GATE 2025 Question Paper Chemical Engineering (CH)

GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude
Q.1 – Q.5 Carry ONE mark Each

Q.1 Is there any good show _______ television tonight?

Select the most appropriate option to complete the above sentence.

(A) in

(B) at

(C) within

(D) on

Q.2 As the police officer was found guilty of embezzlement, he was _______ dismissed
from the service in accordance with the Service Rules.

Select the most appropriate option to complete the above sentence.

(A) sumptuously

(B) brazenly

(C) unintentionally

(D) summarily

Organizing Institute: IIT Roorkee Page 1 of 37

Q.3 The sum of the following infinite series is:

1 1 1 1 1
+ + + + +⋯
1! 2! 3! 4! 5!

(A) 𝜋

(B) 1+𝑒

(C) 𝑒−1

(D) 𝑒

Q.4 A thin wire is used to construct all the edges of a cube of 1 m side by bending,
cutting and soldering the wire. If the wire is 12 m long, what is the minimum number
of cuts required to construct the wire frame to form the cube?

(A) 3

(B) 4

(C) 6

(D) 12

Organizing Institute: IIT Roorkee Page 2 of 37

Q.5 The figures I, II and III are parts of a sequence. Which one of the following options
comes next in the sequence at IV?

?

I II III IV

(A)

(B)

(C)

(D)

Organizing Institute: IIT Roorkee Page 3 of 37

Q.6 – Q.10 Carry TWO marks Each

Q.6 “Why do they pull down and do away with crooked streets, I wonder, which are my
delight, and hurt no man living? Every day the wealthier nations are pulling down
one or another in their capitals and their great towns: they do not know why they do
it; neither do I. It ought to be enough, surely, to drive the great broad ways which
commerce needs and which are the life-channels of a modern city, without
destroying all history and all the humanity in between: the islands of the past.”

(From Hilaire Belloc’s “The Crooked Streets”)

Based only on the information provided in the above passage, which one of the
following statements is true?

(A) The author of the passage takes delight in wondering.

(B) The wealthier nations are pulling down the crooked streets in their capitals.

(C) In the past, crooked streets were only built on islands.

(D) Great broad ways are needed to protect commerce and history.

Organizing Institute: IIT Roorkee Page 4 of 37

Q.7 Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant,
he notices that the hour and minute hands on the wall clock are exactly coinciding.
After about an hour, when he leaves the restaurant, he notices that the clock hands
are again exactly coinciding. How much time (in minutes) did Rohit spend at the
restaurant?

(A) 6
64 11

(B) 5
66 13

(C) 5
65 11

(D) 6
66 13

Organizing Institute: IIT Roorkee Page 5 of 37

Q.8 A color model is shown in the figure with color codes: Yellow (Y), Magenta (M),
Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K).

Which one of the following options displays the color codes that are consistent with
the color model?

(A)

(B)

(C)

(D)

Organizing Institute: IIT Roorkee Page 6 of 37

Q.9 A circle with center at (𝑥, 𝑦) = (0.5, 0) and radius = 0.5 intersects with another
circle with center at (𝑥, 𝑦) = (1, 1) and radius = 1 at two points. One of the points
of intersection (𝑥, 𝑦) is:

(A) (0, 0)

(B) (0.2, 0.4)

(C) (0.5, 0.5)

(D) (1, 2)

Organizing Institute: IIT Roorkee Page 7 of 37

Q.10 An object is said to have an 𝑛-fold rotational symmetry if the object, rotated by an
2𝜋
angle of , is identical to the original.
𝑛

Which one of the following objects exhibits 4-fold rotational symmetry about an
axis perpendicular to the plane of the screen?

Note: The figures shown are representative.

(A)

(B)

(C)

(D)

Organizing Institute: IIT Roorkee Page 8 of 37

Q.11 – Q.35 Carry ONE mark Each

Q.11 To manufacture paper from (i) , the (ii) must be freed from the binding
matrix of (iii) in the pulping step.

Which one of the following is the CORRECT option to fill in the gaps (i), (ii) and
(iii)?

(A) (i) wood, (ii) cellulose fibers, (iii) lignin

(B) (i) lignin, (ii) cellulose fibers, (iii) wood

(C) (i) lignin, (ii) wood, (iii) cellulose fibers

(D) (i) wood, (ii) lignin, (iii) cellulose fibers

Q.12 Consider a Cartesian coordinate system defined over a 3-dimensional vector space
1
with orthogonal unit basis vectors 𝑖̂, 𝑗̂ and 𝑘̂. Let vector 𝒂 = √2𝑖̂ + 𝑗̂ + 𝑘̂, and
√2
1
vector 𝒃 = 𝑖̂ + √2𝑗̂ − 𝑘̂ . The inner product of these vectors (𝒂 ∙ 𝒃) is
√2

(A) 0

(B) 1

(C) −1

(D) 2

Organizing Institute: IIT Roorkee Page 9 of 37

Q.13 Consider two complex numbers 𝑧1 = 1 − 𝑖 and 𝑧2 = 𝑖. The argument of 𝑧1 𝑧2 is

(A) 0

(B) 𝜋
4

(C) 𝜋
2

(D) 𝜋

Q.14 A box contains 3 identical green balls and 7 identical blue balls. Two balls are
randomly drawn without replacement from the box. The probability of drawing
1 green and 1 blue ball is

3P1 × 7P1
(A)
10P2

10P3 × 10P7
(B)
10P2

10C3 × 10C7
(C)
10C2

3C1 × 7C1
(D)
10C2

Organizing Institute: IIT Roorkee Page 10 of 37

Q.15 The number of independent intensive variables that need to be specified to determine
the thermodynamic state of a ternary mixture at vapor-liquid-liquid equilibrium is

(A) 0

(B) 1

(C) 2

(D) 3

Q.16 The boundary of a system does not allow exchange of either mass or energy (in the
form of heat and/or work) with the surroundings. The system is termed

(A) Isolated

(B) Open

(C) Adiabatic

(D) Closed

Organizing Institute: IIT Roorkee Page 11 of 37

Q.17 In industrial heat exchanger design, the overall heat transfer coefficient 𝑈 is estimated
from the equation

1 1 1
= +
𝑈 ℎ𝑖 ℎ𝑜

where ℎ𝑖 and ℎ𝑜 are the convective heat transfer coefficients on the inner and outer
side of the tube, respectively. This is valid for (i) tube of (ii) thermal
conductivity.

Which one of the following is the CORRECT option to fill in the gaps (i) and (ii)?

(A) (i) thick-walled, (ii) high

(B) (i) thin-walled, (ii) high

(C) (i) thin-walled, (ii) low

(D) (i) thick-walled, (ii) low

Q.18 The sum of the components of the force due to pressure and shear at the solid-fluid
boundary of a solid body in the direction normal to the flow is

(A) Drag

(B) Friction

(C) Lift

(D) Buoyancy

Organizing Institute: IIT Roorkee Page 12 of 37

Q.19 Choose the CORRECT option for pathlines, streaklines and streamlines for a
STEADY flow field.

(A) All three lines are identical

(B) Only pathlines and streaklines are identical

(C) Only pathlines and streamlines are identical

(D) Only streamlines and streaklines are identical

Q.20 Choose the CORRECT ordering of the diameter 𝑑 of the different types of pores in a
solid catalyst.

(A) 𝑑 Micro-pore < 𝑑 Macro-pore < 𝑑 Meso-pore

(B) 𝑑 Macro-pore < 𝑑Meso-pore < 𝑑Micro-pore

(C) 𝑑 Meso-pore < 𝑑Micro-pore < 𝑑Macro-pore

(D) 𝑑 Micro-pore < 𝑑 Meso-pore < 𝑑Macro-pore

Organizing Institute: IIT Roorkee Page 13 of 37

Q.21 Schmidt number is defined as

(A) Mass Diffusivity
Thermal Diffusivity

(B) Momentum Diffusivity
Mass Diffusivity

(C) Momentum Diffusivity
Thermal Diffusivity

(D) Thermal Diffusivity
Mass Diffusivity

Q.22 If 𝑘 is the mass transfer coefficient and 𝐷𝑣 is the molecular diffusivity, which one of
the following statements is NOT CORRECT with respect to mass transfer theories?

(A) For Film theory, 𝑘 ∝ 𝐷𝑣

(B) 1/3
For Penetration theory, 𝑘 ∝ 𝐷𝑣

(C) 1/2
For Surface Renewal theory, 𝑘 ∝ 𝐷𝑣

(D) 2/3
For Boundary Layer theory, 𝑘 ∝ 𝐷𝑣

Organizing Institute: IIT Roorkee Page 14 of 37

Q.23 Choose the CORRECT statement that describes the dependence of the variance (𝜎Θ2 )
of the residence time distribution (RTD) with respect to the number of tanks (𝑛) in
the Tanks-in-Series model of non-ideal reactors.

(A) 𝜎Θ2 monotonically increases with 𝑛

(B) 𝜎Θ2 first increases and then decreases with 𝑛

(C) 𝜎Θ2 first decreases and then increases with 𝑛

(D) 𝜎Θ2 monotonically decreases with 𝑛

Q.24 The vortex shedding meter is primarily used for measuring

(A) Fluid Flow Rate

(B) Liquid Level

(C) Fluid Temperature

(D) Fluid Pressure

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Q.25 Choose the transfer function that best fits the output response to a unit step input
change shown in the figure

(A) (𝛼𝑠 + 1)𝑒 −𝜃𝑠
(𝜏1 𝑠 + 1)(𝜏2 𝑠 + 1)2

(B) (𝛼𝑠 + 1)𝑒 −𝜃𝑠
(𝜏1 𝑠 + 1)(𝜏2 𝑠 + 1)

(C) (𝛼𝑠 + 1)
(𝜏1 𝑠 + 1)(𝜏2 𝑠 + 1)2

(D) (𝛼𝑠 + 1)2 𝑒 −𝜃𝑠
(𝜏1 𝑠 + 1)(𝜏2 𝑠 + 1)2

Organizing Institute: IIT Roorkee Page 16 of 37

Q.26 The capital cost (𝐶𝐶) of an industrial equipment varies with its capacity (𝑆)
as 𝐶𝐶 ∝ 𝑆𝛽 . The rule-of-thumb value of the exponent 𝛽 is

(A) 0.4

(B) 0.6

(C) 0.8

(D) 1.0

Q.27 In the production of polyvinyl chloride (PVC) from ethylene and chlorine, the
sequential order of reactions is

(A) Chlorination followed by Dehydrochlorination

(B) Dehydrochlorination followed by Chlorination

(C) Hydrogenation followed by Chlorination

(D) Dehydrochlorination followed by Hydrogenation

Organizing Institute: IIT Roorkee Page 17 of 37

Q.28 In the CONTACT PROCESS for manufacturing sulphuric acid, the reaction
converting SO2 to SO3 is

(A) Exothermic and reversible

(B) Endothermic and reversible

(C) Exothermic and irreversible

(D) Endothermic and irreversible

Organizing Institute: IIT Roorkee Page 18 of 37

Q.29 Choose the option that correctly matches the items in Group 1 with those in
Group 2.

Group 1 Group 2

(P) Coking (I) Prolonged exposure of catalyst to high
temperature

(Q) Poisoning (II) Deposition of carbonaceous material
on catalyst surface

(R) Sintering (III) Irreversible chemisorption of
molecules on active sites of catalyst

(A) (P) – (III), (Q) – (I), (R) – (II)

(B) (P) – (II), (Q) – (III), (R) – (I)

(C) (P) – (II), (Q) – (I), (R) – (III)

(D) (P) – (I), (Q) – (III), (R) – (II)

Organizing Institute: IIT Roorkee Page 19 of 37

Q.30 Which of the following statements regarding multiple effect evaporators is/are
TRUE?

(A) The pressure of the effect with fresh steam is the lowest for both forward feed and
backward feed.

(B) Backward feed is preferred over forward feed for cold feed.

(C) Backward feed is preferred over forward feed for highly viscous concentrated
product.

(D) The temperature of the effect with fresh steam is the lowest for both forward feed and
backward feed.

Q.31 Consider an enzymatic reaction that follows Michaelis-Menten kinetics. Let 𝐾𝑀 , 𝑆,
and 𝑉𝑚𝑎𝑥 denote the Michaelis constant, substrate concentration, and
maximum reaction rate, respectively. Which of the following statements is/are
TRUE?

(A) For 𝑆 ≪ 𝐾𝑀 , the reaction is apparent first-order in 𝑆.

(B) For 𝑆 ≫ 𝐾𝑀 , the reaction rate is nearly independent of 𝑆.

(C) For 𝑆 = 𝐾𝑀 , the rate of reaction equals 𝑉𝑚𝑎𝑥 .

(D) 𝐾𝑀 is independent of the total enzyme concentration.

Organizing Institute: IIT Roorkee Page 20 of 37

Q.32 The following data is given for a ternary 𝐴𝐵𝐶 gas mixture at 12 MPa and 308 K:

Component 𝑖 → 𝐴 𝐵 𝐶

𝑦𝑖 0.55 0.20 0.25

𝜙̂𝑖 0.75 0.80 0.95

𝑦𝑖 : mole fraction of component 𝑖 in the gas mixture

𝜙̂𝑖 : fugacity coefficient of component 𝑖 in the gas mixture
at 12 MPa and 308 K

The fugacity of the gas mixture is _____ MPa (rounded off to 3 decimal places).

Q.33 Ideal nonreacting gases 𝐴 and 𝐵 are contained inside a perfectly insulated chamber,
separated by a thin partition, as shown in the figure. The partition is removed, and the
two gases mix till final equilibrium is reached. The change in total entropy for the
process is ____ J/K (rounded off to 1 decimal place).

GIVEN: Universal gas constant 𝑅 = 8.314 J/(mol K)

Organizing Institute: IIT Roorkee Page 21 of 37

Q.34 Oil is extracted from mustard seeds having 20 wt% oil and 80 wt% solids, using
hexane as a solvent. After extraction, the hexane-free residual cake contains 1 wt%
oil. Assuming negligible dissolution of cake in hexane, the percentage oil recovery
in hexane is ____% (rounded off to the nearest integer).

Q.35 The residence-time distribution (RTD) function of a reactor (in min−1) is

1 − 2𝑡 , 𝑡 ≤ 0.5 min
𝐸(𝑡) = {
0, 𝑡 > 0.5 min

The mean residence time of the reactor is ____ min (rounded off to 2 decimal places).

Organizing Institute: IIT Roorkee Page 22 of 37

Q.36 – Q.65 Carry TWO marks Each

Q.36 Consider a Cartesian coordinate system with orthogonal unit basis vectors 𝑖̂, 𝑗̂ defined over a
domain: 𝑥, 𝑦 ∈ [0,1]. Choose the condition for which the divergence of the vector field
𝒗 = 𝑎𝑥𝑖̂ − 𝑏𝑦𝑗̂ is zero.

(A) 𝑎−𝑏 =0

(B) 𝑎<𝑏

(C) 𝑎>𝑏

(D) 𝑎+𝑏 =0

Q.37 A probability distribution function is given as

1
, 𝑥 ∈ (0, 𝑎)
𝑝(𝑥) = {𝑎
0, otherwise

where 𝑎 is a positive constant. For a function 𝑓(𝑥) = 𝑥 2 , the expectation of 𝑓(𝑥) is

(A) 𝑎2
3

(B) 𝑎3
3

(C) 2𝑎2
3

(D) 2𝑎3
3

Organizing Institute: IIT Roorkee Page 23 of 37

Q.38 A hot plate is placed in contact with a cold plate of a different thermal conductivity as shown
in the figure. The initial temperature (at time 𝑡 = 0) of the hot plate and cold plate are 𝑇ℎ and
𝑇𝑐 , respectively. Assume perfect contact between the plates.

Which one of the following is an appropriate boundary condition at the surface S for solving
the unsteady state, one-dimensional heat conduction equations for the hot plate and cold plate
for 𝑡 > 0?

(A) Temperature at S is same for both the plates

(B) Gradient of temperature at S is same for both the plates

(C) Gradient of temperature vanishes at S

(D) Temperature at S is the average of 𝑇ℎ and 𝑇𝑐

Organizing Institute: IIT Roorkee Page 24 of 37

Q.39 The first-order irreversible liquid phase reaction 𝐴 ⟶ 𝐵 occurs inside a constant
volume (𝑉) isothermal CSTR with the initial steady state conditions shown in the figure.
kmol/m3
The gain, in , of the transfer function relating the reactor effluent 𝐴 concentration,
m3 /h
𝑐𝐴 , to the inlet flow rate, 𝐹, is

(A) 1.2

(B) 0.4

(C) 0.6

(D) 0.8

Organizing Institute: IIT Roorkee Page 25 of 37

Q.40 500 mg of a dry adsorbent is added to a beaker containing 100 mL solution of concentration
100 mg phenol/(L solution). The adsorbent is separated out after 5 h of rigorous mixing. If the
residual concentration in the solution after separating the adsorbent is
30 mg phenol/(L solution), the amount of phenol adsorbed (in mg per gram of dry adsorbent)
is

(A) 7

(B) 14

(C) 28

(D) 18

Organizing Institute: IIT Roorkee Page 26 of 37

Q.41 A catalyst particle is modeled as a symmetrical double cone solid as shown in the figure. For
each conical sub-part, the radius of the base is 𝑟 and the height is ℎ. The sphericity of the
particle is given by

(A) 1⁄3
𝑟 2ℎ
2( )
2
𝑟√(𝑟 2 + ℎ2 )

(B) 1⁄3
𝑟 2ℎ
( )
2
𝑟√(𝑟 2 + ℎ2 )

(C) 2⁄3
𝑟 2ℎ
2( 2 )

𝑟√(𝑟 2 + ℎ2 )

(D) 2⁄3
𝑟 2ℎ
( )
2
𝑟√(𝑟 2 + ℎ2 )

Organizing Institute: IIT Roorkee Page 27 of 37

Q.42 A zero-order gas phase reaction 𝐴 → 𝐵 with rate (−𝑟𝐴 ) = 𝑘 = 100 mol/(L min) is carried out
in a mixed flow reactor of volume 1 L. Pure 𝐴 is fed to the reactor at a rate of 1 mol/min. At
time 𝑡 = 0, the outlet flow is stopped while the inlet flow rate and reactor temperature remain
unchanged. Assume that the reactor was operating under steady state before the flow was
stopped (𝑡 < 0). The rate of consumption of 𝐴, −𝑑𝐶𝐴 /𝑑𝑡, in mol/(L min), at 𝑡 = 1 min is

(A) 63.2

(B) 36.8

(C) 90.6

(D) 99.0

Q.43 For a steady state, fully developed laminar flow of a Newtonian fluid through a cylindrical pipe
at a constant volumetric flow rate, which of the following statements regarding the pressure
drop across the pipe (𝛥𝑃) is/are TRUE?

(A) 𝛥𝑃 increases with fluid viscosity

(B) 𝛥𝑃 increases with pipe length

(C) 𝛥𝑃 increases with pipe diameter

(D) 𝛥𝑃 remains unchanged with fluid viscosity

Organizing Institute: IIT Roorkee Page 28 of 37

Q.44 Consider the differential equation

𝑑𝑦 𝑦
+ =0
𝑑𝑥 𝑥
Choose the CORRECT option(s) for the solution 𝑦.

(A) 𝑦 = 𝑥 + 𝑐 ; 𝑐 is a constant

𝑐
(B) 𝑦 = 𝑥 ; 𝑐 is a constant

(C) 𝑦 = −𝑥 + 𝑐 ; 𝑐 is a constant

(D) 𝑦=0

Q.45 Consider the matrix

2 3
𝑨=[ ]
1 2
The eigenvalues of the matrix are 0.27 and ____ (rounded off to 2 decimal places).

Q.46 The Newton-Raphson method is used to find the root of

𝑓(𝑥) ≡ 𝑥 2 − 𝑥 − 1 = 0

Starting with an initial guess 𝑥(0) = 1, the second iterate 𝑥(2) is ____ (rounded off to 2 decimal
places).

Organizing Institute: IIT Roorkee Page 29 of 37

Q.47 Consider moist air with absolute humidity of 0.02 (kg moisture)/(kg dry air) at 1 bar pressure.
The vapour pressure of water is given by the equation

4000
ln 𝑃 𝑠𝑎𝑡 = 12 −
𝑇 − 40
where 𝑃 𝑠𝑎𝑡 is in bar and 𝑇 is in K. The molecular weight of water and dry air are 18 kg/kmol
and 29 kg/kmol, respectively. The dew temperature of the moist air is _____ ℃ (rounded off
to the nearest integer).

Q.48 An ideal monoatomic gas is contained inside a cylinder-piston assembly connected to a
Hookean spring as shown in the figure. The piston is frictionless and massless. The spring
constant is 10 kN/m. At the initial equilibrium state (shown in the figure), the spring is
unstretched. The gas is expanded reversibly by adding 362.5 J of heat. At the final equilibrium
state, the piston presses against the stoppers. Neglecting the heat loss to the surroundings, the
final equilibrium temperature of the gas is ____ K (rounded off to the nearest integer).

3
GIVEN: For a monoatomic ideal gas, 𝐶𝑣 = 2 𝑅, where 𝑅 = 8.314 J/(mol K)

Organizing Institute: IIT Roorkee Page 30 of 37

Q.49 A leaf filter is operated at 1 atm (gauge). The volume of filtrate collected (𝑉 in m3) is related
with the volumetric flow rate of the filtrate (𝑞 in m3/s) as:

1 1
= = 50 𝑉 + 100
𝑞 𝑑𝑉/𝑑𝑡

The volumetric flow rate of the filtrate at 1 hour is ____ × 10−3 m3/s (rounded off to 2 decimal
places).

Q.50 An adiabatic pump of efficiency 40% is used to increase the water pressure from 200 kPa to
600 kPa. The flow rate of water is 600 L/min. The specific heat of water is 4.2 kJ/(kg ℃).
Assuming water is incompressible with a density of 1000 kg/m3, the maximum temperature
rise of water across the pump is ____℃ (rounded off to 3 decimal places).

Q.51 Water flowing at 70 kg/min is heated from 25 ℃ to 65 ℃ in a counter-flow double pipe heat
exchanger using hot oil. The oil enters at 110 ℃ and exits at 65 ℃. If the overall heat transfer
coefficient is 300 W/(m2 K), the heat exchanger area is ____ m2 (rounded off to 1 decimal
place).

GIVEN: Specific heat of water and oil are 4.2 kJ/(kg ℃) and 2 kJ/(kg ℃), respectively.

Organizing Institute: IIT Roorkee Page 31 of 37

Q.52 Consider laminar flow of water over a wide flat plate maintained at a uniform temperature of
50 °C as shown in the figure. The freestream velocity and temperature of water are 1.0 m/s
(parallel to the plate) and 20 ℃, respectively. The distance 𝑥 from the leading edge, at which
the thermal boundary layer thickness 𝛿𝑇 = 0.01 m, is ____ m (rounded off to 1 decimal place).

GIVEN: kinematic viscosity: 𝜈 = 1.0 × 10−6 m2/s

Prandtl number: 𝑃𝑟 = 7.01
4.91𝑥
velocity boundary layer thickness: 𝛿𝐻 = 𝑉𝑥
√
𝜈

Q.53 An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness
2 mm and thermal conductivity 𝑘 = 0.1 W/(m K). It is exposed to ambient air at 30 °C. For a
current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient
is 20 W/(m2 K). Neglecting the thermal resistance of the wire, the steady state temperature at
the wire-insulation interface is ____°C (rounded off to 1 decimal place).

Q.54 A binary 𝐴𝐵 liquid mixture containing 30 mol% 𝐴 is subjected to differential (Rayleigh)
distillation at atmospheric pressure in order to recover 60 mol% 𝐴 in the distillate. Assuming a
constant relative volatility 𝛼𝐴𝐵 = 2.2, the average composition of the collected distillate
is ____ mol% 𝐴 (rounded off to nearest integer).

Organizing Institute: IIT Roorkee Page 32 of 37

Q.55 Gas containing 0.8 mol% component 𝐴 is to be scrubbed with pure water in a packed bed
column to reduce the concentration of 𝐴 to 0.1 mol% in the exit gas. The inlet gas and water
flow rates are 0.1 kmol/s and 3.0 kmol/s, respectively.

For the dilute system, both the operating and equilibrium curves are considered linear. If the
slope of the equilibrium line is 24, the number of transfer units, based on the gas side,
𝑁𝑂𝐺 is ____ (rounded off to 1 decimal place).

Q.56 Solute A is absorbed from a gas into water in a packed bed operating at steady state. The
absorber operating pressure and temperature are 1 atm and 300 K, respectively. At the
gas-liquid interface

𝑦𝑖 = 1.5 𝑥𝑖

where 𝑦𝑖 and 𝑥𝑖 are the interfacial gas and liquid mole fractions of A, respectively. At a
particular location in the absorber, the mole fractions of A in the bulk gas and in the bulk water
are 0.02 and 0.002, respectively. If the ratio of the local individual mass transfer coefficients
𝑘𝑦
for the transport of A on the gas-side (𝑘𝑦 ) to that on the water-side (𝑘𝑥 ), 𝑘 = 2,
𝑥
then 𝑦𝑖 equals ____ (rounded off to 3 decimal places).

Q.57 Components 𝐴 and 𝐵 form an azeotrope. The saturation vapour pressures of 𝐴 and 𝐵 at the
boiling temperature of the azeotrope are 87 kPa and 72.7 kPa, respectively. The azeotrope
composition is ____ mol% 𝐴 (rounded off to the nearest integer).

GIVEN:
𝛾𝐴
ln = 0.9(𝑥𝐵2 − 𝑥𝐴2 )
𝛾𝐵

where 𝑥𝑖 and 𝛾𝑖 are the liquid phase mole fraction and activity coefficient of component 𝑖,
respectively.

Organizing Institute: IIT Roorkee Page 33 of 37

Q.58 The reaction 𝐴 → 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 with reaction rate, (−𝑟𝐴 ) = 𝑘𝐶𝐴3 , occurs in an isothermal PFR
operating at steady state. The conversion (𝑋) at two axial locations (1 and 2) of the PFR is
shown in the figure.

The value of 𝑙1 /𝑙2 is ____ (rounded off to 2 decimal places).

Q.59 The catalytic gas phase reaction 𝐴 → 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 is carried out in an isothermal batch reactor of
10 L volume using 0.1 kg of a solid catalyst. The reaction is first-order with

(−𝑟𝐴 ) = 𝑘 ′ 𝑎(𝑡)𝐶𝐴

where

L
𝑘′ = 1
(kg catalyst)(h)

and 𝐶𝐴 is the concentration of 𝐴 in mol/L.

The catalyst activity 𝑎(𝑡) undergoes first-order decay with rate constant 𝑘𝑑 = 0.01 per hour and
𝑎(0) = 1.

The reactant conversion after 1 day of operation is ____ (rounded off to 2 decimal places).

Organizing Institute: IIT Roorkee Page 34 of 37

Q.60 Consider a process with transfer function

2𝑒 −𝑠
𝐺𝑝 =
(5𝑠 + 1)2

A first-order plus dead time (FOPDT) model is to be fitted to the unit step process reaction
curve (PRC) by applying the maximum slope method.

Let 𝜏𝑚 and 𝜃𝑚 denote the time constant and dead time, respectively, of the fitted FOPDT model.
𝜏
The value of 𝜃𝑚 is ____ (rounded off to 2 decimal places).
𝑚

GIVEN: For
1
𝐺=
(𝜏𝑠 + 1)2

the unit step output response:
𝑡
𝑦(𝑡) = 1 − (1 + 𝜏) 𝑒 −𝑡⁄𝜏

𝑑𝑦(𝑡) 𝑡
= 𝜏2 𝑒 −𝑡⁄𝜏
𝑑𝑡

𝑑2 𝑦(𝑡) 1 𝑡
= 𝜏2 (1 − 𝜏) 𝑒 −𝑡⁄𝜏
𝑑𝑡 2

Q.61 Methanol is produced by the reversible, gas-phase hydrogenation of carbon monoxide as

𝐶𝑂 + 2𝐻2 ⟷ 𝐶𝐻3 𝑂𝐻

𝐶𝑂 and 𝐻2 are charged to a reactor and the reaction proceeds to equilibrium at 453 K and
2 atm. The reaction equilibrium constant, which depends only on the temperature, is 1.68 at the
reaction conditions. The mole fraction of 𝐻2 in the product is 0.4. Assuming ideal gas
behaviour, the mole fraction of methanol in the product is ____ (rounded off to 2 decimal
places).

Organizing Institute: IIT Roorkee Page 35 of 37

Q.62 The block diagram of a series cascade control system (with time in minutes) is shown in the
figure. For 𝜏𝐼 = 8 min and 𝐾𝑐𝑠 = 1, the maximum value of 𝐾𝑐𝑚 , below which the cascade control
system is stable, is ____ (rounded off to the nearest integer).

Q.63 It is proposed to install thermal insulation in a residence to save on the summer-monsoon
season air-conditioning costs. The estimated yearly saving is 20 thousand rupees. The cost of
installation of the insulation is 150 thousand rupees. The life of the insulation is 12 years. For
a compound interest rate of 9% per annum, the minimum salvage value of the insulation for
which the proposal is competitive, is ____ thousand rupees (rounded off to nearest integer).

Organizing Institute: IIT Roorkee Page 36 of 37

Q.64 Consider the flowsheet in the figure for manufacturing 𝐶 via the reaction 𝐴 + 𝐵 ⟶ 𝐶 in an
isothermal CSTR. The split in the separator is perfect so that the recycle stream is free of 𝐶 and
the product stream is pure 𝐶. Let 𝑥𝑖 denote the mole fraction of species 𝑖 (𝑖 = 𝐴, 𝐵, 𝐶) in the
CSTR, which is operated in excess B with 𝑥𝐵 /𝑥𝐴 = 4. The reaction is first-order in 𝐴 with the
reaction rate (−𝑟𝐴 ) = 𝑘𝑥 𝑥𝐴 , where 𝑘𝑥 = 5.0 kmol/(m3 h).

The reactor volume 𝑉 in m3 is to be optimized to minimize the cost objective 𝐽 = 𝑉 + 0.25𝑅,
where 𝑅 is the recycle rate in kmol/h. For a product rate 𝑃 = 100 kmol/h, the optimum value
of 𝑉 is ____ m3 (rounded off to the nearest integer).

𝑑 𝑧 1
GIVEN: ( ) = (1−𝑧)2
𝑑𝑧 1−𝑧

Q.65 A wet solid of 100 kg containing 30 wt% moisture is to be dried to 2 wt% moisture in a tray
dryer. The critical moisture content is 10 wt% and the equilibrium moisture content is 1 wt%.
The drying rate during the constant rate period is 10 kg/(h m2). The drying curve in the falling
rate period is linear. If the drying area is 5 m2, the time required for drying is ____ h (rounded
off to 1 decimal place).

Note: All the moisture values given are on dry-solid basis.

Organizing Institute: IIT Roorkee Page 37 of 37

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