GATE 2023 Question Paper CH Chemical Engineering

The Graduate Aptitude Test in Engineering

GATE 2023
Question Paper
GATE is an entrance examination conducted in India that
primarily tests the comprehensive understanding of
undergraduate subjects in engineering and sciences for
admission into technical postgraduate programs.

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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 “You are delaying the completion of the task. Send _______ contributions at the
earliest.”

(A) you are

(B) your

(C) you’re

(D) yore

Q.2 References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(C) Cite

(D) Plagiarise

Page 1 of 42

Q.3 In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and
PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

7
P S

5 90°
4
90° V
Q T R

(A) 20
7

(B) 28
5

(C) 9
2

(D) 35
4

Page 2 of 42

Q.4 In 2022, June Huh was awarded the Fields medal, which is the highest prize in
Mathematics.

When he was younger, he was also a poet. He did not win any medals in the
International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be
logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(C) All Fields medalists are part-time poets.

(D) Some Fields medalists have dropped out of college.

Page 3 of 42

Q.5 A line of symmetry is defined as a line that divides a figure into two parts in a way
such that each part is a mirror image of the other part about that line.

The given figure consists of 16 unit squares arranged as shown. In addition to the
three black squares, what is the minimum number of squares that must be coloured
black, such that both PQ and MN form lines of symmetry? (The figure is
representative)

P N

M
Q

(A) 3

(B) 4

(C) 5

(D) 6

Page 4 of 42

Q.6 – Q.10 Carry TWO marks Each

Q.6 Human beings are one among many creatures that inhabit an imagined world. In
this imagined world, some creatures are cruel. If in this imagined world, it is given
that the statement “Some human beings are not cruel creatures” is FALSE, then
which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(C) only (i) and (ii)

(D) (i), (ii) and (iii)

Q.7 To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand
and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what
is the cost (in rupees) of cement used?

(A) 400

(B) 600

(C) 800

(D) 200

Page 5 of 42

The World Bank has declared that it does not plan to offer new financing to Sri
Q.8 Lanka, which is battling its worst economic crisis in decades, until the country has
an adequate macroeconomic policy framework in place. In a statement, the World
Bank said Sri Lanka needed to adopt structural reforms that focus on economic
stabilisation and tackle the root causes of its crisis. The latter has starved it of
foreign exchange and led to shortages of food, fuel, and medicines. The bank is
repurposing resources under existing loans to help alleviate shortages of essential
items such as medicine, cooking gas, fertiliser, meals for children, and cash for
vulnerable households.

Based only on the above passage, which one of the following statements can be
inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that
it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how
to tackle the root causes of its economic crisis.

(C) According to the World Bank, Sri Lanka does not yet have an adequate
macroeconomic policy framework.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for
essentials such as food, fuel, and medicines.

Q.9 The coefficient of 𝑥 4 in the polynomial (𝑥 − 1)3 (𝑥 − 2)3 is equal to _______.

(A) 33

(B) ̶ 3

(C) 30

(D) 21

Page 6 of 42

Q.10 Which one of the following shapes can be used to tile (completely cover by
repeating) a flat plane, extending to infinity in all directions, without leaving any
empty spaces in between them? The copies of the shape used to tile are identical
and are not allowed to overlap.

(A) circle

(B) regular octagon

(C) regular pentagon

(D) rhombus

Page 7 of 42

Q.11 – Q.35 Carry ONE mark Each

Q.11 Which one of the following is the CORRECT value of 𝑦, as defined by the
expression given below?

2𝑥
𝑦 = lim 𝑥
𝑥→0 𝑒 − 1

(A) 1

(B) 2

(C) 0

(D) ∞

Q.12 ⃗ is defined as
The vector 𝒗

⃗ = 𝑧𝑥 𝑖̂ + 2𝑥𝑦 𝑗̂ + 3𝑦𝑧 𝑘̂ .
𝒗
⃗ , evaluated
Which one of the following is the CORRECT value of divergence of 𝒗
at the point (𝑥, 𝑦, 𝑧) = (3, 2, 1) ?

(A) 0

(B) 3

(C) 14

(D) 13

Page 8 of 42

Q.13 Given that

|𝑧1 + 𝑧2 |
𝐹= ,
|𝑧1 | + |𝑧2 |
where 𝑧1 = 2 + 3𝑖 and 𝑧2 = −2 + 3𝑖 with 𝑖 = √−1 , which one of the
following options is CORRECT?

(A)
𝐹<0

(B) 𝐹<1

(C) 𝐹>1

(D) 𝐹=1

Page 9 of 42

Q.14 For a two-dimensional plane, the unit vectors, (𝑒̂𝑟 , 𝑒̂𝜃 ) of the polar coordinate
system and (𝑖̂, 𝑗̂) of the cartesian coordinate system, are related by the following two
equations.

𝑒̂𝑟 = cos𝜃 𝑖̂ + sin𝜃 𝑗̂
𝑒̂𝜃 = −sin𝜃 𝑖̂ + cos𝜃 𝑗̂
𝜕(𝑒̂𝑟 +𝑒̂ 𝜃 )
Which one of the following is the CORRECT value of ?
𝜕𝜃

(A) 1

(B) 𝑒̂𝜃

(C) 𝑒̂𝑟 + 𝑒̂𝜃

(D) −𝑒̂𝑟 + 𝑒̂𝜃

Page 10 of 42

Q.15 Which one of the following statements related to octane number is NOT correct?

(A) Linear alkanes with higher carbon number have higher octane number.

(B) Branching in linear alkanes increases their octane number.

(C) Catalytic reforming of hydrocarbons increases their octane number.

(D) Gasoline quality is measured in terms of octane number.

Q.16 Which one of the following options represents the major components of oleum?

(A) Sulfuric acid and nitric acid

(B) Concentrated sulfuric acid and petroleum jelly

(C) Sulfuric acid and hydrochloric acid

(D) Sulfuric acid and sulfur trioxide

Page 11 of 42

Q.17 For a reversible endothermic chemical reaction with constant heat of reaction over
the operating temperature range, 𝐾 is the thermodynamic equilibrium constant.
Which one of the following figures shows the CORRECT dependence of 𝐾 on
temperature 𝑇?

(A)

(B)

(C)

(D)

Page 12 of 42

Q.18 Nitrile rubber is manufactured via polymerization process. Which one of the
following options is the CORRECT pair of monomers used in this process?

(A) Acrylonitrile and styrene

(B) Acrylonitrile and butadiene

(C) Butadiene and styrene

(D) Butadiene and isoprene

Q.19 John and Jane independently performed a thermodynamic experiment, in which X
and Y represent the initial and final thermodynamic states of the system,
respectively. John performed the experiment under reversible conditions, for which
the change in entropy of the system was 𝚫𝑺𝒓𝒆𝒗 . Jane performed the experiment
under irreversible conditions, for which the change in entropy of the system was
𝚫𝑺𝒊𝒓𝒓 . Which one of the following relationships is CORRECT?

(A) 𝚫𝑺𝒓𝒆𝒗 = 𝚫𝑺𝒊𝒓𝒓

(B) 𝚫𝑺𝒓𝒆𝒗 > 𝚫𝑺𝒊𝒓𝒓

(C) 𝚫𝑺𝒓𝒆𝒗 < 𝚫𝑺𝒊𝒓𝒓

(D) 𝚫𝑺𝒓𝒆𝒗 = 𝟐𝚫𝑺𝒊𝒓𝒓

Page 13 of 42

Q.20 For a packed-bed comprising of uniform-sized spherical particles of diameter 𝐷p ,
the pressure drop across the bed is given by the Kozeny-Carman equation when the
particle Reynolds number (Rep ) < 1. Under this condition, minimum fluidization
velocity is proportional to 𝐷𝑝𝑛 . Which one of the following is the CORRECT value
of exponent 𝑛 ?

(A) 2

(B) −1

(C) −2

(D) 1

Page 14 of 42

Q.21 Match the quantities in Group 1 with their units in Group 2 listed in the table below.

Group 1 Group 2

P) Thermal conductivity I) W. m−2 K −1

Q) Convective heat transfer coefficient II) W. m−1 K −1

R) Stefan-Boltzmann constant III) W. K −1

S) Heat capacity rate IV) W. m−2 K −4

(A) P-II, Q-I, R-IV, S-III

(B) P-I, Q-II, R-III, S-IV

(C) P-III, Q-IV, R-II, S-I

(D) P-IV, Q-I, R-III, S-II

Page 15 of 42

Q.22 A slab of thickness 𝐿, as shown in the figure below, has cross-sectional area 𝐴 and
constant thermal conductivity 𝑘. 𝑇1 and 𝑇2 are the temperatures at 𝑥 = 0 and
𝑥 = 𝐿, respectively. Which one of the following options is the CORRECT
expression of the thermal resistance for steady-state one-dimensional heat
conduction?

(A) 𝐿
𝑘𝐴

(B) 𝑘
𝐿𝐴

(C) 𝑘𝐴(𝑇1 −𝑇2 )
𝐿

(D) 𝐴
𝐿𝑘

Page 16 of 42

Q.23 Spray dryers have many advantages. Which one of the following is NOT an
advantage of a typical spray dryer?

(A) Has short drying time

(B) Produces hollow spherical particles

(C) Has high heat efficiency

(D) Is suitable for heat sensitive materials

Q.24 Which one of the following quantities of a flowing fluid is measured using a
rotameter?

(A) Static pressure

(B) Dynamic pressure

(C) Volumetric flow rate

(D) Viscosity

Page 17 of 42

Q.25 A liquid surge tank has 𝐹𝑖𝑛 and 𝐹𝑜𝑢𝑡 as the inlet and outlet flow rates respectively,
as shown in the figure below. 𝐹𝑜𝑢𝑡 is proportional to the square root of the liquid
level ℎ. The cross-sectional area of the tank is 20 cm2 . Density of the liquid is
constant everywhere in the system. At steady state, 𝐹𝑖𝑛 = 𝐹𝑜𝑢𝑡 = 10 cm3 s−1 and
ℎ = 16 cm. The variation of ℎ with 𝐹𝑖𝑛 is approximated as a first order transfer
function. Which one of the following is the CORRECT value of the time constant
(in seconds) of this system?

(A) 20

(B) 32

(C) 64

(D) 128

Page 18 of 42

Q.26 A packed distillation column, with vapor having an average molecular weight of
45 kg. kmol−1, density of 2 kg. m−3 and a molar flow rate of 0.1 kmol. s −1, has a
flooding velocity of 0.15 m. s−1 . The column is designed to operate at 60 % of the
flooding velocity. Which one of the following is the CORRECT value for the
column diameter (in m)?

(A) 5
√𝜋

(B) 5 √𝜋

(C) 4𝜋

(D) 10
√𝜋

Page 19 of 42

Q.27 An isothermal jacketed continous stirred tank reactor (CSTR) operating at 150 o C
is shown in the figure below. The cold feed entering the system at 30 o C is preheated
to a temperature 𝑇 (𝑇 < 150 o C) using a heat exchanger 𝐻𝑋1 . This preheated feed
is further heated to 150 o C using the utility heater 𝐻𝑋2. The mass flow rate and heat
capacity are same for all the process streams, and the overall heat transfer
coefficient is independent of temperature. Which one of the following statements is
the CORRECT action to take if it is desired to increase the value of 𝑇 ?

(A) Increase both heat transfer area of 𝐻𝑋1 and heat duty of 𝐻𝑋2.

(B) Decrease both heat transfer area of 𝐻𝑋1 and heat duty of 𝐻𝑋2 .

(C) Increase the heat transfer area of 𝐻𝑋1 and decrease the heat duty of 𝐻𝑋2.

(D) Decrease the heat transfer area of 𝐻𝑋1 and increase the heat duty of 𝐻𝑋2 .

Page 20 of 42

Q.28 Consider a system where a Carnot engine is operating between a source and a sink.
Which of the following statements about this system is/are NOT correct?

(A) This engine is reversible.

(B) The engine efficiency is independent of the source and sink temperatures.

(C) This engine has the highest efficiency among all engines that operate between the
same source and sink.

(D) The total entropy of this system increases at the completion of each cycle of the
engine.

Q.29 For a fully developed turbulent flow of an incompressible Newtonian fluid through
a pipe of constant diameter, which of the following statements is/are CORRECT?

(A) Reynolds stress, averaged over a sufficiently long time, is zero everywhere inside
the pipe.

(B) Reynolds stress at the pipe wall is zero.

(C) Average velocity of the fluid is half of its center-line velocity.

(D) Average pressure gradient in the flow direction is constant.

Page 21 of 42

Q.30 Given that 𝐸 (in W. m−2 ) is the total hemispherical emissive power of a surface
maintained at a certain temperature, which of the following statements is/are
CORRECT?

(A) 𝐸 does not depend on the direction of the emission.

(B) 𝐸 depends on the viewfactor.

(C) 𝐸 depends on the wavelength of the emission.

(D) 𝐸 does not depend on the frequency of the emission.

Q.31 The position 𝑥(𝑡) of a particle, at constant 𝜔, is described by the equation

𝑑2 𝑥
= −𝜔2 𝑥 .
𝑑𝑡 2
𝑑𝑥
The initial conditions are 𝑥(𝑡 = 0) = 1 and | = 0. The position of the
𝑑𝑡 𝑡=0

particle at 𝑡 = (3 𝜋/𝜔) is __________ (in integer).

Q.32 Burning of methane in a combustor yields carbon monoxide, carbon dioxide, and
water vapor. Methane is fed to the combustor at 100 mol. hr −1 , of which 50 %
reacts. The theoretical oxygen requirement (in mol. hr −1 ) is ________ (rounded off

to one decimal place).

Page 22 of 42

Q.33 The viscosity of an incompressible Newtonian fluid is measured using a capillary
tube of diameter 0.5 mm and length 1.5 m. The fluid flow is laminar, steady and
fully developed. For a flow rate of 1 cm3 s −1 , the pressure drop across the length of
the tube is 1 MPa. If the viscosity of the fluid is 𝒌 × 𝟏𝟎−𝟑 Pa. s, the value of 𝒌 is
___________ (rounded off to two decimal places).

Q.34 A liquid 𝑳 containing a dissolved gas 𝑺 is stripped in a countercurrent operation
using a pure carrier gas 𝑽. The liquid phase inlet and outlet mole fractions of 𝑺 are
0.1 and 0.01, respectively. The equilibrium distribution of 𝑺 between 𝑽 and 𝑳 is
governed by 𝒚𝒆 = 𝒙𝒆 , where 𝒚𝒆 and 𝒙𝒆 are the mole fractions of 𝑺 in 𝑽 and 𝑳,
respectively. The molar feed rate of the carrier gas stream is twice as that of the
liquid stream. Under dilute solution conditions, the minimum number of ideal stages
required is __________ (in integer).

Q.35 In a binary gas-liquid system, 𝑁𝐴,𝐸𝑀𝐷 is the molar flux of a gas 𝐴 for equimolar
counter diffusion with a liquid 𝐵. 𝑁𝐴,𝑈𝑀𝐷 is the molar flux of 𝐴 for steady one-
component diffusion through stagnant 𝐵. Using the mole fraction of 𝐴 in the bulk
of the gas phase as 0.2 and that at the gas-liquid interface as 0.1 for both the modes
of diffusion, the ratio of 𝑁𝐴,𝑈𝑀𝐷 to 𝑁𝐴,𝐸𝑀𝐷 is equal to ______ (rounded off to two
decimal places).

Page 23 of 42

Q.36 – Q.65 Carry TWO marks Each

Q.36 An exhibition was held in a hall on 15 August 2022 between 3 PM and 4 PM during
which any person was allowed to enter only once. Visitors who entered before
3:40 PM exited the hall exactly after 20 minutes from their time of entry. Visitors
who entered at or after 3:40 PM, exited exactly at 4 PM. The probability distribution
of the arrival time of any visitor is uniform between 3 PM and 4 PM. Two persons
𝑋 and 𝑌 entered the exhibition hall independent of each other. Which one of the
following values is the probability that their visits to the exhibition overlapped with
each other?

(A) 5
9

(B) 4
9

(C) 2
9

(D) 7
9

Page 24 of 42

Q.37 Simpson’s one-third rule is used to estimate the definite integral

1
𝐼 = ∫ √(1 − 𝑥 2 )𝑑𝑥
−1

with an interval length of 0.5. Which one of the following is the CORRECT
estimate of 𝐼 obtained using this rule?

(A) 1 1
−
3 √3

(B) 1 2
+
3 √3

(C) 1 1
+
3 √3

(D) 1 2
−
3 √3

Page 25 of 42

Q.38 Match the products in Group 1 with the manufacturing processes in Group 2 listed
in the table below.

Group 1 Group 2

P) Acetaldehyde I) Sulfate process

Q) Sulfuric acid II) Electric furnace process

R) Pulp III) Wacker process

S) Phosphorus IV) Contact process

(A) P-III, Q-IV, R-I, S-II

(B) P-III, Q-I, R-IV, S-II

(C) P-IV, Q-I, R-II, S-III

(D) P-I, Q-IV, R-II, S-III

Page 26 of 42

Q.39 Match the reactions in Group 1 with the catalysts in Group 2 listed in the table
below.

Group 1 Group 2

I) Mixed oxide
of Mo and Fe

II) V2 O5

III) FeCl3

IV) Ag 2 O

(A) P-III, Q-IV, R-II, S-I

(B) P-III, Q-IV, R-I, S-II

(C) P-IV, Q-II, R-I, S-III

(D) P-IV, Q-III, R-I, S-II

Page 27 of 42

Q.40 Water in a container at 290 K is exposed to air containing 3 % CO2 by volume. Air
behaves like an ideal gas and is maintained at 100 kPa pressure. The liquid phase
comprising of dissolved CO2 in water behaves like an ideal solution. Use Henry’s
constant of CO2 dissolved in water at 290 K as 12 MPa. Under equilibrium
conditions, which one of the following is the CORRECT value of the mole fraction
of CO2 dissolved in water?

(A) 2.9 × 10−4

(B) 0.9 × 10−4

(C) 2.5 × 10−4

(D) 0.5 × 10−4

Page 28 of 42

Q.41 The enthalpy (𝐻, in J. mol−1 ) of a binary liquid system at constant temperature and
pressure is given as

𝐻 = 40𝑥1 + 60𝑥2 + 𝑥1 𝑥2 (4𝑥1 + 2𝑥2 ) ,

where 𝑥1 and 𝑥2 represent the mole fractions of species 1 and 2 in the liquid,
respectively. Which one of the following is the CORRECT value of the partial
∞
molar enthalpy of species 1 at infinite dilution, 𝐻1 (in J. mol−1 ) ?

(A) 100

(B) 42

(C) 64

(D) 40

Q.42 Which one of the following represents the CORRECT effects of concentration
polarization in a reverse osmosis process?

(A) Reduced water flux and reduced solute rejection

(B) Increased water flux and increased solute rejection

(C) Reduced water flux and increased solute rejection

(D) Increased water flux and reduced solute rejection

Page 29 of 42

Q.43 CO and H2 participate in a catalytic reaction. The partial pressures (in atm) of the
reacting species CO and H2 in the feed stream are 𝑝CO and 𝑝H2 , respectively. While
CO undergoes molecular adsorption, H2 adsorbs via dissociative adsorption, that is,
as hydrogen atoms. The equilibrium constants (in atm−1 ) corresponding to
adsorption of CO and H2 to the catalyst sites are 𝐾CO and 𝐾H 2 , respectively. Total
molar concentration of active sites per unit mass of the catalyst is 𝐶𝑡 (in
mol. (g cat)−1). Both the adsorption steps are at equilibrium. Which one of the
following expressions is the CORRECT ratio of the concentration of catalyst sites
occupied by CO to that by hydrogen atoms?

(A)

(B)

(C)

(D)

Page 30 of 42

Q.44 A cascade control strategy is shown in the figure below. The transfer function
between the output (𝑦) and the secondary disturbance (𝑑2 ) is defined as

𝑦(𝑠)
𝐺𝑑2 (𝑠) = .
𝑑2 (𝑠)

Which one of the following is the CORRECT expression for the transfer function
𝐺𝑑2 (𝑠) ?

(A) 1
(11𝑠+21)(0.1𝑠+1)

(B) 1
(𝑠+1)(0.1𝑠+1)

(C) (𝑠+1)
(𝑠+2)(0.1𝑠+1)

(D) (𝑠+1)
(𝑠+1)(0.1𝑠+1)

Page 31 of 42

Q.45 Level (ℎ) in a steam boiler is controlled by manipulating the flow rate (𝐹) of the
make-up (fresh) water using a proportional (P) controller. The transfer function
between the output and the manipulated input is

ℎ(𝑠) 0.25(1 − 𝑠)
= .
𝐹(𝑠) 𝑠(2𝑠 + 1)
The measurement and valve transfer functions are both equal to 1. A process
engineer wants to tune the controller so that the closed-loop response gives decaying
oscillations under servo mode. Which one of the following is the CORRECT value
of the controller gain to be used by the engineer?

(A) 0.25

(B) 2

(C) 4

(D) 6

Q.46 Which of the following statements is/are CORRECT?

(A) Bond number includes surface tension.

(B) Jakob number includes latent heat.

(C) Prandtl number includes liquid-vapor density difference.

(D) Biot number includes gravity.

Page 32 of 42

Q.47 If a matrix 𝑀 is defined as 𝑀 = [10 6 ], the sum of all the eigenvalues of 𝑀3 is
6 10
equal to __________ (in integer).

Q.48 The first derivative of the function

1 12 1 6
𝑈(𝑟) = 4 [( ) − ( ) ]
𝑟 𝑟
evaluated at 𝑟 = 1 is ______ (in integer).

Q.49 Wet air containing 10 mole percent water vapor is dried by continuously passing it
through a column of CaCl2 pellets. The pellets remove 50 percent of water from wet
air entering the column. The mole percent of water vapor in the product stream
exiting the column is ___________ (rounded off to two decimal places).

Q.50 Orsat analysis showing the composition (in mol %, on a dry basis) of a stack gas is
given in the table below. The humidity measurement reveals that the mole fraction
of H2 O in the stack gas is 0.07. The mole fraction of N2 calculated on a wet basis
is ________ (rounded off to two decimal places).

Species N2 CO2 CO O2

mol % 65 15 10 10

Page 33 of 42

Q.51 A pump draws water (density = 1000 kg. m−3 ) at a steady rate of 10 kg. s −1 . The
pressures at the suction and discharge sides of the pump are −20 kPa (gauge) and
350 kPa (gauge), respectively. The pipe diameters at the suction and discharge side
are 70 mm and 50 mm, respectively. The suction and discharge lines are at the
same elevation, and the pump operates at an efficiency of 80 %. Neglecting
frictional losses in the system, the power (in kW) required to drive the pump is
______ (rounded off to two decimal places).

Q.52 A cylindrical tank with a diameter of 500 mm contains water (density = 1 g. cm−3)
upto a height ℎ. A 5 mm diameter round nozzle, whose center is 1 cm above the
base of the tank, has its exit open to the atmosphere as shown in the schematic
below. The pressure above the water level in the tank is maintained at
2 bar (absolute). Neglect all frictional and entry/exit losses. Use acceleration due
to gravity as 10 m. s −2 and atmospheric pressure as 1 bar. The absolute value of
𝑑ℎ
initial (in mm. s−1) when ℎ = 51 cm is equal to ________ (rounded off to two
𝑑𝑡
decimal places).

Page 34 of 42

Q.53 A large tank is filled with water (density = 1 g. cm−3 ) upto a height of 5 m. A
100 μm diameter solid spherical particle (density = 0.8 g. cm−3) is released at the
bottom of the tank. The particle attains its terminal velocity (𝑣𝑡 ) after traveling to a
certain height in the tank. Use acceleration due to gravity as 10 m. s −2 and water
viscosity as 10−3 Pa. s . Neglect wall effects on the particle. If Stokes law is
applicable, the absolute value of 𝑣𝑡 (in mm. s −1 ) is ____________(rounded off to
two decimal places).

Q.54 A fluid is flowing steadily under laminar conditions over a thin rectangular plate at
temperature 𝑇𝑠 as shown in the figure below. The velocity and temperature of the
free stream are 𝑢∞ and 𝑇∞ , respectively. When the fluid flow is only in the 𝑥-
direction, ℎ𝑥 is the local heat transfer coefficient. Similarly, when the fluid flow is
only in the 𝑦-direction, ℎ𝑦 is the corresponding local heat transfer coefficient. Use
the correlation Nu = 0.332 (Re)1/2 (Pr)1/3 for the local heat transfer coefficient,
where, Nu, Re, and Pr, respectively are the appropriate Nusselt, Reynolds and
Prandtl numbers. The average heat transfer coefficients are defined as
1 𝑙 1 𝑤
ℎ̅𝑙 = ∫0 ℎ𝑥 𝑑𝑥 and ℎ̅𝑤 = ∫0 ℎ𝑦 𝑑𝑦. If 𝑤 = 1 m and 𝑙 = 4 m, the
𝑙 𝑤
̅ ̅
value of the ratio of ℎ𝑤 to ℎ𝑙 is _______ (in integer).

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Q.55 A perfectly insulated, concentric tube countercurrent heat exchanger is used to cool
lubricating oil using water as a coolant (see figure below). Oil enters the outer
annulus at a mass flow rate of 2 kg. s−1 with a temperature of 100 o C and leaves at
40 o C. Water enters the inner tube at a mass flow rate of 1 kg. s −1 with a temperature
of 20 o C and leaves at 80 o C. Use specific heats of oil and water as 2089 J. kg −1 K −1
and 4178 J. kg −1 K −1, respectively. There is no phase change in both the streams.
Under steady-state conditions, the number of transfer units (NTU) is _______ (in
integer).

Q.56 Partially saturated air at 1 bar and 50 o C is contacted with water in an adiabatic
saturator. The air is cooled and humidified to saturation, and exits at 25 o C with an
absolute humidity of 0.02 kg water per kg dry air. Use latent heat of vaporization
of water as 2450 kJ. kg −1 , and average specific heat capacity for dry air and water,
respectively as 1.01 kJ. kg −1 K −1 and 4.18 kJ. kg −1 K −1 . If the absolute humidity of
air entering the adiabatic saturator is 𝓗 × 𝟏𝟎−𝟑 kg water per kg dry air, the value
of 𝓗 is __________ (rounded off to two decimal places).

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Q.57 Distillation of a non-reactive binary mixture with components 𝐴 and 𝐵 is carried
out in a batch still as shown in the figure below. The initial charge of the mixture in
the still is 1 kmol. The initial and final amounts of 𝐴 in the still are 0.1 kmol and
0.01 kmol, respectively. Use a constant relative volatility of 4.5. The mole fraction
of 𝐵 remaining in the vessel is _______ (rounded off to three decimal places).

Q.58 Fresh catalyst is loaded into a reactor before the start of the following catalytic
reaction.

The catalyst gets deactivated over time. The instantaneous activity 𝑎(𝑡), at time 𝑡,
is defined as the ratio of the rate of reaction −𝑟𝐴′ (𝑡) (mol. (g cat)−1 hr −1) to the rate
of reaction with fresh catalyst. Controlled experimental measurements led to an
empirical correlation

−𝑟𝐴′ (𝑡) = −0.5𝑡 + 10
where 𝑡 is in hours. The activity of the catalyst at 𝑡 = 10 hr is _______ (rounded
off to one decimal place).

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Q.59 A unimolecular, irreversible liquid-phase reaction

was carried out in an ideal batch reactor at temperature 𝑇. The rate of the reaction
(−𝑟𝐴 ) measured at different conversions 𝑋𝐴 is given in the table below. This
reaction is also carried out in an ideal continuous stirred tank reactor (CSTR) at the
same temperature 𝑇 with a feed concentration of 1 mol. m−3, under steady-state
conditions. For a conversion of 0.8, the space time (in s) of the CSTR is
__________ (in integer).

𝑋𝐴 0 0.1 0.2 0.4 0.6 0.8

−𝑟𝐴 (mol. m−3 s −1 ) 0.45 0.35 0.31 0.18 0.11 0.05

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Q.60 An irreversible liquid-phase second-order reaction

with rate constant 𝑘 = 0.2 liter. mol−1 min−1, is carried out in an isothermal
non-ideal reactor. A tracer experiment conducted on this reactor resulted in a
residence time distribution (𝐸-curve) as shown in the figure below. The areas of the
rectangles (i), (ii), and (iii) are equal. Pure 𝐴 at a concentration of 1.5 mol. liter −1
is fed to the reactor. The segregated model mimics the nonideality of this reactor.
The percentage conversion of 𝐴 at the exit of the reactor is ______ (rounded off to
the nearest integer).

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Q.61 The outlet concentration 𝐶𝐴 of a plug flow reactor (PFR) is controlled by
manipulating the inlet concentration 𝐶𝐴0 . The following transfer function describes
the dynamics of this PFR.

𝐶𝐴 (𝑠) 𝑉
= exp [− ( ) (𝑘 + 𝑠)]
𝐶𝐴0 (𝑠) 𝐹
In the above equation, 𝑉 = 1 m3 , 𝐹 = 0.1 m3 min−1 and 𝑘 = 0.5 min−1 . The
measurement and valve transfer functions are both equal to 1. The ultimate gain,
defined as the proportional controller gain that produces sustained oscillations, for
this system is ______ (rounded off to one decimal place).

Q.62 The transfer function of a measuring instrument is

1.05
𝐺𝑚 (𝑠) = exp(−𝑠) .
2𝑠 + 1
At time 𝑡 = 0, a step change of +1 unit is introduced in the input of this instrument.
The time taken by the instrument to show an increase of 1 unit in its output is _____
(rounded off to two decimal places).

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Q.63 A design engineer needs to purchase a membrane module (M) for a plant. Details
about the two available options, M1 and M2, are given in the table below. The
overall plant has an expected life of 7 years. If the interest rate is 8 % per annum,
compounded annually, the difference in the net present value (NPV) of these two
options, in lakhs of rupees, is ______ (rounded off to one decimal place).

M1 M2

Purchase cost (in lakhs of rupees) 10 5

Expected life (years) 5 3

Q.64 The purchase cost of a new distillation column is Rs. 10 lakhs with an installation
factor of 5.8. The cost of the capital is to be annualized over a period of 6 years at
a fixed rate of interest of 5 % per annum, compounded annually. The annual cost
(in lakhs of rupees) of the installed capital is _______ (rounded off to one decimal
place).

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Q.65 Pumps 𝐴 and 𝐵 are being considered for purchase in a chemical plant. Cost details
for these two pumps are given in the table below. The interest rate is 10 % per
annum, compounded annually. For both the pumps to have the same capitalized
cost, the salvage value (in Rs.) of pump B should be ______ (rounded off to the
nearest integer).

Item Pump 𝑨 Pump 𝑩

Installed cost (Rs.) 16000 32000

Uniform end of year maintenance (Rs.) 2400 1600

Salvage value (Rs.) 1000 ?

Service life (year(s)) 1 2

END OF QUESTION PAPER

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