GATE Chemical Engineering 2000

8/10/2019 GATE Chemical Engineering 2000

1/8

ww

w.exa

mrace

.com

IGATE - 20011

CHEMIC L ENGINEERING

SEcnONA

ONE M RKS

QUESTION8

2 i

for

M(h

of the

fol.lowing questions

(I

to 29)

four allemativts A,

ll , C >md

Dare

pro

vi

ded.

lttdicate the con u t answe.oby

writing A,

B,

C

or D,

as

-uppoopo

iule

,

against

the too

-r

esponding

question

number in the

box

in the

answer

book.

(

Ma

ks: I

x.

29 = 19)

1\

pa

or

oil';11

dice

is

roll

ed

Simul tan

eously

1lte pro

ba

bllity that the sum of lhe

n

um

bers from dice equals ~ l x is

a

b

c.

d

I

6

7

36

5

36

1

12

2. For an e1en fu

nct

ion

a f (x)dx'= ll

'

b.

J(( x)d

=I

'

c.

J .+ =-J- x)

d j (x) =

f -

x)

3

l'he

lmegraung facror for d1e

differential

equation. (ces' ~ ) e l y -t J' = tan x. IS

dx

a.

l l l l l

b.

cos2

.1:

c>

'

d

s' 2x

In n binary liquid so lution of

cornponeniS

A

and

B. of

co

mponent-A etme thai benzene is insoluble in wa ter

1lte normal

boi

ling points

of

bcmcue

aJJd

~ > a t e r

arc

80.1c and 1ooc. resuecti1

el

y

AI a pressure of 1-atm, dtc boiling point of

a of e n z ~ n c and wntor is

a c

b

le

ss lhan su.1c

c. wo

c

d,

greater ihml

80 tc

but less t

han

t

c

On

a P -

V diagram

of nn

i

dea

l

~ ; n s

suppose a rc1

ers

i

bl

e adiabatic line

uner,;ects

a reversible

tsot

herm


2/8

ww

w.exa

mrace

.com

().

11

.

13.

14

.

In

o lull) lurbulenl flo11 (Rt: 10

3

1 in n

pipe

of cJiamcl

er for a c

ons

tam pressun.

grndicnL Ulc i l u n < ~ lay

.W

now

lh l

plate, the

t

l1 t

() (i

)t) vorics

3$;

J ,

R""

b JRc

where ,; the boandniJ' layer tht10knes

and x is Ute distance fronl the leading edge

in

the

dirc:ctlu

n.of 11ow.

Por laminnr

flow

of

nshcnr-lbfnning liquid

in a pipe. if lhe volumetric

ilo rnte

doubled. the pressure gradient

will

in.,.e.sc

by Q

fcto.r or

a.

b. < 2

c. > 2

d. 112

The Gtushof number i l defined as che r.c io

I)

I

:c buO)'OI\ey IH inertial rurcc:s,

h.

buo

ynt\O) lu v

i>Wu

l i n ' C c

c:

.. lneni:.ltd

on

tile cryshtl size.

'

lbc 'P timc

nllllly dctenninod ovemll

or

der tO

r

t1Ha

re:u

tio

n A

~

B

_.

C t- D l ;

lwo.11en the

a.

rca


3/8

ww

w.exa

mrace

.com

1

J4

.

25.

E

80 JIMOl

r

1

c q C, : F.t 110

k.J ,o

tho dcslf\.-d

pt1JJucl

R A high"r

:>declivity or

R

will be l1Cn

1

CVL':

tn

a CSTR

b lugh temperature m a

CS

'

J'R

c. lo11 lcmp\lratu

rc

In a

PFR.

d.

higb

temperature

m nPJ7R

ln

solid cawtysed

reac.lt

W1S

tlte dtl'Fusm

nal

e J T ~ c t s nre

more

llkelv 10 affect

the O\'emll

mtc of reacuoo l'or

IL fast reactions '" catolysL of

smal

l f'lWC

dia meter

b fnsl reDctitlns 111 t ~ l y s t s . of Drg pore

d i a m e t ~

c.

T i l ~

llllltJl i

tude

raliu ui a pme cnpac

i

l)

'

proc:e:

m v ~ 1 ' l ' < l prupurtionu.l

(n the

frcqu"ncy

d llle ump

litude

rnuo of u

~

lim"

del

a) S)

~ t e r n

incrca l< s

11 ith freq u


4/8

ww

w.exa

mrace

.com

3l

35

d rr

rhe nverse

of

the IJlatrJ.,

[I

a. Doe1;

not exist

b LS [

c.

. [

o

5

.s]

IS

--{)

.5 -0.5

d

~

]

5 05

- I

I]

-I

Tbe

complex co n llgale

of' -

1

-

ts

I I

1

a,

1-1

b. (I 1)

e

0.

5(1

- 1)

d. Ul

\lie

Ursl

quadrant

or

compl

ex

plane

lite genera l so

.l

ut1on of

tl

v

d

1

y

- - + +J =O

S

< -

and the pressure drop ac

ro

ss

the

bed

ts I0 kPa, tl1

en

tbe density o.f panicles 1s

L

2.5

74 kg/tn

b. J5 14 kg/m

3

c.

4000

kg/rn

3

d

4350

kgtm'

A

free jei

of

waicr of cross-secuooaJ aren

0.02 m

1

and velocity of 20 m/s stnkes d

plate and

d1en

tlm>JS in plane parallel to

U1e

plate as shown 10 the figure below. 1l1e

hQtizontal cumpqni O\ of the force: on

U1e

suppoti

1s

ll 200

b

-l

OON

c, :woo N

d 40

00

N

A s1ee l sphere of rndtus () I m at 400 K rs

unmersed tn

an oil Qt 39Q K. If the centre


5/8

ww

w.exa

mrace

.com

o

the sphere rcoche

350

K

in

20 n u n ~ l

e s .

how long will

it

take f

or

a 0.05 m rndin

s f

ee

l sphere to teach the sante tempet'oture

(at

Ut

e coult" ) under

identi

ca

l

co

odilioru?

t \ . ~ J o t m e lltat lh,. u.)nv..owc hl llt

tran5fer

cl1ell'icient

iR

in finitely lllrgt.

s. 5 min

h. LO tttin

c. 10Jttlo

d,

40

111 in

41 , A

uompo

5Jte

J'Wt

waU o

fu ona


6/8

ww

w.exa

mrace

.com

Heat eapacities, CI'A

= Cn =

l00

kJ

/

km o1

K (may be assmned to be independent of

tempernture.)

49 'T'he t .)'

I lhe point (1, 2,

3)

I ltirecHon llom

(1 , 2, 3)to l, - l, -3)

5 1. Futd whether or not tht> vcct"rs (1,1,2),

(1

.

2, J) ru1d (0, 3, -3) are linearly

independent

52 [ndnstrial sraie metlumol

ClU1

he

E00UOed

according to tlte reacdon

CO g)+2H

1

g)C

C pR(g)

Fo

r Ui9 fffiction

.c.o

4

uu

= -

U484

kl. 1

-

ru

t equi.toolril .

mi..'dllJ

e Df 00 llld liz is fed

l > a retc

t.or

rr

ru

rJtlnne4 at..

4

00

. K a11

d 10

bar,

detemune,

tl

te fraction of CO

lhat is

conv.erted

into

CHPH

a1

egui.b'brium.

Ao."Uln

e

il tat

ilte

reactio11

mixture .behaves

like 9:11 ideal gas.

53 .

b

a binruy mixture the aotiVll;y coefficienl

rt

of compon011t I, in the cutirc range of

ro

nrpo>11ion,

is

g1 ven by

.R

ln

r

1

=lr]+

&;

wltere R. A 1llld B are constants. Denve

lhe e . > , p . r e s ~ o n for

Ute

activity coefficient

ofCOJtlponenl

2.

54 A

Jt

ydrocarbou oil (visce>slly 0.025 Pa s

and density 900 leline, i t

. r e q u i r e d ~ use a Q4 m

diam

eter, 10 km

55

1.) ors

long prpo

to

pump

ihe

oil

at tl

tc same.

volnmeiric .flow rate as

in

Ute prev

tous

case. Estintatethc pressutEf drop f01 llte O

. i

m

di

amet

er

pipe.

Asawne

hotiJ

pipejt to be

ltydtodynmnicaJJy smoofll and in tlte range

of opet'iding eonffirians ,

l.he

Fanning

Diction factor is i v e n ~

/ =

Q.079Re-OJ'

A rree

Jet

ofwater ls produ ced usi ng a 75

mm

diarr

tet,er u,

1ZZJe

ui.mehed to

>L

200 fllm

diameter pipe, m; -.b.owu .in the .figure.. f

the

average vclooi ty of'water

at

plane B is

3.8 mJ., calculate tlw velocity f w ~ at

point A

i.it

tlte fr

oo

jet Neglect friction

l.:,gses in llte

1lll:(21E' and

pipe

T

Obtain

the eqnalion

1pr

fltc.

qclinc givc11

th

aL

lhe.

OJ

Jt'f>l

l:htg

limsare.

/. D ., , . cfi

y -

.lllJTm

ls used

to

extract

a solute from rutaqtteous

stream (F t Sing an o.q;anic .


7/8

ww

w.exa

mrace

.com

7,

58.

59,

1\ir at

1 n is

blown past

the bulb

of a

mercuty m

o m ~

111e

bu

tb is

covered

with a wick. l11e wick is Immersed

in rut

orgamc liqwd (molecular wcight

=

58).

'The reading of tho them10meter is 7.6 "

C.

At Otis temperature,

the

vapour pressureof

01e

liqul

d

c 5

k

Pa

.

fi

ud

Oc air

t.emperttture;

given tha

t

t

he

r

ah t

of

the

tru.qsfer

c.oet1'icents

to the o>ass ITansfer

coeflicie

nt

(psychromeu

ic

mtio)

ts

2 kJ

lll

K and the latent heat

of

vapourisat

io

n

of

the

liqui

d is 360

kJ

ikg.

Ass

u

me ih

m the

arr,

wh

ich ts

blown

.

is fre

e

fro

m

the

org nic v pour

A piau

1s

designed

to

produ

ce. 1.2

I

k

i lvte of

an a

gro< 10. The followitlf\

oost datn

are

available;

Raw

m

at

cnals:

0. 9/Kg product

Labour and uulino

s.

c.tc.:

Rs

0.27/

iql:

product

prlce u

fpr

odu cf: Rs 10/Kg

O

ilc

r

costs

(O

n pet ycur inc ludin

H,

mamlertance. tnsurace.

etc

,

@W% or

lixed capital.

Indirect

costs of d m i t S U m i o t ~ R&D.

marketing.

c(c

.

@20%

f

sal

e

pnx;

c

eds

.

'n 1e plant wi

ll

be tit

ll

) depreciated ovet u

period

of

5

years us ing the stmlslu line

tueO

od.. l l

te

ra

te

of

t

it

cmue tax is 10%.

C

uku

l

at

a,

rl1e net

pro

it at th

e end

of

firs

t yenr

ll, dte payout period.

l he

r

e;-ponse

of a

tlicnuoeouplc can be

.

mode lled as u

first

order process to

changes

tn

the temperarure

of

the

60

61

.

63

.

7on

environment.

If

such a thcnnocouple

31

25C is

inuuersed s

udden

ly in a

fluid

at

80C

ana

held tht'l'C . it Is fOlDld that

Ot

ec

thcnn lCOup le reading (in C) re:whc

:>

63.

2%of

the final steady sta te value in 41l

seoo11ds. Find the time coostaut of tlte

Olimll()COUille:

A

tcedi,Hk control

loop

wit

h n

propottio

na

l cont

ro ll

er has an open loop

trlU $ler fuuctiou

where rime i$

ill

miuuteS; Obtain

Ute

crussover liequency wtd U e ultinm lc

controlh:r gail).

Given

th

e

(Q II

owing bloc

.

tll lgrnm,

. EA

llllSS the

trnnsii:r Jimcoon (Y/X\ ns

a ratio ur

po

lynoultals in s.

b. Ca lculare tlte

off.o;e

r ' C

du

e io o un

it

~ : h _ a n g e n lhc

rcrcren e Sl

g_n

al

\S

et-point) R.

1'he el

ement

a

ry.

second

-or

der. ltqutd

phase r"nction D is

conducccd

.n

an.

tSI,l

therma1

plug

fl

ow

r e ~ c t o r

or

I m

1

capacity. The inlet ' 'ol ume trfc flllW rate is

10

m' tb and C.-.

1

= C

1

' 2 lunolltu' At

th

ese

c o n d t i o n s con

version o f

is 5 0 ~ - o

Now

. if a stirred tank reactor of 2

rn

3

capacity is installed in series, upstream

of

lhe plug 0Qw reactor,

lb

cu

wilaL

con

version tmu

bt: e

xpec

te

d_

h1 the

nd w

system Qf reactors?

The f o l l o w

~ liqu

id pbnse t


8/8

ww

w.exa

mrace

.com

64,

65.

66.

Each of tlto .

products men

uoned 111 the left

hand column requires one

or

Jnore of the

reactants mel\fio

ned

In the right-hand

column, March

the products

wi1h

the

approprinte r e a c m n t { s ~

(I) Phthalic anhydride

(U

1

Cu111ene

tAl Benzene

( l) N.aphthale}le

(C)

Carbon

monoXIde

(D) Phenol

(E) Propylene

(F) Atr

(G) EtltyJ benzene

(H)

Hydrogen

SyttU,.lSis gas

rs 11 n iurc

of

n.

CO

and H,

b. a n d H,

n II_, and CO

d COt and H,

The ttction A ZB

+

C takes place

ru

.a

caw

l

yt

ic

reuttor

(see

diagnun

be

low), The

reactor effluent

IS

sent to u separator

The

overall conversiOn of A is 95% 11te

product

stream from the separator consists

Qf B. ( and 0.5o/o of A enterrng the

separator, while

rh

e recycle Sll'eam

consistS of lbc rema1nder of the unrcactcd

A aud 1% of B entcriug tlt separaJor.

Calculate he

a, swgle

P8

couvorsooo of A

ill

tl1e

reactor

b molar

ratoo

of

recycle

to

feed

:. I L l _ _ . . . _

-

..

.....,_

lfl

67 "'he 11

1S1de surface

temperature

ofa pipe

(ra

dms = 0. I m) IS 400 K

The

ptpe

ts

los tog hear to atmosphere,

wbJch

IS

at

300

K

The

ftllll .beat transfer CQefficieut

IS 10

68.

>C)

K k

W/m

1

K.. To reduce

tltc ra

te of heat loss,

lbe

pipe is 1nsula t

ed

by a 50mm thick

a y ~

ofnsbestos (k = 0.5

Wlm K)

.

Calculate Ut

percentage reduction m the rnte of heat

loss.

In a 1-1 counter flow she

ll

and tube hear

exchanger, a process stream (Cr = 4.2

kJ kg

K)

is cooloo

limn

450

to

J5(l

us

ing '""ter (

c .

=

4.2 kJ/kg J.:) a1

JOO

K

The

proCes

.stream flows on the she

ll

-side

ar a

rare

of I kg/s and the warer on the

tuhes1de at a,rJte of 5

4;

/s, f heatlmnsfer

coefficients

on

the shel l

nnd rube

s1des are

1000 Wtm K

and

1500 Wtm

K,

respectively, d

Documents

GATE Chemical Engineering 2000