Matematika Teknik II Fix

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*+&,)"#'*-


2/20

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


3/20

A((,&,)"#'*- '-,#*,#,#%-%+"#'*-(*-,'*-

G'>%- +*& #$% ,%#'*- :8 032 +"(#'*- &*)% * %-;%-% '- %%/ 20 L&*) &*)% *),#'*-F 10 )&*)"*+ 2?F'-/ : #'&% #* +%,'+%/ *+ #$% (*&*'#'*- **>%+$%"/ +*/,6 Y/ 0? &*)% +"(#'*- *

%-;%-%

O>%+ ")) &" ")"-(% :

Solution :

/@


4/20

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 =


5/20

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

==

=


6/20

Toluene

$$

$ X."

"Y =


7/20

-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

"

"#

#

$#

#

+=


8/20

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 $

$$#

## ==


9/20

!o"

.............................. #eq.4+#

$

#$

$

##$

$$$

###

#$

"

"

'

1

"

"'

X/X.

"

"

X/X."

"

'

=

=

=


10/20

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=


11/20

!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

+=

+=


12/20

!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 =


13/20

!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


14/20

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

=

=


15/20

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 =


16/20

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

+

=

+=

+=

+=

===

++=

+

=


17/20

.. #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

=

+

+=

==

+

+=

+=

=


18/20

*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


19/20

#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

=

+

+

=


20/20

TH!" #$% &

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Matematika Teknik II Fix