# +n +l "n+= !+ #+'+(m$n" 4u+ +!'+ +! #+ un 1 (++"n# 4u+ ¨+ &n l $#+"l 4u+ +! '+n+( un (&+n'"+ #+ +((( m+n( " 107 P( '(" "('+ +! !$8l+ &m"("( +!'! "l(+! &n l" $!'+(m" #+ BET (++"n# n'($"m+n'+ 4u+ GAB !+ "u!'" #+ m+( .(m"7 Lu+- #+ "u!'"( l! #"'! " l" $!'+(m" #+ GAB (+!+n'"#! +n +l "n+= !+ '$+n+ un M ?@8! (+&"l&ul"# &n !u (+!+&'$" "&'$$#"# #+ "-u" #+ l" !$-u$+n'+ .(m":
T"8l" : D"'! 8'+n$#! "(" m#+l"&$3n #+ l" $!'+(m" #+ GAB " 0111 019 0 05; 01 0;91 0911
M ?@8! 0901 0190 ; 0115 5 01;5 05 0;; 9; 05 99 055;;9
9 D3n#+: M ?@8!: E! l" >um+#"# +n 8"!+ !+&" (+&"l&ul"#" "(" m#+l"&$3n #+ $!'+(m" #+ GAB Cn l! "n'+&+#+n'+! 8'+n$#! #+ l" '"8l" !+ #+'+(m$n" -(6&"m+n'+ +l "u!'+ #+ l! #"'! +=+($m+n'"l+! ( +l m/'# #+ GAB7 07; 07 075 07 Xbs (g masa agua/ g masa seca) 07 07 071 0
D"'! E=+($m+n'"l+! GAB
aw
F$-u(" 5: $!'+(m" #+ "#!(&$3n #+ GAB "(" "+n" " ;
CAPITULO CONCLUSIONES /e acuerdo a los resultados obtenidos en este estudio, se puede concluir -ue de las dos ecuaciones utiliadas para la modelación, la ecuación de &'$ fue la -ue mejor se ajustó" En el caso de la modelación por la ecuación $E%, para valores inferiores a 0,) de aw, se ve un desajuste en las isotermas" o obstante, destaca el ajuste por el modelo &'$, con valor de r ) superior a 0,!2 con un +E inferior al 10+"
BIBLIOGRAFIA
ANE@OS An+= 1 D"'! O8'+n$#! #+l L"8("'($ L! #"'! 8'+n$#! " "('$( #+ l"! !u&+!$"! m+#$&$n+! "(" l" &n!'(u&&$3n #+ l"! &u("! #+ !(&$3n !n l! m!'("#! +n l" !$-u$+n'+ '"8l" "(" &"#" un" #+ l"! !"l+! u'$l$*"#"!:
" ( ' ! ! + + P u M " ( ' ! ! + + P u M 5 " ( ' ! ! + + P u M F " ( ' ! ! + + P u M " ( ' ! ! + + P u M
D ; 0 E 0
1 D 1 E 0
F 0 E E 0
D ; 5 E 0
1 1 D E 0
9 1 ; E 0
E E D E 0
E E 9 5 0
; 5 0 E 0
E F E E 0
: E F E 0
E 0 D E 0
; 1 ; E 0
D ; E 0
E 9 5 0
F F 0 E 0
1 F E E 0
; F : E 0
D 9 ; E 0
9 D E E 0
: F E E 0
1 5 9 5 0
; 0 E 0
: E E 0
D : E 0
F 9 F E 0
9 5 F E 0
E 1 E E 0
D F 9 5 0
F 0 0 E 0
5 5 E 0
1 : E 0
5 D F E 0
D : F E 0
D D 5 E 0
: 9 F 9 1 9 9 5 5 5 E 0 0 0 F " 0 ! a partir 0del %abla 1 /atos 4btenidos de la avena d.a cero" " " % 1 D 1 9 5 # m 0 : 0 5 5 " ! & 0 0 + + P ! 1 9 F 1 1 : 1 : F " 0 0 0 ( 1 9 F H 1 1 : 1 : F
5 D E 0
; ; F E 0
F E 0
E 5 5 E 0
F F : 5 0
F 9 : 5 0
E 0 9 F 0
E 9 F 0
; : 5 0
D 1 E 0
1 9 ; 0
1 1 9 0
; : 5
D 1 E
1 9 ;
1 1 9
" ( ' ! ! + + P u M
F
Un"
+*
! + l " S
l C $ L
l C M
:
O C G
( B " N
O N " N
O S A F H N ?
F
O P H F H N
4u+
!+
ll+-" " +! &n!'"n'+ ( &"#" un" #+ l"! mu+!'(" #+ "+n" ?8'+n$# +l #%" !+ #+'+(m$n" l" &"n'$#"# #+ "-u" "#!(8$#" ( l" "+n" #+ l" !$-u$+n'+ m"n+(": Masa de agua adsorbida= peso muestra dia 6 − peso masa seca dia 0
•
E+ml #+ &6l&ul "(" l" !"l L$Cl: Masa de agua adsorbida=0,6078 −0,5104 = 0,0974 g
Qu+#"n# +l (+!ul'"# (+(+!+n'"# "(" '#! l! #"'! +=+($m+n'"l+! +n l" !$-u$+n'+ '"8l" T"8l" : D"'! #+ m"!" "-u" "#!(8$#" +n l" "+n" "(" #$.+(+n'+! !"l+!7 Slu&$3n S"l$n" L$Cl M-Cl CO N"B( N"NO ?NH SO NHHPO
M"!" #+ "-u" "#!(8$#" 009; 01099 011 01 011; 011 05;
An+= C6l&ul! "(" I!'+(m" #+ S(&$3n
P"(" (+(+!+n'"( l" &u(" #+ "#!(&$3n +! n+&+!"($ !"8+( l" "&'$$#"# #+ "-u" , l" >um+#"# +n 8"!+ !+&" #+ &"#" mu+!'(" 4u+ !+ m"n$ul3 +n l" +=+($+n&$" #+l l"8("'($7
71 A&'$$#"# #+ "-u" P"(" #+'+(m$n"( l" "&'$$#"# #+ "-u" +n &"#" !"l 4u+ !+ u'$l$*3 !+ (+(+!+n'" #+ l" !$-u$+n'+ m"n+("7
aw =
Hr
100
D3n#+: ": A&'$$#"# #+ "-u" H(: P(&+n'"+ #+ >um+#"# (+l"'$" •
aw =
E+ml #+ &6l&ul "(" l" !"l L$Cl:
11,1 100
=0,111
7 Hum+#"# +n 8"!+ !+&" P"(" #+'+(m$n"( +n &"#" mu+!'(" l" >um+#"# +n 8"!+ !+&" !+ 8'u #+ l" !$-u$+n'+ .(m":
Xbs =
masade agua adsorbida peso demasa seca dia 0
D3n#+: @8!: >um+#"# +n 8"!+ !+&"
E+ml #+ &6l&ul "(" l" !"l L$Cl:
Xbs =
0,0974 0,5104
=0,1908307
An+= M#+l"&$3n #+ l" Cu(" #+ D+!(&$3n " l" I!'+(m" #+ BET S+ m#+l" ( l" +&u"&$3n:
M =
M mon ∙ C ∙ aw
( 1−a w ) ∙ ( 1+( C −1 )∙ aw )
D3n#+: M:
Hum+#"# "l +4u$l$8($ #+l "l$m+n' +n 8"!+ !+&"7
Mmon: C:
Hum+#"# #+l "l$m+n' +n l" mn&""7
&n!'"n'+ 4u+ (+(+!+n'" l" #$.+(+n&$" #+ +n+(-%" +n'(+ l"! ml/&ul"!
"#!(8$#"! +n l" ($m+(" &"" , l" #+ l"! &""! !$-u$+n'+!7 aw:
A&'$$#"# #+ "-u"7
L" +&u"&$3n l" #+m! l$n+"l$*"( 4u+#"n# #+ l" !$-u$+n'+ .(m": aw M ∙ ( 1− aw )
=
1
+
C − 1
∙ aw M mon ∙ C M mon ∙ C
Cm l" +&u"&$3n (+!ul'"n'+ +! l$n+"l !+ (+"l$*" un" (+-(+!$3n l$n+"l &n l! #"'! +=+($m+n'"l+! 8'+n$#! #+l l"8("'($ "(" M ?+n nu+!'( &"! &((+!n#+ +n l"! '"8l"! " @8! , aw #+ '"l .(m" #+ 8'+n+( +ll !+ >"&+ l !$-u$+n'+:
Mmon
, C7 P"("
aw M ∙ ( 1− aw )
=Y
a w = X
1
M mon ∙ C
C − 1 M mon ∙ C
=b
=m
Lu+- !+ m#+l" l" $!'+(m" (+&"l&ul"n# l! "l(+! "(" M ? !+" (+&"l&ul"n# "(" @8! "(" !u &((+!n#$+n'+ "7
E+ml #+ &6l&ul "(" l" !"l L$Cl:
Y =
0,111
0,1908307 ∙ ( 1−0,111 )
=0,654293983
En l" !$-u$+n'+ '"8l" !+ (+(+!+n'" l! @ + 2 "(" >"&+( (+-(+!$3n l$n+"l &n l! #"'! +=+($m+n'"l+!7 T"8l" : D"'! +=+($m+n'"l+! &n l! 4u+ !+ (+"l$*" (+-(+!$3n l$n+"l7 @ 0111 019 0 05;
2 059 9 1110 1 0;0 1 50; 95
01 0;91 0911
15; 0 1011 5 1;110;
D+ l" '"8l" "n'+($( !+ #+'+(m$n" l" +&u"&$3n ,J 191= 0 &n un RJ 05 (++ml"*"n# l! #"'! #+ l" (+-(+!$3n l$n+"l !+ #+'+(m$n" l! "l(+! #+ Mmn , #+ C +n +l !$-u$+n'+ !$!'+m" #+ +&u"&$3n7
1 M mon ∙ C
C − 1 M mon ∙ C
=−3,8042
=19,186
D+l !$!'+m" #+ +&u"&$3n !+ #+'+(m$n" 4u+ C J K0; , Mmn J 00501 P"(" +l &"! #+ l" !"l L$Cl !+ #+'+(m$n" 4u+ "(" +l m#+l #+ BET !+ '$+n+ un M ?@8! (+&"l&ul"# #+ l" !$-u$+n'+ m"n+(":
M =
0,065012 ∙ −4,04337 ∙ 0,111
( 1−0,111 ) ∙ (1 +(−4,04337 −1) ∙ 0,111)
=−0,0745628
Cn '#! l! #"'! (+&"l&ul"#! !+ #+'+(m$n" +l (&+n'"+ #+ +((( ( +l m#+l #+ BET &n l" !$-u$+n'+ +&u"&$3n7
¿ X 1− X 2 ∨ ¿
X 1
%Error =
100 n
n
∗∑ ¿ i=1
D3n#+: @1: Hum+#"# +n 8"!+ !+&" #+ l! #"'! +=+($m+n'"l+!7 @: Hum+#"# +n 8"!+ !+&" +!'$m"#" #+ l! #"'! #+l m#+l #+ BET7 n: Nm+( #+ mu+!'("!7 •
E+ml #+ &6l&ul &n '#"! l"! !"l+! &n l"! 4u+ !+ '("8"3
%Error =
100 7
(
∗
0,190830721 −−0,074562777 0,190830721
+
0,216253444 − 0,20224647 0,216253444
+
0,225004637 −0,169548232 0,225004637
An+= M#+l"&$3n #+ l" Cu(" #+ D+!(&$3n " l" I!'+(m" #+ GAB S+ m#+l" ( l" +&u"&$3n:
M =
M mon ∙ C ∙ k ∙ aw
( 1−k ∙ a w) ∙ ( 1 +( C −1) ∙ k ∙ a w)
D3n#+: C:
Cn!'"n'+ &"("&'+(%!'$&" #+l (#u&' #+l m#+l #+ GAB
k :
F"&'( #+ &((+&&$3n #+l M#+l #+ GAB
M:
>um+#"# #+ +4u$l$8($ +n +l "l$m+n' +n 8"!+ !+&"
Mmon:
Hum+#"# #+l (#u&' &((+!n#$+n'+ " l" mn&""7
L" +&u"&$3n l$n+"l$*"#" (+!+n'" l" !$-u$+n'+ .(m":
aw M
=a
2 w
∙(
1 C
−1 ) ∙
k M mon
2
1
C
M mon
+ a ∙ (1− )∙ w
+
1 M mon ∙ C ∙ k
Cm l" +&u"&$3n (+!ul'"n'+ +! un l$nm$ #+ -("# #+m! (+"l$*"( un" (+-(+!$3n &u"#(6'$&" &n l! #"'! +=+($m+n'"l+! 8'+n$#! #+l l"8("'($ "(" M ?+n nu+!'( &"! &((+!n#+ +n l"! '"8l"! " @8! , aw: aw M
=Y
a w = X
Dn#+ l! &+&$+n'+! #+ l" +&u"&$3n !+ #+!&($8+n #+ l" !$-u$+n'+ m"n+(":
( )
∙
(− )
∙
1
−1
C
1
2
k M mon
1
C M mon
=a
=b
1
=c
M mon ∙ C ∙ k
Lu+- !+ m#+l" l" $!'+(m" (+&"l&ul"n# l! "l(+! "(" M ?@8! "(" !u &((+!n#$+n'+ " 8" l"! &u"l+! !+ '("8"37
E+ml #+ &6l&ul "(" l" !"l L$Cl:
Y =
0,111 0,19083072
=0,581667351
En l" !$-u$+n'+ '"8l" !+ (+(+!+n'" l! @ + 2 "(" >"&+( (+-(+!$3n l$n+"l &n l! #"'! +=+($m+n'"l+!7
T"8l" : D"'! +=+($m+n'"l+! &n l! 4u+ !+ (+"l$*" (+-(+!$3n l$n+"l7 @ 0111 019 0 05; 01
2 051; 5 1;511 0 199 1 559 599 5
0;91 0911
1055 15 5
D+ l" '"8l" "n'+($( !+ #+'+(m$n" l" +&u"&$3n ,J K;05;= 5 090 &n un RJ 0901 (++ml"*"n# l! #"'! #+ l" (+-(+!$3n l$n+"l !+ #+'+(m$n" l! "l(+! #+ Mmn , #+ C +n +l !$-u$+n'+ !$!'+m" #+ +&u"&$3n7
( ) 1
−1 ∙
C
(− ) 1
2
k =−7,06557 M mon
1
∙
C M mon
1
=8,6586
=−0,3906
M mon ∙ C ∙ k
D+l !$!'+m" #+ +&u"&$3n !+ #+'+(m$n" 4u+ C J K151 Mmn J 0150; , J 0511 P"(" +l &"! #+ l" !"l L$Cl !+ #+'+(m$n" 4u+ "(" +l m#+l #+ GAB !+ '$+n+ un M ?@8! (+&"l&ul"# #+ l" !$-u$+n'+ m"n+(":
M =
0,125067 ∙−24,1251 ∙ 0,848511 ∙ 0,111
( 1 ∙− 0,848511 ∙ 0,111 ) ∙ ( 1+(−24,1251 −1 )∙ 0,848511 ∙ 0,111)
=0,22960146
Cn '#! l! #"'! (+&"l&ul"#! !+ #+'+(m$n" +l (&+n'"+ #+ +((( ( +l m#+l #+ GAB &n l" !$-u$+n'+ +&u"&$3n7
¿ X 1− X 2 ∨ ¿
X 1
%Error =
100 n
n
∗∑ ¿ i=1
D3n#+: @1: Hum+#"# +n 8"!+ !+&" #+ l! #"'! +=+($m+n'"l+!7 @: Hum+#"# +n 8"!+ !+&" +!'$m"#" #+ l! #"'! #+l m#+l #+ BET7 n: Nm+( #+ mu+!'("!7
•
E+ml #+ &6l&ul &n '#"! l"! !"l+! &n l"! 4u+ !+ '("8"3
%Error =
100 7
(
∗
0,190830721 − 0,22960146 0,190830721
+
0,216253444 −0,19304376 0,216253444
+
0,225004637 −0,21312552 0,225004637
+
0,2
