Download Elementary Principles of Chemical Processes PDF

TitleElementary Principles of Chemical Processes
TagsPhysical Quantities Quantity Units Of Measurement Physics Physics & Mathematics
File Size133.3 KB
Total Pages16
Table of Contents
                            chap02-1-33.pdf
chap02-34-45.pdf
                        
Document Text Contents
Page 1

2- 1

CHAPTER TWO


2.1 (a)
3 24 3600

1
18144 109

wk 7 d h s 1000 ms
1 wk 1 d h 1 s

ms.

(b)
38 3600

25 98 26 0
.

. .
1 ft / s 0.0006214 mi s

3.2808 ft 1 h
mi / h mi / h

(c)
554 1 1

1000 g
3

m 1 d h kg 10 cm
d kg 24 h 60 min 1 m

85 10 cm g
4 8 4

4
4 4. / min



2.2 (a)
760 mi

3600
340

1 m 1 h
h 0.0006214 mi s

m / s

(b)
921 kg

35.3145 ft
57 5

2.20462 lb 1 m
m 1 kg

lb / ftm
3

3 3 m
3.

(c)
5 37 10 1000 J 1

1
119 93 120

3.
.

kJ 1 min .34 10 hp
min 60 s 1 kJ J / s

hp hp
-3




2.3 Assume that a golf ball occupies the space equivalent to a 2 2 2in in in cube. For a

classroom with dimensions 40 40 15 ft ft ft :

nballs
3 3

6 ft (12) in 1 ball
ft in

10 5 million balls40 40 15
2

518
3

3 3 3 .

The estimate could vary by an order of magnitude or more, depending on the assumptions made.


2.4 4 3 24 3600 s
1 0 0006214

.
.

light yr 365 d h 1.86 10 mi 3.2808 ft 1 step
1 yr 1 d h 1 s mi 2 ft

7 10 steps5 16


2.5 Distance from the earth to the moon = 238857 miles


238857 mi 1

4 1011
1 m report
0.0006214 mi 0.001 m

reports


2.6



19 0 0006214 1000
264 17

44 7

500
25 1

14 500 0 04464

700
25 1

21 700 0 02796

km 1000 m mi L
1 L 1 km 1 m gal

mi / gal

Calculate the total cost to travel miles.

Total Cost
gal (mi)

gal 28 mi

Total Cost
gal (mi)

gal 44.7 mi



Equate the two costs 4.3 10 miles

American

European

5

.
.

.

$14,
$1.

, .

$21,
$1.

, .

x

x
x

x
x

x

Page 2

2- 2

2.7



6 3

3

5

5320 imp. gal 14 h 365 d 10 cm 0.965 g 1 kg 1 tonne

plane h 1 d 1 yr 220.83 imp. gal 1 cm 1000 g 1000 kg

tonne kerosene
1.188 10

plane yr



= ×






9

5

4.02 10 tonne crude oil 1 tonne kerosene plane yr

yr 7 tonne crude oil 1.188 10 tonne kerosene

4834 planes 5000 planes

× ⋅

×

= ⇒





2.8 (a)
25 0

25 0
.

.
lb 32.1714 ft / s 1 lb

32.1714 lb ft / s
lbm

2
f

m
2 f⋅
=

(b)
2

2

25 N 1 1 kg m/s
2.5493 kg 2.5 kg

9.8066 m/s 1 N


= ⇒

(c)
10 1000 g 980.66 cm 1

9 109
ton 1 lb / s dyne

5 10 ton 2.20462 lb 1 g cm / s
dynesm

2

-4
m

2× ⋅
= ×



2.9
50 15 2 85 3 32 174

1
4 5 106

× ×


= ×
m 35.3145 ft lb ft 1 lb

1 m 1 ft s 32.174 lb ft s
lb

3 3
m f

3 3 2
m

2 f
. .

/
.



2.10
500 lb

5 10
1
2

1
10

252m
3

m

3 1 kg 1 m
2.20462 lb 11.5 kg

m≈ × FHG
I
KJ
F
HG
I
KJ ≈


2.11


(a)
m m V V h r H r

h
H

f f c c f c

c
f

displaced fluid cylinder

3
3 cm cm g / cm

30 cm
g / cm

= ⇒ = ⇒ =

= =


=

ρ ρ ρ π ρ π

ρ
ρ

2 2

30 14 1 100
0 53

( . )( . )
.



(b) ρ
ρ

f
c H
h

= = =
( )( . )

.
30 0 53

171
cm g / cm

(30 cm - 20.7 cm)
g / cm

3
3

H

h
ρf

ρc



2.12
V

R H
V

R H r h R
H

r
h

r
R
H

h

V
R H h Rh

H
R

H
h
H

V V
R

H
h
H

R H

H

H
h
H

H
H h h

H

s f

f

f f s s f s

f s s s

= = − = ⇒ =

⇒ = −
F
HG
I
KJ = −

F
HG

I
KJ

= ⇒ −
F
HG

I
KJ =

⇒ =


=


=


F
HG
I
KJ

π π π

π π π

ρ ρ ρ
π

ρ
π

ρ ρ ρ ρ

2 2 2

2 2 2 3

2

2 3

2

2

3

2

3

3 3 3

3 3 3

3 3 3

3 3

1

1

; ;





ρfρs

R

r
h

H

Page 8

2- 8

2.29 (a) p*
. .

( . )=



− + =
60 20

199 8 166 2
185 166 2 20 42 mm Hg


(b) c MAIN PROGRAM FOR PROBLEM 2.29

IMPLICIT REAL*4(A–H, 0–Z)
DIMENSION TD(6), PD(6)
DO 1 I = 1, 6
READ (5, *) TD(I), PD(I)

1 CONTINUE
WRITE (5, 902)

902 FORMAT (‘0’, 5X, ‘TEMPERATURE VAPOR PRESSURE’/6X,
* ‘ (C) (MM HG)’/)
DO 2 I = 0, 115, 5

T = 100 + I
CALL VAP (T, P, TD, PD)
WRITE (6, 903) T, P

903 FORMAT (10X, F5.1, 10X, F5.1)
2 CONTINUE

END
SUBROUTINE VAP (T, P, TD, PD)
DIMENSION TD(6), PD(6)
I = 1

1 IF (TD(I).LE.T.AND.T.LT.TD(I + 1)) GO TO 2
I = I + 1
IF (I.EQ.6) STOP
GO TO 1

2 P = PD(I) + (T – TD(I))/(TD(I + 1) – TD(I)) * (PD(I + 1) – PD(I))
RETURN
END

DATA OUTPUT
98.5 1.0 TEMPERATURE VAPOR PRESSURE
131.8 5.0 (C) (MM HG)
100.0 1.2
215.5 100.0 105.0 1.8

215.0 98.7


2.30 (b) ln ln

(ln ln ) / ( ) (ln ln ) / ( ) .

ln ln ln . ( ) . .

y a bx y ae
b y y x x

a y bx a y e

bx

x

= + ⇒ =
= − − = − − = −

= − = + ⇒ = ⇒ = −
2 1 2 1

0.693

2 1 1 2 0 693

2 0 63 1 4 00 4 00



(c) ln ln ln
(ln ln ) / (ln ln ) (ln ln ) / (ln ln )

ln ln ln ln ( ) ln( ) /

y a b x y ax
b y y x x
a y b x a y x

b= + ⇒ =
= − − = − − = −
= − = − − ⇒ = ⇒ =

2 1 2 1 2 1 1 2 1
2 1 1 2 2



(d) / /

2 1 2 1
3 /

ln( ) ln ( / ) ( / ) [can't get ( )]
[ln( ) ln( ) ]/[( / ) ( / ) ] (ln807.0 ln 40.2) /(2.0 1.0) 3

ln ln( ) ( / ) ln807.0 3ln(2.0) 2 2

[can't solve explicitly for

by x by x

y x

xy a b y x xy ae y a x e y f x
b xy xy y x y x

a xy b y x a xy e

= + ⇒ = ⇒ = =
= − − = − − =

= − = − ⇒ = ⇒ =

( )] y x

Page 9

2- 9

2.30 (cont’d)
(e) ln( / ) ln ln( ) / ( ) [ ( ) ]

[ln( / ) ln( / ) ] / [ln( ) ln( ) ]
(ln . ln . ) / (ln . ln . ) .

ln ln( / ) ( ) ln . . ln( . ) .

/ . ( ) . ( )

/

.33 / .

y x a b x y x a x y ax x

b y x y x x x

a y x b x a

y x x y x x

b b2 2 1 2

2
2

2
1 2 1

2

2 4 1 2 2 165

2 2 2

2 2
807 0 40 2 2 0 10 4 33

2 807 0 4 33 2 0 40 2

40 2 2 6 34 2




2.31 (b) Plot vs. on rectangular axes. Slope Intcpt2 3y x m n,

(c)
1 1 1 a 1

Plot vs. [rect. axes], slope = , intercept =
ln( 3) ln( 3) b b

a
x x

y b b y


(d)
1

1
3

1
1

3
2

3
2

3

( )
( )

( )
( ) , ,

y
a x

y
x a Plot vs. [rect. axes] slope = intercept = 0


OR





2 1 3 3
1 3

2

ln( ) ln ln( )
ln( ) ln( )

ln

y a x

y x

a

Plot vs. [rect.] or (y +1) vs. (x - 3) [log]

slope =
3
2

, intercept =





(e) ln

ln

y a x b

y x y x Plot vs. [rect.] or vs. [semilog ], slope = a, intercept = b





(f)

Plot vs. [rect.] slope = a, intercept = b

log ( ) ( )

log ( ) ( )
10

2 2

10
2 2

xy a x y b

xy x y






(g) Plot vs. [rect.] slope = , intercept =

OR
b

Plot
1

vs.
1

[rect.] , slope = intercept =

1

1 1

2 2

2 2

y
ax

b
x

x
y

ax b
x
y

x a b

y
ax

b
x xy

a
x xy x

b a

,

,

Page 15

2- 15

2.43



y ax a d y ax
d
da

y ax x y x a x

a y x x

i i i
i

n

i i
i

n

i i
i

n

i i i
i

n

i
i

n

i i
i

n

i
i

n

( )

/

2

1

2

1 1 1

2

1

1

2

1

0 2 0b g b g




2.44 DIMENSION X(100), Y(100)

READ (5, 1) N
C N = NUMBER OF DATA POINTS
1FORMAT (I10)

READ (5, 2) (X(J), Y(J), J = 1, N
2FORMAT (8F 10.2)

SX = 0.0
SY = 0.0
SXX = 0.0
SXY = 0.0
DO 100J = 1, N
SX = SX + X(J)
SY = SY + Y(J)
SXX = SXX + X(J) ** 2

100SXY = SXY + X(J) * Y(J)
AN = N
SX = SX/AN
SY = SY/AN
SXX = SXX/AN
SXY = SXY/AN
CALCULATE SLOPE AND INTERCEPT
A = (SXY - SX * SY)/(SXX - SX ** 2)
B = SY - A * SX
WRITE (6, 3)

3FORMAT (1H1, 20X 'PROBLEM 2-39'/)
WRITE (6, 4) A, B

4FORMAT (1H0, 'SLOPEb -- bAb =', F6.3, 3X 'INTERCEPTb -- b8b =', F7.3/)
C CALCULATE FITTED VALUES OF Y, AND SUM OF SQUARES OF

RESIDUALS
SSQ = 0.0
DO 200J = 1, N
YC = A * X(J) + B
RES = Y(J) - YC
WRITE (6, 5) X(J), Y(J), YC, RES

5FORMAT (3X 'Xb =', F5.2, 5X /Yb =', F7.2, 5X 'Y(FITTED)b =', F7.2, 5X
* 'RESIDUALb =', F6.3)
200SSQ = SSQ + RES ** 2

WRITE (6, 6) SSQ
6FORMAT (IH0, 'SUM OF SQUARES OF RESIDUALSb =', E10.3)

STOP
END

$DATA
5
1.0 2.35 1.5 5.53 2.0 8.92 2.5 12.15
3.0 15.38
SOLUTION: a b6 536 4 206. , .

Page 16

2- 16


2.45 (a) E(cal/mol), D0 (cm2/s)
(b) ln D vs. 1/T, Slope=-E/R, intercept=ln D0.
(c) Intercept = ln = -3.0151 = 0.05 cm / s2D D0 0 .

Slope = = -3666 K = (3666 K)(1.987 cal / mol K) = 7284 cal / molE R E/


ln D = -3666(1/T) - 3.0151

-14.0

-13.0

-12.0

-11.0

-10.0

2
.0

E
-0

3

2
.1

E
-0

3

2
.2

E
-0

3

2
.3

E
-0

3

2
.4

E
-0

3

2
.5

E
-0

3

2
.6

E
-0

3

2
.7

E
-0

3

2
.8

E
-0

3

2
.9

E
-0

3

3
.0

E
-0

3

1/T

ln
D


(d) Spreadsheet


T D 1/T lnD (1/T)*(lnD) (1/T)**2
347 1.34E-06 2.88E-03 -13.5 -0.03897 8.31E-06

374.2 2.50E-06 2.67E-03 -12.9 -0.03447 7.14E-06
396.2 4.55E-06 2.52E-03 -12.3 -0.03105 6.37E-06
420.7 8.52E-06 2.38E-03 -11.7 -0.02775 5.65E-06
447.7 1.41E-05 2.23E-03 -11.2 -0.02495 4.99E-06
471.2 2.00E-05 2.12E-03 -10.8 -0.02296 4.50E-06


Sx 2.47E-03
Sy -12.1
Syx -3.00E-02
Sxx 6.16E-06
-E/R -3666
ln D0 -3.0151

D0 7284

E 0.05

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