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7/24/2019 Matematika Teknik II Fix
1/20
CREATED BY : GROUP 5
ISABEL TRIESTY NRP 2315105007
RIZQA FAUZIYAH NRP2315105019
HARMIDIA Q. NRP 231510502
PUNDHI TRIONGGO !. NRP2315105031
HANINDHITO S. NRP 2315105033
Matematika Teknik IIPresentation
M"#$%&"#'(")F*+&,)"#'*-
7/24/2019 Matematika Teknik II Fix
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C*-'/%+ T$% P+*(% OS#"+#'- T$% E,')'+',& S#')).S#')) I I-'#'"))4 C$"+%/ '#$ 20
L&*) O F%%/ S#*(6 OC*&*#'#'*- 8 032 M*)F+"(#'*- O B%-;%-%. F%%/ IS,)'%/ A# T$% R"#% 10 L
7/24/2019 Matematika Teknik II Fix
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A((,&,)"#'*- '-,#*,#,#%-%+"#'*-(*-,'*-
G'>%- +*& #$% ,%#'*- :8 032 +"(#'*- &*)% * %-;%-% '- %%/ 20 L&*) &*)% *),#'*-F 10 )&*)"*+ 2?F'-/ : #'&% #* +%,'+%/ *+ #$% (*&*'#'*- **>%+$%"/ +*/,6 Y/ 0? &*)% +"(#'*- *
%-;%-%
O>%+ ")) &" ")"-(% :
Solution :
/@
7/24/2019 Matematika Teknik II Fix
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Component Mass Balance of Benzene
.............................. (eq.1)
D
W
DFW
DFW
Y10.-0,32.10dt
dX
.20
YD.-X.Fdt
dX. W
YD.-X.Fdt
dW
.X
nconsumptio-generationoutput-inputonccumulati
=
=
=
+=
D! 10.Y-3,2
dt
dX.20 =
7/24/2019 Matematika Teknik II Fix
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The system benzene and toluene follows Raoults
Law. To calculate mole fraction benzene in vapourcan be calculate from this equation
!o" mole toluene and benzene in vapour
Benzene
#$ean%oplis" &'() equation ((.(*'+
.............................. #eq.2+
,apor pressure of pure -
Total pressure"
X."Y =
##
D#
##
#
X."
"YY
X.""Y
==
=
7/24/2019 Matematika Teknik II Fix
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Toluene
$$
$ X."
"Y =
7/24/2019 Matematika Teknik II Fix
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-n ideal law" Raoults law can be defined for vapor*liquid phases in equilibrium
!o"
#$ean%oplis" &') equation ((.(*(+
.............................. #eq.3+
/artial /ressure of -
,apor pressure of pure -
X."p =
%X-&1."X.""$hen,
%X-&1XX."X."pp"
X."p
X."p
#$##
#$$$##$#
$$$
###
+==+=+=
+==
%X-&1
"
"X
"
"#
#
$#
#
+=
7/24/2019 Matematika Teknik II Fix
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Relative volatility #0+ of benzene to toluene can beformulated as
!o"
1e have
#$ean%oplis" &'2) equation ((.3*(+##
#
X/Y
X/Y' =
$$
###$
X/Y
X/Y' =
X."
"YandX.
"
"Y $
$$#
## ==
7/24/2019 Matematika Teknik II Fix
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!o"
.............................. #eq.4+#
$
#$
$
##$
$$$
###
#$
"
"
'
1
"
"'
X/X.
"
"
X/X."
"
'
=
=
=
7/24/2019 Matematika Teknik II Fix
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1e have equation
!ubtitute #eq.'+ to #eq.3+
.............................. #eq.3+
.............................. #eq.4+
.............................. #eq.5)
%X-&1"
"
X"
"
##
$
##
+=
%X-&1'.X
'
'
%X-&1'.X
1
"
"
'
%X-&1X
1
"
"
'
%X-&1X
"
"
##$#
#$
#$
##$#
#
#$
##
#
#$
##
#
+=
+=
+=
+=
#
$
#$ "
"
'
1=
7/24/2019 Matematika Teknik II Fix
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!ubstitute #eq.2+ to #eq.4+eq.4
.............................. #eq.6)
11%-&'X
'.XY
X.%X-&1'.X
'
X."
"Y
#$#
#$#D
#
##$#
#$
##
D
+=
+=
=
1X.1,()
X.(),2
1X1%-&2,()
X.2,()Y*o,
W
W
W
WD
2,().o+alueaerageanatconstantattaenbema%#$&'olatilitrelatie$he
+=
+=
7/24/2019 Matematika Teknik II Fix
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!ubstitute #eq.&+ to #eq.(+
.............................. #eq.1)
dt%20,1X-&3,2%1,()X&1dX20
1,()X1
X20,1-3,2
dt
dX20
1,()X1
2(,)X-(,/X3,2
dt
dX20
1,()X1
2(,)X-%1,()X&13,2
dt
dX20
1,()X1
2(,)X
-3,2dt
dX
20
11,()X
2,()X10-3,2
dt
dX20
WWW
W
WW
W
WWW
W
WWW
W
WW
W
WW
=++
=
+
+=
++
=
+=
+
=
D
!
10.Y-3,2dt
dX
.20 =
7/24/2019 Matematika Teknik II Fix
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!eparable 567 Modellin8
+=
+=
+=
+=
+=
W
W
WW
W
W
W
WW
W
W
W
W
W
W
W
W
WW
dX20,1X-3,2
X2,dX
20,1X-3,2
120dt
dX20,1X-3,2
,X2dX20,1X-3,220dt
dX20,1X-3,2
%1&1,()X20dt
dX20,1X-3,2
%1&1,()X20dt
20,1X-3,2
%1,()X&1dX20dt
7/24/2019 Matematika Teknik II Fix
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Let
...................... #eq.7) += WW
WW
W
dX20,1X-3,2
X2,dX
20,1X-3,2
120t
W
W
W
W
W
dXX20,1-3,2
X2,#
dXX20,1-3,2
120
=
=
7/24/2019 Matematika Teknik II Fix
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1e inte8rated - "
%20,1X-2,3&ln1,20
20
uln1,20
20du
1
1,20
20
20,1-
d
120
20,1
d-dX
20,1-dX
d
20,1X-3,2let
W
W
W
W
=
=
=
=
=
=
=
WWdXX20,1-3,2
1
20 =
7/24/2019 Matematika Teknik II Fix
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1e inte8rated B
%X20,1-&3,2ln20,1
3,2-
20,1-
X2,#
%20,1X&3,2ln20,1
3,2-
20,1-
X
%%20,1X&3,2ln3,2--20,1X&20,1
1
20,1%%&3,2ln3,2--20,1X&&-20,1%
1
X20,1-3,2
X
so,X20,1-b43,2a4X5et,
cb%%&alna-b&
b
1d
ba
dXX20,1-3,2
X2,#
W2
W
W2
W
WW2
W2
W
W
WW
2
W
W
W
+
=
+=
+=
+=
===
++=
+
=
7/24/2019 Matematika Teknik II Fix
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.. #eq.8
. #eq.%20,1&0,32%-&3,2ln20,1
3,2
20,1-
0,322,%20,1&0,32%-&3,2ln
20,1
20
%20,1&0,32%-&3,2ln20,1
3,2
20,1-
0,322,%20,1&0,32%-&3,2ln
20,1-
200
0,32X0t+or
%20,1X-&3,2ln20,1
3,2-
20,1-
X2,%20,1X-&3,2ln
20,1-
20t
dX20,1X-3,2X2,dX
20,1X-3,2120t
t*o,
2
2
W
W2
WW
W
W
WW
W
=
+
+=
==
+
+=
+=
=
7/24/2019 Matematika Teknik II Fix
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*ubstitue e6. to e6.)
+
+
=
++
+
=
+
+=
%%20,1X-&3,2
%20,1%&0,32-&3,2ln
20,1
3,2%X-&&0,32
20,1
2,
%%20,1X-&3,2&ln-%20,1&0,32%-&3,2&ln
20,1
20t
%%20,1%&0,32-&3,2ln20,1
32&0,32%20,1X-&3,2ln
20,1
3,2-&&-X
20,1
2,
%%20,1X-&3,2&ln
20,1
20-%%20,1&0,32%-&3,2&ln
20,1
20t
%20,1&0,32%-&3,2ln20,1
3,2
20,1
0,322,%20,1&0,32%-&3,2ln
20,1
20
%20,1X-&3,2&ln20,1
3,2
20,1-
0,322,%20,1X-&3,2ln
20,1-
20t
W
W
W
WW
W
2
W2W
7/24/2019 Matematika Teknik II Fix
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#eq.10)
S* #$% (*&*'#'*- * *>%+$%"/+*/,6 Y/ 0? &*)% +"(#'*- *
%-;%-% @$%- # 151 $+
++=
%W
20,1X-&3,2
%2%&20,1%&0,3-&3,2
ln2
20,1
3,2
20,1
%W
X-&0,32
2,
%W
20,1X-&3,2
%20,1&0,32%-&3,2
ln
20,1
20
t
0,21X
1,()X1
2,()X(,0
1,()X1
2,()XYthatproblem,the+romgien
W
W
W
W
WD
=+
=+
=
hr1,7)1t
%20,1&0,21%-&3,2
%2%&20,1%&0,3-&3,2ln
20,1
3,2
20,1
0,21%-&0,322,
%20,1&0,21%-&3,2
%20,1&0,32%-&3,2ln
20,1
20t
10e6uationtoX!substitute
2
=
+
+
=
7/24/2019 Matematika Teknik II Fix
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TH!" #$% &