Gate Chemical Engineering Solved Paper 2014

Q.No-1-5 Carry One Mark Each 1.

A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is (A) understanding (B) meaning (C) concentration (D) stability Answer: (A) 2.

Choose the most appropriate word from the options given below to complete the following sentence.

One of his biggest ___ was his ability to forgive. (A) vice Answer: (B )

(B ) virtues

(C) choices

(D) strength

Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences? (A) Rajan has decided to work only in a group. (B) Raj an and Sajan were formed into a group against their wishes. (C) Sajan had decided to give in to Raj an's request to work with him. (D) Rajan had believed that Sajan and he would be working together. Answer: (D) 3.

If y = 5x2 + 3, then the tangent at x = 0, y = 3 (A) passes through x = 0, y = 0 (C) is parallel to the x-axis Answer: (C) 2 dy Exp: y = 5x +3,- = 10x dx

4.

Slope of tan gent = ( :

(B) has a slope of +1 (D) has a slope of -1

l =o. y=J= 1Ox 0 = 0

Slope= 0 => tangent is parallel to x-axis.

5.

A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes? Answer: 1300 to 1300 Exp: Fixed cost= Rs. 50,000 Variable cost = Rs. 800Q Q = daily production in tones For 100 tonnes of production daily, total cost of production = 50,000+800x100 = 130,000 130 000 . per tonne o fdaily pro duction . = • Rs. 1300. So, cost of production 100 www.examrace.com

Q.No-6-10 Carry Two Marks Each

6.

Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK (A) ALRVX (B) EPVZB (C) ITZDF Answer: (D)

(D) OYEIK

Exp:

ALRVX---+only one vowel EPVZB---+only one vowel ITZDF---+only one vowel OYEIK ---+three vowels

7.

Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal's floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisallives three floors above Dilip. Which of the following floor-person combinations is correct? Anuj (A) (B) (C) (D)

6 2 4 2

Bhola 2 6 2 4

Chandan 5 5 6 6

Dilip 1 1 3 1

Eswar 3 3 1 3

Faisal 4 4 5 5

Answer: (B) Exp:

(a) (b) (c) (d) (e)

Anuj: Even numbered floor (2,4,6) Bhola: Even numbered floor (2,4,6) Chandan lives on the floor above that ofFaisal. Dilip: not on 2nd floor. Eswar: does not live immediately above or immediately below Bhola From the options its clear, that only option (B) satisfies condition (e). So, correct Ans is (B).

8.

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral? Answer: 180 to 180 Exp:

Let the angles of quadrilateral are 3x, 4x, 5x, 6x So, 3x+4x+5x+6x = 360 x =20 Smallest angle of quadrilateral = 3x20 = 60° Smallest angle of triangle= 3.x 60° = 40° 3 Largest angle of triangle= 2x40° = 60° Three angles of triangle are 40°, 60°, 80° Largest angle of quadrilateral is 120° Sum (2nd largest angle of triangle + largest angle of quadrilateral) = 60°+120°=180°.

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9.

One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft? (D) 1.25 (A ) 3.0 (B) 2.5 (C) 1.5 Answer: (D) Exp:

Let number of people in country y = 100 So, number of people in country x = 300 Total number of people taller than 6ft in both the countries 1 = 300x-- + 100x__2_ = 5 100 100 5 % of people taller than 6ft in both the countries = - - x1 00 = 1.25%. 400

10.

The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percenWe is the value such that k percent of the data fall below that value) 800

- - Average • ------ 5 percentile -·.:--.------ 95 percentile ' '' ' ' '' '' ' '\

700

. .. .

600

.

500 400

\

300

\

\

200 100 0

\

....... __ Ｍ ＭＭ

Ｍ

'

·..

''

·-

ｾ＠

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

(i) On average, it rains more in July than in December (ii) Every year, the amount of rainfall in August is more than that in January (iii) July rainfall can be estimated with better confidence than February rainfall (iv) In August, there is at least 500 mm of rainfall (B) (i) and (iii) (C) (ii) and (iii) (D) (iii) and (iv) (A) (i) and (ii) Answer: (B) Exp:

In the question the monthly average rainfall chart for 50 years has been given . Let us check the options. (i) On average, it rains more in July than in December ｾ＠ correct. (ii) Every year, the amount of rainfall in August is more than that in January. ｾ ｭ｡ｹ＠ not be correct because average rainfall is given in the question. (iii) July rainfall can be estimated with better confidence than February rainfall. ｾ＠ From chart it is clear the gap between 5 percentile and 95 percentile from average is higher in February than that in ｊｵｬｹ ｾ＠ correct. (iv) In August at least 500 mm rainfall ｾ＠

May not be correct, because its 50 year average.

So correct option (B) (i) and (iii).

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Q.No-1-25 Carry One Mark Each

1.

Gradient of a scalar variable is always (A) a vector (B) a scalar Answer: (A) Exp.

Aa Aa

(C) a dot product

(D) zero

ｾ｡＠

Gradient V=i- + j- + k Cix Cly Clz If f is a scalar point function (If (If ｾＨｉｦ＠ Vf =grad f = i - + j- + k - is a vector. dX dy dZ A

2.

A

For the time domain function, f(t) =

e,which ONE of the following is the Laplace transform

t

of Jf ( t)dt ? 0

( B) _1 4s2

Answer: (D)

Exp.

Wehave L[!f(t)dt]

ｾ＠ 3.

= ｆｾｳＩ＠

2

L[ [ t dt] =

where F(s)

Ｈ ｾ＠

)/3

=

ｾ＠

= L[f(t)]

( ·: L[ e ] =

If f*(x) is the complex conjugate of f(x)

ｾ Ｉ＠

= cos(x) + i

sin(x), then for real a and b,

b

J f *(x)f (x)dx is ALWAYS a

(A) positive Answer: (C)

( B) negative

(C) real

(D) imaginary

f(x)=cos(x)+isin(x)

Exp.

f * ( x) =cos( x) - isin ( x) b

b

J f *( x) .f (x )dx = J ( cosx - isinx )( cos+isinx )dx b

= JLdx = b-aER (·:a, b,E R) ｾ＠

Real for real a & b.

If f(x) is a real and continuous function of x, the Taylor series expansion of f(x) about its minima will NEVER have a term containing (A) first derivative (B) second derivative (C) third derivative (D) any higher derivative www.examrace.com Answer: (A)

4.

Exp.

For a real valued function y = f(x) Taylor series expansion about 'a' 2

x-a ) f (x)=f(a) + (x - a)f '(a)+ f"(a)+ ..... 2! For minima at x = a, f'( a) = 0. (

So, Taylor series expansion of f(x) about 'a' will never contain first derivative term.

5.

From the following list, identify the properties which are equal in both vapour and liquid phases at equilibrium P. Density Temperature R. Chemical potential S. Enthalpy (B) Q and R only (A) P and Q only (C) RandS only (D) P and S only Answer: (B ) Exp. For phase equilibrium Temperature; Tg = T Pressure; p& = P 1

1 }

correct Ans is (B). 1

Chemical potential; l!g = j!

6.

In a closed system, the isentropic expansion of an ideal gas with constant specific heats is represented by

(B)

v (c)

ｬｮ Ｈ ｐＩｾ＠

l / ln(v)

ｰｾ＠

r" v

(D)

ｬｮＨｐＩｾ＠

l""' ln(v)

Answer: (D) Exp. For isentropic expansion, pyr = cons tan t

Taking log on both sides ln P+yln V=O ln P . - - = -y = negative lnV ·: yis positive slope of lnP vs ln Vis negative.

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7.

Match the following :

Group 1

Group 2

(P) ( dG l lan) T.P.n_..,

I. Arrhenius equagtion

(Q) ( ao1 l dni) S,Y,n_..,

II. Reaction equilibrium constant

( Ｍｾｇ (R) expl

Ｐ＠

ｒｾ

｣ｵｯｮＩ＠

.

l

III. Chemical potential

N. Gibbs-Duhem equation

(S) I:(nidJ.-li )T,P = 0

(B) Q-III, R-II, S-N (D) P-Ill, R-N, S-I

(A) Q-III, R-I, S-II (C) P-Ili, R-II, S-N Answer: (C)

8.

In order to achieve the same conversion under identical reaction conditions and feed flow rate for a non-autocatalytic reaction of positive order, the volume of an ideal CSTR is (A) always greater than that of an ideal PFR (B) always smaller than that of an ideal PFR (C) same as that of an ideal PFR (D) smaller than that of an ideal PFR only for first order reaction Answer: (A) Exp.

For CSTR, volume V

= FAoX A - "(A

dX For PFR volume V = FAo __ A

J - "(A

-1

-:-:-:-:-:-:-:-:-:-:-: . ..... :-:-::-:-::-:-:-- :---: ｾＭﾭ -:-:-:-:-:-:-:·. ＭｌＺｾ ＭＺ ＭＺ＠ ------- -- ---

,;ｾ

］ ］ｾｲｴ＠

ｾ＠

PFRvolume

ｾ ］ ｾ＠

CSTR volume

XA

From plot it is clear that volume of ideal CSTR (area) is higher than that of the ideal PFR. 9.

Integral of the time-weighted absolute error (ITAE) is expressed as (A)

flc(2t)Idt 0

(B)

t

0

=

(C)

Jtic( t)ldt 0

Answer: (C)

flc (t)l dt

(D)

t

Jelc( t)ldt

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Exp.

Let number of people in country y = 100 So, number of people in country x = 300 1 Total number of people taller than 6ft in both the countries = 300x- - + 100x_3_ = 5 100 100

5 % of people taller than 6ft in both the countries = - x 100 = 1.25% 400

10.

A unit IMPULSE response of a first order system with time constant 't and steady state gain Kp is given by 1 (A) - -eu" (B) Kre-u ' (C) 'tKre-u ' (D) Kr't

Answer: (D) Exp.

Unit Impulse input x(t) = o(t) So, X(s) = 1

Y(s) K K G(s) = X(s) = 'ts:l =>y(s) = 'ts:t" 1

y( t) =

K -

P

e- t/•.

't

11.

In a completely opaque medium, if 50% of the incident monochromatic radiation is absorbed, then which of the following statements are CORRECT? (P) 50% of the incident radiation is reflected (Q ) 25% of the incident radiation is reflected (R) 25% of the incident radiation is transmitted (S) No incident radiation is transmitted (A) P and S only (B ) Q and R only (C) P and Q only (D) R and S only Answer: (A) Exp.

For a completely opaque system 1: = 0 => S Given ex:

ex:

=

0.5

+1:+y= 1

So, y = 0.5 => P Final Ans is (A) P and S only. 12.

In case of a pressure driven laminar flow of a Newtonian fluid of viscosity (jl) through a horizontal circular pipe, the velocity of the fluid is proportional to (A) 1-.l (B ) l-.lo5 (C) 1-.l-1 (D) 1-.l-o.s

Answer: (C) Exp.

Pressure drop in case laminar flow is LiP 321-!LV =---'--::-L D2 clearly V ex: 1-.l-1. www.examrace.com

13.

Which of the following statements are CORRECT? (P) For a rheopectic fluid, the apparent viscosity increases with time under a constant applied shear stress (Q) For a pseudoplastic fluid, the apparent viscosity decreases with time under a constant applied shear stress (R) For a Bingham plastic, the apparent viscosity increases exponentially with the deformation rate (S) For a dilatant fluid, the apparent viscosity increases with increasing deformation rate (A) P and Q only (B) Q and R only (C) RandS only (D) P and S only Answer: (D) 14.

Assume that an ordinary mercury-in-glass thermometer follows first order dynamics with a time constant of 1Os. It is at a steady state temperature of 0°C. At time t = 0, the thermometer is suddenly immersed in a constant temperature bath at l00°C. The time required (in s) for the thermometer to read 95°C, approximately is (A)60 (B)40 (C)30 (D)20 Answer: (C) Exp.

Given 1: = 1Os For first order system

y( t) =K PA ( 1-

e-t/t )

95 = 100( 1- e-t/t)

ｾ ＮＡ］ＲＹＵ

't

Ｍ Ｓ ｾ＠

t =30sec.

15.

Packed towers are preferred for gas-liquid mass transfer operations with foaming liquids because (A) in packed towers, high liquid to gas ratios are best handled (B) in packed towers, continuous contact of gas and liquid takes place (C) packed towers are packed with random packings (D) in packed towers, the gas is not bubbled through the liquid pool Answer : (D) 16.

A spherical storage vessel is quarter-filled with toluene. The diameter of the vent at the top of the vessel is 1/20th of the diameter of the vessel. Under the steady state condition, the diffusive flux of toluene is maximum at (A) the surface of the liquid (B) the mid-plane of the vessel (C) the vent (D) a distance 20 times the diameter of the vent away from the vent Answer: (C) Exp.

17.

Diffusive flux is maximum at the vent and remains same throughout the vent line at steady state.

In order to produce fine solid particles between 5 and 10 !liD. the appropriate size reducing equipment is (A) fluid energy mill (B) hammer mill www.examrace.com (C) jaw crusher (D) smooth roll crusher Answer: (A)

Slurries are most conveniently pumped by a (A) syringe pump (B) diaphragm pump (C) vacuum pump (D) gear pump Answer: (B) 18.

Assuming the mass transfer coefficients in the gas and the liquid phases are comparable, the absorption of C02 from reformer gas (C02 +H2) into an aqueous solution of diethanolarnine is controlled by (A) gas phase resistance (B) liquid phase resistance (C) both gas and liquid phase resistances (D) composition of the reformer gas Answer: (A) 19.

Which ONE of the following statements is CORRECT for the surface renewal theory? (A) Mass transfer takes place at steady state (B) Mass transfer takes place at unsteady state (C) Contact time is same for all the liquid elements (D) Mass transfer depends only on the film resistance Answer: (B)

20.

21.

Steam economy of a multiple effect evaporator system is defined as (A) kilogram of steam used per hour (B) kilogram of steam consumed in all the effects for each kilogram of steam fed (C) kilogram of steam used in all the effects for each kilogram of water vaporized per hour (D) kilogram of water vaporized from all the effects for each kilogram of steam fed to the first effect Answer: (D)

Decomposition efficiency (llD) of an electrolytic cell used for producing NaOH is defined as (A) 11 D = (grams of NaOH produced I grams of NaCl decomposed) x 100 (B) ilD= (grams of NaOH produced I grams of NaCl charged) x 100 (C) ilD= (gram equivalents ofNaOH produced/ gram equivalents of NaCl charged) x 100 (D) ilD= (theoretical current to produce one gram equivalent I actual current to produce one gram equivalent) x 100 Answer: (C)

22.

23.

The vessel dispersion number for an ideal CSTR is (A) -1

(B) 0

(C) 1

(D)

oo

Answer: (D) . . number = - D D1spers10n Exp.

UL

For an ideal CSTR, _.!2._ ---7 oo.

UL

24.

Catalytic cracking is (A) a hydrogen addition process (C) an exothermic process Answer: (B)

(B) a carbon rejection process (D) a coking process

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25.

Which ONE of the following statements is CORRECT? (A) The major components ofbiodiesel are triglycerides (B) Biodiesel is essentially a mixture of ethyl esters (C) Biodiesel is highly aromatic (D) Biodiesel has a very low aniline point Answer: (B) Q.No-26-55 Carry Two Marks Each

26.

Consider the following differential equation :

= x + ln (y) ; y = 2 at x = 0

The solution of this equation at x = 0.4 using Euler method with a step size of h= 0.2 is Answer: 2.3 to 2.4 Exp.

dy - =x + f ny dx dy = f(x,y) => f(x,y) = x + fny dx

given x 0 = 0, y 0 = 2 We have, Yn+l = yn +h r (xn , Yn) n = 0,1,2 ,3, ...... for x=O Y1 =y 0 +h r (X 0 , Yo) h = 0.2, y1 = y(x 1 )= y(x 0 +h) = y(0+0.2) = y(0.2) :. y(0.2) = y 1 =2+ 0.2f(0,2)= 2 + 0.2( 0+ f n 2 )=2+ 0.2( 0.69315)=2 .13863 Y2 = y(x2 ) = y(x1 +h) = y(0.2+0.2) = y(0.4) :. y(0.4) = y2 = y1 +hr( xl> y1 ) = 2.13863+0.2f(0.2,2. 13863) = 2 .13863 + 0.2[ 0.2 + 1h( 2.13863)

J

= 2.13863 +0.2 ( 0.2 +0.76016) = 2.33066 27.

The integrating factor for the differential equation dy- - y = (1+x) IS . dx 1+x 1 (A) - (B) (1+x) (C) x(1+x) 1+x Answer: (A) Exp.

X

(D ) 1+x

Given differential equation dy - _ Y_ = 1+ x dx 1+x dy -1 - +Py = Q => P=dx 1+ x I.F = eJpdx

］ ･ｌ Ｚｾ＠ ｣ｾｸ＠

=e-Iog(Jn) =

1 1+x

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2

28.

The differential equation d ; + x 2 dy + x 3 y =ex is a dx dx

(A) non-linear differential equation of first degree (B) linear differential equation of first degree (C) linear differential equation of second degree (D) non-linear differential equation of second degree Answer: (B) Exp.

Given equation d2 d ____r+ x 2___r + x 3y =ex 2 dx dx

This is clearly a linear differential equation Order= 2 Degree = 1. 29.

Consider the following two normal distributions f1 (x) = exp( -1tx2 )

1 1 2 f2 (x) = - exp{- -( x + 2x + 1)} 21t 41t

If ll and cr denote the mean and standard deviation, respectively, then (A) ll1 < ll2 and cr; < cr;

(B) ll1 < ll2 and cr; > cr;

(C) 1-LJ > j.12 and cr; < cr; Answer: (C)

(D) j.11 > Jl2 and cr; > cr;

Exp.

=e

- :'t:x?

2

Comparing with, f ( x )= ｾ

ｉｬ ｬ＠ =0 &

f2 ( X )

= -1

21t

(jl

ｾ＠

= 1

1ｾ＠ e _.!_(X2 __ ll ) crv2n cr

1

v 2n

- (x e 4"

2

= -1

+2x +l )

21t

ｾ＠

Comparing with , f ( x) =

_...!_(x+l / 4x

e

1

(X-l'r

e2 ---;;-

crv21t

ｾ＠

ll2 = -

ｾ＠

Jl1 > ll2 & cr; < cr; ｾ

1&

(j2

=

.J21t ＨｃＩ＠

30.

In rolling of two fair dice, the outcome of an experiment is considered to be the sum of the numbers appearing on the dice. The probability is highest for the outcome of ______ Answer: 6.99 to 7.01 Exp. X

2

3

4

5

6

7

8

9

10

11 12 www.examrace.com

P(x)

1 36

2 3 4 5 6 5 4 3 2 36 36 36 36 36 36 36 36 36 Where X is a random variable denotes the sum of the numbers appearing on the dice.

-

1 36

-

P ( x) = corresponding probabilities :. The probability is highest for the outcome "7" i.e.,

£

36

A spherical ball of benzoic acid (diameter = 1. 5 em) is submerged in a pool of still water. The solubility and diffusivity of benzoic acid in water are 0.03 kmol/m' and 1.25 x 10·9 m2/s respectively. Sherwood number is given as Sh = 2.0 + 0.6 Re0·5 Sc033 . The initial rate of dissolution (in kmolls) of benzoic acid approximately is (A) 3.54 x10-11 (B ) 3.54 x 10-12 (C) 3.54 x l0-13 (D) 3.54x10-14 Answer: (B ) 31.

ｦｵｾ＠

ｓｨ

］ ＲＫｑＶｒ

ｾ

ｓｾ

ｾ＠

Diameter = 1.5 em Solubility = 0.03 k mol/m3 Diffusivity = 1.25x10-9 m 2/s Given Sh = 2 + 0.6( Re

t.s (Sct

3

Initially Sh - 2 Ked= 2, Kc =Mass transfer coefficient ( rnjs) D AB 9

K = 2x1.25x10- = 167 10_7 => c 1.5x1o-2 . x

m/

sec

Initial rate of dissolution= KcA( C, - 0) = KcAC, = 1.67 x1 0-7 X 7tX (1 .5x1 0-2)2X 0.03 = 3.54x 1 0-12 kmolfsec

32.

A wet solid of 100 kg is dried from a moisture content of 40wt% to 10wt%. The critical moisture content is 15wt% and the equilibrium moisture content is negligible. All moisture contents are on dry basis. The falling rate is considered to be linear. It takes 5 hours to dry the material in the constant rate period. The duration (in hours) of the falling rate period is

Answer: 1.1 to 1.3 Exp. Given X 1 = 0.4 x2= 0.10 Xc = 0.15 X* = O

Constant rate period www.examrace.com

s

s

5

5 = -(X - X )=> - = - = 20 ANC 1 c ANC 0.25 Falling rate period, N = m(X -X *) =

(X - X;) XC- X*

dX

t = - JS f

ｾ ｣＠

Xc A [

Nc XC- X*

=S(Xc -X*) nxc - X * 1 ) {X - X*) ANc X2- X*

0.15 tr = 20x0.15ln = 1.216 hr. 0.10 1

1

A brick wall of 20 em thickness bas thermal conductivity of 0. 7 W m- K • An insulation of thermal conductivity 0.2 W m-1 K-1 is to be applied on one side of the wall, so that the heat transfer through the wall is reduced by 75%. The same temperature difference is maintained across the wall before and after applying the insulation. The required thickness (in em) of the insulation is ______ Answer: 17.0to 17.3 ....---... Insulation k 2 = 0.2 W/rnk Exp. Before insulation heat flux 33.

Q = - k A dT : = - k A .llT 1 1 dx1 1 0.2 After applying insulation heat transfer decreases by 75%

Q2 = L1x

.llT L1x

_1+ __ 2

k 1A

k 2A

Taking A = 1m2 .llT .llT Q2 = 0.25 Q1 = 0.25 0.2 = 0.2 L1x.2 0.7

-

0.7

+-

0.2

0.8 0.2 L1x.2 => - = - + - 0.7 0.7 0.2 06 => L1x 2 = · x0.2 = 0 .1 7 14 m=l 7 .1 4 em. 0.7

..I

20cm k 1 =0.7W/mk

34.

An oil with a flow rate of 1000 kglh is to be cooled using water in a double-pipe counter-flow heat exchanger from a temperature of 70°C to 40°C. Water enters the exchanger at 25°C and leaves at 40°C. The specific heats of oil and water are 2 kJ kg-1 K 1 and 4.2 kJ kg-1 K 1, 2 1 respectively. The overall heat transfer coefficient is 0.2 kW m- K . The minimum heat exchanger area (in m2 ) required for this operation is _ _ _ _ __ Answer: 3.75 to 3.95

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Exp. Given Cro = 2 kJ kg -JK- 1 U = 0.2 kW m-2 K - 1

1000 Heat transfer Q = - -x2x(70° - 40°) = 16.67 kJ 3600

40°C

Q = UA(LMTD) A=

35.

16.67 0.2x21.64

3.85m2.

Which ONE of the following is CORRECT for an ideal gas in a closed system? (A) ( au) V=nR(au )

av

as

s

(B) - ( aH ) P=nR ( aH) s p

aP

v

(C) ( au) V=nR(aH)

av

as

s

as

(D) ( aH) P=nR ( au)

aP

p

s

as

v

Answer: (D) Exp.

(A)

(ｾＺ＠ J

v- nR (

ｾ＠

l

Fundamental property relation dU =Tds - Pdv

J

J

::::? ( au = - P and ( au = T av s as v - PV = nRT ::::? Incorrect

(B)

- ( aH ) P = nR ( aH)

aP ,

as

p

Fundamental property relation dH = Tds+ Vdp ( aH ) = Vand ( aH ) p = T

aP ,

as

- PV = nRT ::::? incorrect (C)

- PV = nR T ::::? incorrect

(D)

PV = nRT ::::? correct. www.examrace.com

36.

A binary distillation column is operating with a mixed feed containing 20 mol% vapour. If the feed quality is changed to 80 mol% vapour, the change in the slope of the q-line is

Answer: 3.6 to 3.9 Exp. Feed contains 20% vapour, so q = 0.8 Slope of q

ｬｩ ｮ･ ］Ｍ

ｱ Ｍ］

ｾ

q - 1 - 0.2

］ ＭＴ＠

Now feed contains 80% vapour, q = 0.2 q 02 -1 Slope = - - = -·- = q -1 -0.8 4

Change in slope = _ .!_ + 4 = 3 .75. 4

A homogeneous reaction ( R -? P) occurs in a batch reactor. The conversion of the reactant R is 67% after 10 minutes and 80% after 20 minutes. The rate equation for this reaction is (A)-rR=k (B)-rR=kCi (C)-rR=kCi ＨｄＩＭｲｒ］ｫｃ ｾ Answer: (B) 37.

Ｕ＠

Exp.

For an ideal batch reactor A =

c CA d c J__ = J__ ken

CA d

A

CAo

for reaction R -? P;

Y

A

CAo

A

XA = 0.67, t = 10 minutes

XA= 0.80 t = 20 minutes 10 = ｣

ｾ＠

20 =

｣ Ｚｾ＠

[ 0.331-n - 1] _ (1) 1- n k

[ o.i-n - 1] __ (2) 1-n

Dividing equation (1) by equation (2) 1 0.331-n - 1 =--:----

2 O.i-n - 1 Solving we get n = 2 So, - yR =k Ci .

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38.

A vapour phase catalytic reaction ( Q + R ｾ＠ S) follows Rideal mechanism (RandS are not adsorbed). Initially, the mixture contains only the reactants in equimolar ratio. The surface reaction step is rate controlling. With constants a and b, the initial rate of reaction (-r0 ) in terms of total pressure (PT) is given by 2 aPT (A) -r.0 = aPT (B) -r0 - aPT (D) (C) -r0 =-....__ - 1 + bP_J 1 + bPT 1 + bPT ｡ｐｾ＠

Answer: (C) Exp.

Ricteal mechanism A (g)+ s (

K, K-1

A - S+ B (g)< ａｂ

Ｍ

ｓ ｾ

)

A-

Kz K _z

s

> AB -

S

(rate controlling)

ａｂ＠

Heres = adsorption site on catalyst surface

and for rate controlling step -y =

K2 (A - s )(B) - K_2 ( AB - S) __ (II)

Also, total number of sites is ST ST = (S) + (A - S) + (AB - S) _

(III)

Initially surface coverage of AB will be very low, so ( AB - S) = 0

F

rom

(I)

,

K1 -

(A - S) (A) ( ST - (A - S))

=> K1 (A)ST- K1 (A - S) (A) = (A - S) => (A - S) = K1 ( A)ST 1+ K1 (A) Now, for rate controlling step, - y = K2 (A - S)(B ) - K_2 (AB - S) Initial rate mean concentration of ( AB - S) ｾ＠

0

So, - Yo= K 2 (A - S)( B)

K2 K1 (A)(B )ST - Yo =

1 + Kl (A)

For the given reaction -y 0 -

ｑＫｒｾｓ＠

a p_; K2 K 2 PT.PT ---'-1+K 1PT - 1+ bPT

with reactants in equimolar ratio

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39.

A incompressible fluid is flowing through a contraction section of length L and has a 1-D (x 2 direction) steady state velocity distribution, u = u0 ( 1 + : ) . If u 0 =2m/ s and L = 3m, the

convective acceleration (in m/s2 ) of the fluid at Lis ____ Answer: 7.99 to 8.01 Exp.

_ -U 0

( 1+2x ) 2u 0

L

Putting u 0

L

=2, L =3

=0 t.=O

*

Convective acceleratio

= du + u

dt

dx

+ .....

at x = L, convective acceleration = 2 ( 1+ 40.

t)(ｾ

2

Ｒ

Ｉ＠

= 8 rnfs2 .

Match the following:

Group 1 (P) Tank in series model (Q) Liquid-liquid extraction (R) Optimum temperature progression (S) Thiele modulus (A) P-II, Q-IV, R-I, S-Ill (C) P-Ill, Q-I, R-II, S-IV Answer: (D) Exp.

Ｒ

Group 2 (I) Non-isothermal reaction (II) Mixer-settler (III) PFR with axial mixing (IV) Solid catalyzed reaction (B) P-I, Q-II, R-Ill, S-IV (D) P-Ill, Q-II, R-I, S-IV

Tank in series model ---? PFR with axial mixing Liquid-liquid extraction ---? Mixer settler Optimum temperature progression ---? Non-isothermal reaction Thiele modulus ---? Solid catalyst reaction.

41.

Two elemental gases (A and B) are reacting to form a liquid (C) in a steady state process as per the reaction. A+ B---? C. The single-pass conversion of the reaction is only 20% and hence recycle is used. The product is separated completely in pure form. The fresh feed has 49 mol% of A and Beach along with 2 mol% impurities. The maximum allowable impurities in the recycle stream is 20 mol%. The amount of purge stream (in moles) per 100 moles of the fresh feed is ______ Answer: 9.99 tolO.Ol Exp. Feed t---.-------.c (product) A+B

--·· c

100%

(R + P), z= 20% ｾＭＮｰｵｲｧ･

Z=20o/o Ｌ ｐ Ｌ ｺ］ＲＰＥ＠

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Basis = 100 moles of fresh feed A = 49 moles; B = 49 moles; Inert, z = 2 moles Overall balance on inert 2 = Px0.2=> P = 10 42.

Carbon monoxide (CO) is burnt in presence of 200% excess pure oxygen and the flame temperature achieved is 2298 K. The inlet streams are at 25 °C. The standard heat of formation (at 25 °C) of CO and C02 are -llOkJ mor 1 and -390kJ mor \ respectively. The heat capacities (in J mor 1 K- 1) of the components are cp =25 + 14 x 1o-3 T 0,

c Pco.

= 25+ 42x10-3 T

where, T is the temperature in K. The heat loss (in kJ) per mole of CO burnt is_______ Answer: 32.0 to 38.0 Exp.

1 CO + - 0 2 -----? C02 2 Basis: 1 mole of CO burnt 0 2 supplied= 0.5x3 = 1.5 mole Unreacted 0 2 in product = 1 mole Standard heat of reaction = - 390 - ( -11 0) = - 280 kJ!rnol. Heat of reactants= 0 (at 298k) 2298

Heatofproduct =

J{(25+14xl0- T)+ (25 + 42 xl0- T)}dT 3

3

298

= 86.344 + 159.032 = 245.376 kJjmole Heat loss= 280- 245.376 = 34.624 kJ 43.

A cash flow of Rs. 12,000 per year is received at the end of each year (uniform periodic payment) for 7 consecutive years. The rate of interest is 9% per year compounded annually. The present worth (in Rs.) of such cash flow at time zero is ____ _ Answer: 60000 to 61 000 Exp.

1 1 Present worth P=R [ ( + i r - ] i (1+iY P=12000 [

(1.09f -

1 7

] = 60395.43

0.09x(1.09) 44.

A polymer plant with a production capacity of 10,000 tons per year has an overall yield of 70%, on mass basis (kg of product per kg of raw material). The raw material costs Rs. 50,000 per ton. A process modification is proposed to increase the overall yield to 75% with an with investment of Rs. 12.5 crore. In how many years can the invested amount be recovered www.examrace.com the additional profit? _ _ _ __

Answer: 2.55 to 2 .70 Exp. Let number of years= n Total product= 10,000 n 10,000 ;__n Raw maten.al used =____; 0.7 . 10,000 n Total cost of Raw matenal= x 50,000 0.7 from question 50,000xl0, 000n 50,000x10,000n = . x 107 12 5 0.75 0.7 Solving, n = 2.625 years.

45.

A step change of magnitude 2 is introduced into a system having the following transfer function: 2 G ( s) = -:: s 2,-+-2_s_ +_4

The percent overshoot is _ _ _ _ _ _ _ __ Answer: 16.0 to 16.8 Exp.

G(s)-

2 _ 0.5 - s 2 +2s+4- 0.25s2 +0.5s+1

Comparing with G ( s) = 't 2 = 0.25

K P

2 2

't s + 2p'ts + 1

and 2p't = 0.5

't =0.5 overshoot = exp(

ｾ

p=0.5

1- p

2

Ｉ＠

= exp(

05 ;1tX · ) = 0.1630 1- 0.25

% overshoot = 16.3%.

46.

Given below is a simplified block diagram of a feedforward control system.

D(s)

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5 The transfer function of the process is G P = - - and the disturbance transfer function is s+1 1 . The transfer function of the PERFECT feed forward controller, Gt(s) is Gd = 2 s +2s + 1

-5

-5

(A) (s+ 1r

-1

(B ) (s+ 1)

(C) 5(s + 1)

(D) -5 (s + 1)

Answer: (C) Exp.

D(s)

Y((s)) = Gr(s)xG (s) +Gd(s)

D s

P

For perfect feed forward controller, no effect of load disturbances. => Gr(s)xGP (s) + Gd (s) = 0 => G r ( s) = - G d ( s) = -1 GP(s) (s + 1l-_ 5_ s+1

-1

5( s+ 1)

+

} - - - - + Y(s) +

The bottom face of a horizontal slab of thickness 6 mm is maintained at 300°C. The top face is exposed to a flowing gas at 30°C. The thermal conductivity of the slab is 105 W m 1 K 1 and the convective heat transfer coefficient is 30 W m-2 K 10 At steady state, the temperature (in 0 C) of the top face is _____ 0 T= =30°C Answer: 268 to 274 Expo

47 0

ｾＭｋ｟］ＱＮＵｷ＠

ｭ｟Ｍ ｾ ｟ｋＭ ｾ ｾｉｲｮｭ＠

__

At steady state heat flux due to conduction = heat flux due to convection => - kA

( 573 - T) ' = hA(T. - 303) 6x10- 3 s

=> 105( 573 - T,) = 6x 10- 3 x30(T, - 303) 85905 - 105T, = 0018 ｾ＠

- 54 054

T, = 544007 K = 271.07°C. www.examrace.com

48.

In a steady incompressible flow, the velocity distribution is given by V = 3xl- PyJ + 5zk, where, Vis in m/s and x, y, and z are in m. In order to satisfy the mass conservation, the value of the constantP (in s-1) is _ _ _ __ Answer: 7.99 to 8.01 A

Exp.

A ｾ＠

Given V = 3xi- Py j + 5zk For mass conservation at constant density t:J..V = O :::::> avx + avy + avz = 0 ax ay a z :::::> 3- p + 5 = 0 :::::> p = 8.

49.

M ateh the ｾ＠ o11owmg

Group II

Group I

(I) Reciprocating pump (II) Packed bed (III) Fluctuating velocity (IV) Impeller (V) Vena contracta (B) Q-V, R-II, S -Ill (D) Q-III, S-V, T-IV

(P) Turbulence (Q) NPSH (R) Ergun equation (S) Rotameter (T) Power number (A) P-Ili, R-II, T-IV (C) P-Ili, R-IV, T-Il Answer: (A) Exp.

Turbulence: Characterized by flu ctuating velocity. Ergun equation: for calculating pressure drop in packed bed. Power number: For calculating power consumption in mixing tank. 3

50.

In a steady and incompressible flow of a fluid (density = 1.25 kg m - ), the difference between stagnation and static pressures at the same location in the flow is 30 rnrn of mercury (density= 13600 kg m-3) . Considering gravitational acceleration as 10m s-2, the fluid speed (in m s-1) is Answer: 79 to 82 Exp.

Bernoulli's equation

P, v' p l Prg +2g = pfg + O:::::> v =

(P-P,) Pr 3

Given P - P, = pgh = 13600x 10x 30x 10- = 3264 Pr Pr 1.25 v = .J2x 3264 = 80.8 rnjsec .

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51.

Consider a binary liquid mixture at equilibrium with its vapour at 25°C. Antoine equation for this system is given as log10 p;•t ］ａＭｾ＠

t+C

where tis in °C and pin

Torr. The Antoine constants (A, B, and C) for the system are given in the following table. Component

A

B

c

1

7.0

1210

230

2

6.5

1206

223

The vapour phase is assumed to be ideal and the activity coefficients {'Yi) for the non-ideal liquid phase are given by ln(y1 ) = x; [2-0.6x1 ] ln {')' 2 ) = x; [1.7 + 0.6x 2 ] If the mole fraction of component 1 in liquid phase (x1) is 0.11, then the mole fraction of component 1 in vapour phase (y,) is _____ Answer: 0.65 to 0.75 Exp.

B

log P'"1 = A - - 10 1 t +c For component 1, lo

g iO

P'"1 = 7I

1210 = 2.2549 25 +230

1

Pt" =179 .846Torr and ln ( y1 ) = x; (2- 0.6x1 ) put X1 = 0. 11 ')'1

= exp [ 0.89 ( 2- 0.6x 0.1 1) Jｾ＠ 2

')'

1

= 4.627

1206 =1.637 25 + 223 p;•t = 43.36Torr andln( yJ = x; (1.7 + 0.6x 2 )

Forcomponent2, log10 P;"1 =6. 5 -

')'2

= exp[ 0.112 (1.7 + 0.6x0.11)

ｾ＠

1'2 = 1.021598

J

Frommodified Raoult 'slaw, y1P=x1y1 Pt X ')' psat ｾ ｹ＠ = Il l I X 'II psat + X 'II psat Ill I 2 12 2

and y 2 P=x 2y2 P;•t

O.l l x 4.627x179.846 1 - O. l lx4.627x179.846+ 0.89x1.021598x43.36 ｬ＠ = 0.699.

ｾ＠

y ----------------ｾ

ｹ

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A process with transfer function, G P = _3__ is to be controlled by a feedback proportional s-1 controller with a gain Kc. If the transfer functions of all other elements in the control loop are unity, then which ONE of the following conditions produces a stable closed loop response? (A) Kc = 0.25 (B ) 0 < Kc < 0.25 (D) Kc > 0.5 (C) 0.25 < Kc < 0.5 Answer: (D) 52.

Exp.

k cGp G ( s) =------'-1 + kcGp

characteristic equation 1 + kcG P = 0 2 1+kc.- = (s-1)+2kc = 0 s- 1 S+ ( 2kc - 1) = 0

for stable closed loop response 2kc -1 > 0 => k c >0.5 => (D).

Consider the following block diagram for a closed-loop feedback control system D(s)

53.

! -2 s

Gd = -

R(s)

A proportional controller is being used with Kc = -4. If a step change in disturbance of magnitude 2 affects the system, then the value of the offset is ______ Answer: 0.49 to 0.51 C(s)

Exp.

- 2/ s

D(s) = 1+ 2kc.o.5(

- 2/ s

ｾＲ Ｉ＠

-2

= 1-

2:c

s-->0

Ｈ＠ S

2 D(s) = s

ｯｦｳ･ｴ

］ ｏＭｬｩｭｳｃＨＩ

s-->0

］ ＭｬｩｭｳＮｾ

2 ) = .i = 0.50. S- 2kc 8

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54.

Determine the correctness or otherwise of the following Assertion [a] and Reason [r]. Assertion: Significant combustion of coke takes place only if it is heated at higher temperature in presence of air. Reason: C+ 0 2 --7 C0 2 is an exothermic reaction. (A) Both [a] and [r] are true and [r] is the correct reason for [a] (B) Both [a] and [r] are true but [r] is not the correct reason for [a] (C) [a] is correct but [r] is false (D) Both [a] and [r] are false Answer: (B) Exp.

Both [a] and [r] are true but [r] is not the correct reason for [a].

55.

Match the raw materials of Groups 1 and 2 with the final products of Group 3 Group 1 P 1: Ethylene P2 : Propylene P3 : Adipic acid P 4 : Terephthalic acid

ＨａＩｾＫ＠

Group 2 Q1: Ammonia Qz: 1-Butene Q3: Ethylene glycol Q 4: Hexamethylene diarnine

Group 3

R( Synthetic fibre Rz: Nylon 66 R3: LLDPE R 4 : Acrylonitrile

Q2 --7 R3; P2 + Ql --7 R 4;P3 +Q4 --7 R 2; P4 +Q3 --7 Rl

Ｈ ｂＩｾ

Ｋ＠ Ql --7 R3; P2 + Q3 --7 R 4; P3 + Q4 --7 R 4; P4 + Q2 --7 R2

(c) PI +Q2 --7 R 2; P2 + Q3 --7 R1 ; P3 + Q4 --7 R3; P4 +Ql --7 R 4 Ｈ ｄ Ｉ ｾ＠ +Ql --7 R4; P2 + Q2 --7 R3;P3 +Q4 --7 R 2;P4 +Q3 --7 Rl Answer: (D) Exp. Raw material Product Ethylene + 1- Butene

LLDPE (linear low density PE)

Propylene+ Ammonia

Aerylonetrile

Adipic Acid+ Hexomethylene diarnine

Nylon -66

Terephthalic acid + Ethylene glycol

Synthetic fibre

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