GATE question papers: Chemical Engineering 2011 (CH)

Q. 1 – Q. 25 carry one mark each.

Match the polymerization mechanisms in Group I with the corresponding polymers in Group II.

	GROUP I		GROUP II
P.	Chain growth/addition polymerisation	I.	Polyethylene
Q.	Step growth / condensation polymerisation	II.	Polyvinyl chloride
		III.	Polyethylene terephthalate

(A) P – III; Q – I, II

(B) P – I, II; Q – III,

(D) P – I; Q – II, III

Which ONE of thee following sequences is arranged according to INCREASING calorific value?

(A) Producer gas, Natural gas, Water gas

(B) Natural gas, Producer gas, Water gas

(D) Water gas, Natural gas, Producer gas

The CORRECT sequence of process equipment used in the production of sulphuric acid from sulphur by contact process is

(A) burner, catalytic converter, 98% sulphuric acid absorption tower, oleum absorption column

(B) catalytic converter, oleum absorption column, 98% sulphuric acid absorption tower, burner

(D) burner, oleum absorption column, catalytic converter, 98% sulphuric acid absorption tower

Hydrotreating is used for

(A) removal of water from crude oil,

(B) treatment of crude oil with water

(D) removal of sulphur and nitrogen from petroleum fractions

Zeolite ZSM-5 is added to commercial FCC catalyst for

(A) promoting SO₂ reduction

(B) promoting CO oxidation

(D) enhancing Octane number

Minimum input required to calculate the 'blank diameter' for a torispherical head is

(A) crown radius,

(B) crown radius, knuckle radius and length of straight flange

(D) crown radius, and knuckle radius

Match the process parameters in Group I, with the measuring instruments in Group II.

	GROUP I		GROUP II
P.	Flame temperature	I.	Thermocouple
Q.	Composition of LPG	II.	Radiation pyrometer
R.	Liquid air temperature	III.	Gas chromatograph

(A) P – III Q – I, R – II

(B) P – I, Q – III, R – II

(D) P – II, Q – I, R – III

The range of standard current signal in process instruments is 4 to 20 mA. Which ONE of the following is the reason for choosing the minimum signal as 4 mA instead of 0 mA?

(A) To minimize resistive heating in instruments,

(B) To distinguish between signal failure and minimum signal condition

(D) To ensure compatibility with other instruments.

Minimum work (W) required to separate a binary gas mixture at a temperature T₀ and pressure P₀ is

W = -RT₀

where y₁ and y₂ are mole fractions. f_pure.1 and f_pure.2 are fugacities of pure species at T₀ and P₀ and and are fugacities of species in the mixture at T₀ , P₀and y₁. If the mixture is ideal then W is

(A) 0

(B) – RT₀ [y₁ln y₁ + y₂ ln y₂]

(D) RT₀

10.

R is a closed planar region as shown by the shaded area in the figure below. Its boundary C consists of the circles C₁ and C₂.

If are all continuous everywhere in R. Green's theorem states that Which ONE of the following alternatives CORRECTLY depicts the direction of integration along C?

11.

Which ONE of the following functions y (x) has the slope of its tangent equal to ?

Note: a and b are real constants.

(A)

(B) y = ax + b

(C)

(D)

12.

Let λ₁ = – 1 and λ₂ = 3 be the eigenvalues and and be the corresponding eigenvectors of a real 2 ´ 2 matrix. Given that , which ONE of the following matrixes represents?

(A)

(B)

(C)

(D)

13.

The partial molar enthalpies of mixing (in J/mol) for benzene (component 1) and cyclohexane (component 2) at 300 K and 1 bar are given by and , where x₁ and x₂ are the mole fractions. When ONE mole of benzene is added to TWO moles of cyclohexane, the enthalpy change (in J) is

(A) 3600

(B) 2400

(D) 800

14.

One mole of methane is contained in a leak proof piston-cylinder assembly at 8 bar and 1000 K. The gas undergoes isothermal expansion to 4 bar under reversible conditions. Methane can be considered as an ideal gas under these conditions. The value of universal gas constant is 8.314 J mol^–1 K^–1. The heat transferred (in kJ) during the process is

(A) 11.52

(B) 5.76

(D) 2.38

15.

Consider the following two cases of movement of particles. In Case I, the particle moves along the positive y-direction and in Case II, the particle moves along negative y-direction. Gravity acts along the positive y-direction. Which ONE of the following options corresponds to thee CORRECT directions of buoyancy acting on the particles?

(A) Positive y–direction for both the case

(B) Negative y–direction for Case I, positive y–direction for Case II

(D) Positive y–direction for Case I, negative y–direction for Case II

16.

Match the pumps in Group I with the corresponding fluids in Group II.

	GROUP I		GROUP II
P.	Gear pump	I.	Highly viscous liquid
Q.	. Peristaltic pump	II.	Aqueous sterile liquid
		III.	Slurry

(A) P – III ; Q – I,

(B) P – II, Q – I,

(D) P – I, Q – II

17.

Consider two black bodies with surfaces S₁ (area = 1 m²) and S₂ (area = 4 m²). They exchange heat only by radiation. 40% of the energy emitted by S₁ is received by S₂. The fraction of energy emitted by S₂that is received by S₁is,

(A) 0.05

(B) 0.1

(D) 0.6

18.

In film type condensation over a vertical tube, local heat transfer coefficient is

(A) inversely proportional to local film thickness

(B) directly proportional to local film thickness

(D) independent of local film thickness

19.

Ammonia (component 1) is evaporating from a partially filled bottle into surrounding air (component 2). The liquid level in the bottle and the concentration of ammonia at the top of the bottle are maintained constant. N_i is the molar flux relative to a fixed location in space and J_i is the molar flux with respect to the average molar velocity of the constituent species in the gas phase. Assume that air in the bottle is stagnant. Which ONE of the following is CORRECT?

(A) N₁ = constant, N₂ = 0, J₁+ J₂ = 0

(B) N₁+ N₂= 0, J₁+ J₂ = 0

(D) N₁ = constant, N₂ = 0, J₁= constant, J₂= 0

20.

Simultaneous heat and mass transfer is occurring in a fluid flowing over a flat plant. The flow is laminar. The concentration boundary layer will COINCIDE with the thermal boundary layer, when

(A) Sc = Nu

(B) Sh = Nu

(D) Sc = Pr

21.

Consider an irreversible, solid catalysed, liquid phase first order reaction. The diffusion and the reaction resistances are comparable. The overall rate constant (k_o) is related to the overall mass transfer coefficient (k_m) and the reaction rate constant (k) as

(A)

(B)

(C)

(D) k_o = k + k_m

22.

Reactant R forms three products X, Y and Z irreversibly, as shown below,

The reaction rates are given by r_X = k_X C_R , r_Y = k_Y and r_Z = k_Z C_R. The activation energies for formation of X, Y and Z are 40, 40 and 5 kJ/mol respectively. The pre-exponential factors for all reactions are nearly same. The desired conditions for MAXIMIZING the yield of X are

(A) high temperature, high concentration of R

(B) high temperature, low concentration of R

(D) low temperature, low concentration of R

23.

In an orifice meter, if the pressure drop across the orifice is overestimated by 5% then the PERCENTAGE error in the measured flow rate is

(A) + 2.47

(B) + 5

(D) – 5

24.

Two systems are available for compressing 6 m³ /hr of ambient air to 10 bar. The first one uses a single stage compressor (K1) and the second one uses a multistage compressor with inter-stage cooling (K2). Which ONE of the following statements is INCORRECT?

(A) K2 will have knockout pots in between the stages

(B) Discharge temperature of K1 will be higher than that of K2

(D) Cost of K2 will be more than that of K1

25.

In a thin-walled cylindrical vessel of thickness t with inside radius r, the internal gauge pressure is p. The hoop stress and the longitudinal stress in the shell are s_h and s_l respectively. Which ONE of the following statements is TRUE?

(A)

(B)

(C)

(D)

Q. 26 to Q. 55 carry two marks each

26.

Unit vectors in x and z directions areand respectively. Which ONE of the following is the directional derivative of the function F (x, z) = ln (x² + z²) at the point P: (4, 0), in the direction of ?)

(A)

(B)

(D)

27.

Which ONE of the following choices is a solution of the differential equation given below?

Note : c is a real constant

(A)

(B)

(C)

(D)

28.

The value of the improper integral is

(A) – 2p

(B) 0

(D) 2p

29.

Fuel cell stacks are made of NINE membrane electrode assembles (MEAs) interleaved between TEN bipolar plates (BPs) as illustrated below. The width of a membrane electrode assembly and a bipolar plate are normally distributed with μ_MEA = 0.15, σ_MEA = 0.01 and μ_BP = 5, σ_BP = 0.1 respectively. The widths of the different layers are independent of each other.

Which ONE of the following represents the CORRECT values of ( μ_stack, σ_stack) for the overall fuel cell stack width?

(A) (51.35, 0.32)

(B) (51.35, 1.09)

(D) (5.15, 0.11)

30.

In the fixed point iteration method for solving equations of the form x = g(x), the

(n +1)^th iteration value is x_n+1 =g(x_n), where x_n represents the n^th iteration value. g(x) and corresponding initial guess value x₀ in the domain of interest are shown in the following choices. Which ONE of these choices leads to a converged solution for x?

31.

Ammonia is synthesized at 200 bar and 773 K by the reaction N₂ + 3H₂ 2NH₃. The yield of ammonia is 0.45 mol/mol of fresh feed. Flow sheet for the process (along with available compositions) is shown below.

The single pass conversion for H₂ in the reactor is 20%. The amount of H₂ lost in the purge as a PERCENTAGE of H₂ in fresh feed is

(A) 10

(B) 20

(D) 55

32.

The following combustion reactions occur when methane is burnt.

CH₄ + 2O₂ → CO₂ + 2H₂O

2CH₄ + 3O₂ → 2CO + 4H₂O

20 % excess air is supplied to the combustor. The conversion of methane is 80 % molar ratio of CO to CO₂ in the flue gas is 1: 3. Assume air to have 80 mol % N₂ and rest O₂. The O₂ consumed as a PERCENTAGE of O₂ entering the combustor is

(A) 20

(B) 62.5

(D) 83.3

33.

Consider a binary mixture of methyl ethyl ketone (component 1) and toluene (component 2). At 323 K the activity coefficients γ₁ and γ₂ are given by

ln g₁ = (Ψ₁ – Ψ₂ + 4Ψ₂ x₁),

ln g₂ = (Ψ₁ + Ψ₂ – 4 Ψ₂ x₂)

where x₁ and x₂ are the mole fractions in the liquid mixture, and Ψ₁ and Ψ₂ are parameters independent of composition. At the same temperature, the infinite dilution activity coefficients, and are given by ln = 0.4 and ln = 0.2. The vapour pressure of methyl ethyl ketone and toluene at 323 K are 36.9 and 12.3 kPa respectively. Assuming that the vapour phase is ideal, the equilibrium pressure (in kPa) of a liquid mixture containing 90 mol % toluene is

(A) 19

(B) 18

(D) 15

34.

Two liquids (P and Q) having same viscosity are flowing through a double pipe heat exchanger as shown in the schematic below.

Densities of P and Q are 1000 and 800 kg/m³ respectively. The average velocities of the liquids P and Q are 1 and 2.5 m/s respectively. The inner diameters of the pipes are 0.31 and 0.1 m. Both pipes are 5 mm thick. The ratio of the Reynolds numbers Re_P to Re_Q is

(A) 2.5

(B) 1.55

(D) 4

35.

The particle size distributions of the feed and collected solids (sampled for same duration) for a gas cyclone are given below.

Size range (μm)	1–5	5–10	10–15	15–20	20–25	25–30
Weight of feed in the size range (g)	2.0	3.0	5.0	6.0	3.0	1.0
Weight of collected solids in the size range (g)	0.1	0.7	3.6	5.5	2.9	1.0

What is the collection efficiency (in PERCENTAGE) of the gas cyclone?

(A) 31 (B) 60 (C) 65 (D) 69

36.

A liquid is flowing through the following piping network. The length of pipe sections P, Q, R and S shown in the schematic are equal. The diameters of the sections P and R are equal and the diameter of the section Q is twice that of S. The flow is steady and laminar. Neglecting curvature and entrance effects, the radio of the volumetric flow rate in the pipe section Q to that in S is

(A) 16 (B) 8 (C) 2 (D) 1

37.

Oil at 120 °C is used to heat water at 30 °C in a 1–1 co-current shell and tube heat exchanger. The available heat exchange area is S₁. The exit temperatures of the oil and the water streams are 90 °C and 60 °C respectively. The co-current heat exchanger is replaced by a 1–1 counter -current heat exchanger having heat exchange area S₂. If the exit temperatures and the overall heat transfer coefficients are same, the ratio of S₁toS₂is

(A) ∞ (B) 1.1 (C) 0.91 (D) 0

38.

An aqueous sodium chloride solution (10 wt %) is fed into a single effect evaporator at a rate of 10000 kg/hr. It is concentrated to a 20 wt % sodium chloride solution. The rate of consumption of steam in the evaporation is 8000 kg/hr. The evaporator capacity (kg/hr) and economy are

(A) 5000, 0.625 (B) 10000, 0.625 (C) 5000, 1.6 (D) 10000, 1.6

39.

Heat is generated uniformly within a solid slab. The slab separates fluid 1 from fluid 2. The heat transfer coefficients between the solid slab and the fluids are h₁ and h₂ (h₂> h₁) respectively. The steady state temperature profile (T vs. x) for one-dimensional heat transfer is CORRECTLY shown by

40.

A gas mixture is in contact with a liquid. Component P in the gas mixture is highly soluble in the liquid. Possible concentration profiles during absorption of P are shown in the choices, where

x : mole fraction of P in bulk liquid

y : mole fraction of P in bulk gas,

x _i : mole fraction of P at the interface in liquid

y _i : mole fraction of P at the interface in gas

y* : equilibrium gas phase mole fraction corresponding to x _i

The CORRECT profile is

41.

A batch of 120 kg wet solid has initial moisture content of 0.2 kg water/kg dry solid. The exposed area for drying is 0.05 m²/kg dry solid. The rate of drying follows the curve given below.

The time required (in hours) for drying this batch to a moisture content of 0.1 kg water/kg dry solid is

(A) 0.033 (B) 0.43 (C) 0.6 (D) 2.31

For a first order catalytic reaction the Thiele modulus (f) of a spherical pellet is defined as

where, ρ_p = pellet density R_s = pellet radius

D_e = effective diffusivity k = first order reaction rate constant

If ф > 5, then the apparent activation energy (E_a) is related to the intrinsic (or true) activation energy (E) as

(A) E_a= E^0.5(B) E_a= 0.5 E (C) E_a= 2 E (D) E_a= E²

The following figures show the outlet tracer concentration profiles (c vs. t) for a pulse input.

Match the figures in Group I with the reactor configurations in Group II.

	GROUP I		GROUP II
P.	Figure 1	I.	PFR
Q.	Figure 2	II.	CSTR
R.	Figure 3	III.	PFR and CSTR in series
		IV.	PFR and CSTR in parallel

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

The following diagram shows a CSTR with two control loops. A liquid phase, endothermic reaction is taking place in the CSTR, and the system is initially at steady state. Assume that the changes in physical properties of the system are negligible.

TC: Temperature controller, LC: Level controller, TT: Temperature transmitter, LT: Level transmitter, V₁ and V₂: Control valves.

Which ONE of the following statements is TRUE?

(A) Changing the level controller set point affects the opening of V₂ ONLY

(B) Changing the temperature controller set point affects the opening of V₂ ONLY

(D) Changing the level controller set point affects the opening of BOTH V₁and V₂

A process plant has a life of 7 years and its salvage value is 30 %. For what MINIMUM fixed-percentage factor will the depreciation amount for the second year, calculated by declining balance method be EQUAL to that calculated b the straight line depreciation method?

(A) 0.1 (B) 0.113 (C) 0.527 (D) 0.887

A continuous fractionator system is being designed. The following cost figures are estimated for a reflux ratio of 1.4.

Fixed cost including all accessories (Rs.) for			Operating cost (Rs./year) for
Column	Condenser	Reboiler	Condenser cooling water	Reboiler heating steam
6 ´ 10⁶	2 ´ 10⁶	4 ´ 10⁶	8 ´ 10⁶	1 ´ 10⁶

The annualized fixed charge is 15 % of the fixed cost. The total annualized cost (in Rs.) is

(A) 10.8 × 10⁶ (B) 13.35 × 10⁶

Match the reactions in Group I with the products in Group II.

	GROUP I		GROUP II
P.	Ammoxidation	I.	Aniline from benzene
Q.	Nitration	II.	Benzoic acid from toluene
R.	Dehydrogenation	III.	Acrylonitrile from propylene
S.	Oxidation	IV.	Styrene from ethylbenzene

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

Common Data Questions

Common Data for Questions 48 and 49 :

For a liquid flowing through a packed bed, the pressure drop per unit length of the bed is

where, is the superficial liquid velocity, ε is the bed porosity, is average particle size, f_s is particle sphericity, r_f is liquid density and μ_f is liquid viscosity.

Given data : = 1 × 10^–3 m, f_s = 0.8_, ρ_f = 1000 kg/m³, μ_f= 1 x 10^–3 kg m^–1 s^–1,

particle density, r_p = 2500 kg/m³ and acceleration due to gravity, g = 9.8 m/s²

When is 0.005 m/s and ε = 0.5, which ONE of the following is the CORRECT value for the ratio of the viscous loss to the kinetic energy loss?

(A) 0.09 (B) 1.07 (C) 10.71 (D) 93

On further increasing, incipient fluidization is achieved. Assuming that the porosity of the bed remains unaltered, the pressure drop per unit length (in Pa/m) under incipient fluidisation condition is

(A) 3675 (B) 7350 (C) 14700 (D) 73501

Common Data for Questions 50 and 51 :

A binary feed mixture containing equimolar quantities of components S and T is to be distilled in a fractionating tower at atmospheric pressure. The distillate contains 96 mol % S. The q-line (feed line) intersects the equilibrium line at x¢ = 0.46 and y¢ = 0.66, where x¢ and y¢ are mole fractions. Assume that the McCabe-Thiele method is applicable and the relative volatility is constant.

The MINIMUM reflux ratio is

(A) 1.6 (B) 1.5 (C) 0.66 (D) 0.6

The feed is

(A) at dew point (B) at bubble point

Linked Answer Questions

Linked Answer Questions 52 and 53 :

In an aqueous solution, reaction P → Q occurs under isothermal conditions following first order kinetics. The feed rate is 500cm³/min and concentration of P in the feed is

1.5 x 10^–4mole/cm³. The reaction is carried out in a 5 litre CSTR. At steady state, 60 % conversion is observed. The rate constant (in min^–1) is

(A) 0.06 (B) 0.15 (C) 0.21 (D) 0.28

The 5 litre CSTR is replaced by five CSTRs in series. If the capacity of each new CSTR is 1 litre, then the overall conversion (in %) is

(A) 65 (B) 67 (C) 73 (D) 81

Statement for Linked Answer Questions 54 and 55 :

A PID controller output p(t), in time domain, is given by

where e(t) is the error at time t. The transfer function of the process to be controlled is . The measurement of the controlled variable is instantaneous and accurate.

The transfer function of the controller is

(A)

(B)

(C)

(D)

The characteristic equation of the closed loop is

(A) 6s² + 102s +1 = 0 (B) 700s² + 102s + 25 = 0

General Aptitude (GA) Questions

Q. 56 – Q. 60 carry one mark each.

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

I contemplated ________ Singapore for my vacation but decided against it.

(A) to visit (B) having to visit

If Log (P) = (1/2) Log (Q) = (1/3) Log (R), then which of the following options is TRUE?

(A) P² = Q³ R² (B) Q² = P R

Which of the following options is the closest in the meaning to the word below :

Inexplicable

(A) Incomprehensible (B) Indelible

Choose the word from the options given below that is most nearly opposite in meaning to the given world :

Amalgamate

(A) merge (B) split

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

If you are trying to make a strong impression on your audience, you cannot do so by being understated, tentative or __________

(A) hyperbolic (B) restrained

Q. 61 to Q. 65 carry two marks each.

The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V + F)?

(A) 5 (B) 4 (C) 7 (D) 6

P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below:

A pharmaceutical company is contemplating the developing of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

(A) P (B) Q (C) R (D) S

Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting.

Based on the above passage which topic would not be included in a unit on bereavement?

(A) how to write a letter of condolence

(B) what emotional stages are passed through in the healing process

(D) how to give support to a grieving friend

A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?

(A) 7.58 litres (B) 7.84 litres (C) 7 litres (D) 7.29 litres

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4^th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10^th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5^th day?

(A) 4 (B) 5 (C) 6 (D) 7

End of Question Paper