GATE question papers: Chemical Engineering 2009 (CH)

Q. 1 - Q. 20 carry one mark each.

1. The direction of largest increase of the function xy³ - x² at the point (1, 1) is

(A) (B) (C) (D)

2. The modulus of the complex number is

(A) (B) (C) 1 (D)

3. The system of linear equations Ax = 0, where A is an n ´ n matrix, has a non-trivial solution ONLY if

(A) rank of A > n (B) rank of A = n

4. A dehumidifier (shown below) is used to completely remove water vapor from air.

Which ONE of the following statement is TRUE?

(A) Water is the ONLY tie component

(B) Air is the ONLY tie component

(D) There are no tie components

5. Dehydrogenation of ethane, C₂H₆ (g) ® C₂H₄ (g) + H₂ (g), is carried out in a continuous stirred tank reactor (CSTR). The feed is pure ethane. If the reactor exit stream contains unconverted ethane along with the product, then the number of degrees of freedom for the CSTR is

(A) 1 (B) 2 (C) 3 (D) 4

6. An ideal gas at temperature T₁ and pressure P₁ is compressed isothermally to pressure P₂ (> P₁( in a closed system. Which ONE of the following is TRUE for internal energy (U) and Gibbs free energy (G) of the gas at the two states?

(A) U₁ = U₂, G₁ > G₂ (B) U₁ = U₂, G₁ < G₂

7. Under fully turbulent flow conditions, the frictional pressure drop across a packed bed varies with the superficial velocity (V) of the fluid as

(A) V^-¹ (B) V (C) V^3/2(D) V²

8. For a mixing tank operating in the laminar regime, the power number varies with the Reynolds number (Re) as

(A) Re^-^1/2(B) Re^1/2(C) Re (D) Re^-¹

9. During the transient convective cooling of a solid object, Biot number ® 0 indicates

(A) uniform temperature throughout the object

(B) negligible convection at the surface of the object

(D) significant temperature gradient within the object

10. The Prandtl number of a fluid is the ratio of

(A) thermal diffusivity to momentum diffusivity

(B) momentum diffusivity to thermal diffusivity

(D) thermal diffusivity to kinematic viscosity

11. According to the penetration theory of mass transfer, the mass transfer coefficient (k) varies with diffusion coefficient (D) of the diffusing species as

(A) D (B) D^-^1/2(C) D^1/2(D) D^3/2

12. The ratio of the liquid to gas flow rate in a counter-current gas absorption column is increased, at otherwise identical conditions. Which ONE of the following statements is TRUE?

(A) The operating line shifts towards the equilibrium curve

(B) The operating line shifts away from the equilibrium curve

(D) The operating line does not shift

13. For a homogenous reaction system, where

C_j is the concentration of j at time t

N_j is the number of moles of j at time t

V is the reaction volume at time t

t is the reaction time

The rate of reaction for species j is defined as

(A) (B) (C) (D)

14. The half-life of a first order liquid phase reaction is 30 seconds. Then the rate constant, in min^-¹, is

(A) 0.0231 (B) 0.602 (C) 1.386 (D) 2.0

15. For a solid-catalyzed reaction, the Thiele modulus is proportional to

(A) (B)

16. Which ONE of the following sensors is used for the measurement of temperature in combustion process (T > 1800°C)?

(A) Type J thermocouple (B) Thermistor

17. The roots of the characteristic equation of an underdamped second order system are

(A) real, negative and equal (B) real, negative and unequal

18. The total fixed cost of a chemical plant is Rs. 10.0 lakhs; the internal rate of return is 15%, and the annual operating cost is Rs. 2.0 lakhs. The annualized cost of the plant (in lakhs of Rs.) is

(A) 1.8 (B) 2.6 (C) 3.5 (D) 4.3

19. In petroleum refining operations, the process used for converting paraffins and naphthenes to aromatics is

(A) catalytic reforming (B) catalytic cracking

20. The active component of catalysts use in steam reforming of methane to produce synthesis gas is

(A) Nickel (B) Iron (C) Platinum (D) Palladium

Q. 2 1 to Q. 60 carry two marks each.

21. The value of the limit is

(A) -¥ (B) 0 (C) 1 (D) ¥

22. The general solution of the differential equation

-6y = 0,

with C₁ and C₂ as constants of integration, is

(A) C₁ e^-^3x + C₂ e^-^2x(B) C₁ e^3x + C₂ e^-^2x

23. Using the residue theorem, the value of the integral (counterclockwise)

around a circle with center at z = 0 and radius = 8 (where z is a complex number and i = , is

(A) -20p i (B) -40p (C) -40pi (D) 40pi

24. Consider the integral

over the surface a sphere of radius = 3 with center at the origin, and surface unit normal pointing away from the origin. Using the Gauss divergence theorem, the value of this integral is

(A) -180 p (B) 0 (C) 90p (D) 180p

25. Using the trapezoidal rule and 4 equal intervals (n = 4), the calculated value of the integral (rounded to the first place of decimal) is

(A) 1.7 (B) 1.9 (C) 2.0 (D) 2.1

26. The eigenvalues of matrix A = and 5 and -1. Then the eigenvalues of -2A + 3I (I is a 2 ´ 2 identity matrix) are

(A) -7 and 5 (B) 7 and -5 (C) - and (D) and -

27. A fair die is rolled. Let R denote the event of obtaining a number less than or equal to 5 and S denote the event of obtaining an odd number. Then which ONE of the following about the probability (P is TRUE?

(A) P (R / S) = 1 (B) P (R/S) = 0 (C) P(S/R) = 1 (D) P(S/R) = 0

28. Pure water (stream W) is to be obtained from a feed containing 5 wt % salt using a desalination unit as shown below

If the overall recovery of pure water (through stream W) is 0.75 kg/kg feed, then the recycle ratio (R/F is

(A) 0.25 (B) 0.5 (C) 0.75 (D) 1.0

29. For a binary mixture at constant temperature and pressure, which ONE of the following relations between activity coefficient (g_i) and mole fraction (x_i) is thermodynamically consistent?

(A) ln g₁ = -1 + 2x₁ - , ln g₂ = (B) ln g₁ = -1 + 2x₁ - , ln g₂ =

30. Two identical reservoirs, open at the top, are drained through pipes attached to the bottom of the tanks as shown below. The two drain pipes are of the same length, but of different diameters (D₁ > D₂)

Assuming the flow to be steady and laminar in both drain pipes, if the volumetric flow rate in the larger pipe is 16 times of that in the smaller pipe, the ratio D₁/D₂ is

(A) 2 (B) 4 (C) 8 (D) 16

31. For an incompressible flow, the x- and y-components of the velocity vector are

v_x = 2(x + y); v_y = 3 (y + z)

where x, y, z are in metres and velocities are in m/s. Then the z-component of the velocity vector (v_z) of the flow for the boundary condition v_z = 0 at z = 0 is

(A) 5z (B) -5z (C) 2x + 3z (D) -2x - 3z

32. The terminal settling velocity of a 6 mm diameter glass sphere (density: 2500 kg/m³) in a viscous Newtonian liquid (density: 1500 kg/m³) is 100 mm/s. If the particle Reynolds number is small and the value of acceleration due to gravity is 9.81 m/s², then the viscosity of the liquid (in Pa×s) is

(A) 100 (B) 196.2 (C) 245.3 (D) 490.5

33. A well-insulated hemispherical furnace (radius = 1m) is shown below: The self-view factor of radiation for the curved surface 2 is

(A) 1/4 (B) 1/2 (C) 2/3 (D) 3/4

34. A double-pipe heat exchanger is to be designed to heat 4 kg/s of a cold feed from 20 to 40°C using a hot stream available at 160°C and a flow rate of 1 kg/s. The two streams have equal specific heat capacities and the overall heat transfer coefficient of the heat exchanger is 640 W/m² × K. Then the ratio of the heat transfer areas required for the co-current to counter-current modes of operation is

(A) 0.73 (B) 0.92 (C) 1.085 (D) 1.25

35. For the composite wall shown below (case 1) the steady state interface temperature is 180 °C. If the thickness of layer P is doubled (Case 2), then the rate of heat transfer (assuming 1-D conduction) is reduced by

(A) 20% (B) 40% (C) 50% (D) 70%

36. Species A is diffusing at steady state from the surface of a sphere (radius = 1 cm) into a stagnant fluid. If the diffusive flux at a distance r = 3 cm from the center of the sphere is 27 mol/cm²×s, the diffusive flux (in mol/cm²×s) at a distance r = 9 cm is

(A) 1 (B) 3 (C) 9 (D) 27

37. The feed to a binary distillation column has 40 mol % vapor and 60 mol % liquid. Then, the slope of the q-line in the McCabe-Thiele plot is

(A) -1.5 (B) -0.6 (C) 0.6 (D) 1.5

38. The equilibrium moisture curve for a solid is shown below:

The total moisture content of the solid is X and it is exposed to air of relative humidity H. In the table below, Group I lists the types of moisture, and Group II represents the region in the graph above.

Group I Group II

P. Equilibrium moisture 1

Q. Bound moisture 2

R. Unbound moisture 3

S. Free moisture 4

Which ONE of the following is the correct match?

(A) P - 1, Q - 2, R - 3, S - 4 (B) P - 1, Q - 3, R - 4, S - 2

39. The liquid-phase reaction A ® B is conducted in an adiabatic plug flow reactor.

Date:

Inlet concentration of A = 4.0 kmol/m³

Density of reaction mixture (independent of temperature) = 1200 kg/m³

Average heat capacity of feed stream (independent of temperature) = 2000 J/kg×K

Heat of reaction (independent of temperature) = -120 kJ/mol of A reacting

If the maximum allowable temperature in the reactor is 800 K, then the feed temperature (in K) should not exceed

(A) 400 (B) 500 (C) 600 (D) 700

40. An isothermal pulse test is conducted on a reactor and the variation of the outlet tracer concentration with time is shown below:

The mean residence time of the fluid in the reactor (in minutes) is

(A) 5.0 (B) 7.5 (C) 10.0 (D) 15.0

41. The inverse Laplace transform of is

(A) e^-^t/2 - e^-^t(B) 2e^-^t/2 - e^-^t

42. The characteristic equation of a closed loop system using a proportional controller with gain K_c is

12s³ + 19s² + 8s + 1 + K_c = 0

At the onset of instability, the value of K_c is

(A) 35/3 (B) 10 (C) 25/3 (D) 20/3

43. The block diagram for a control system is shown below:

For a unit step change in the set point, R(s), the steady state offset in the output Y(s) is

(A) 0.2 (B) 0.3 (C) 0.4 (D) 0.5

44. For a tank of cross-sectional area 100 cm² and inlet flow rate (Q_i in cm³/s), the outlet flow rate (Q_o in cm³/s) is related to the liquid height (H in cm) as Q_o = 3 (see figure below).

Then the transfer function (overbar indicates deviation variables) of the process around the steady-state point, Q_{i, s} = 18 cm³/s and H_s = 36 cm, is

(A) (B)

45. A column costs Rs. 5.0 lakhs and has a useful life of 10 years. Using the double declining balance depreciation method, the book value of the unit at the end of five years (in lakhs of Rs.) is

(A) 1.21 (B) 1.31 (C) 1.64 (D) 2.05

46. An equi-molar mixture of four hydrocarbons (1, 2, 3, 4) is to be separated into high purity individual components using a sequence of simple distillation columns (one overhead and one bottom steam). Four possible schemes are shown below.

Component K_i

1 6

2 3

3 2.5

4 1.1

Using the K_i (=) values given above, the optimal scheme is

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

47. Match the equipment in Group I to the internals in Group II.

Group I Group II

P. Centrifugal pump 1. Baffle

Q. Distillation column 2. Impeller

R. Heat exchanger 3. Tray

R. Heat exchanger 4. Volute

(A) P - 2, Q - 1, R - 4 (B) P - 2, Q - 4, R - 3

48. Match the product in Group I with the name of the process in Group II

Group I Group II

P. Sodium carbonate 1. Haber

Q. Ammonia 2. Solvay

R. Sulphuric acid 3. Fischer-Tropsch

4. Contact

(A) P - 2, Q - 1, R - 4 (B) P - 4, Q - 1, R - 2

49. Match the product in Group I to the raw material in Group II.

Group I Group II

P. Ethylene 1. Natural gas

Q. Methanol 2. Synthesis gas

R. Phthalic anhydride 3. Naphtha

4. Naphthalene

(A) P - 1, Q - 2, R - 3 (B) P - 2, Q - 1, R - 4

50. Match the unit process in Group I with the industry in Group II

Group I Group II

P. Steam cracking 1. Petroleum refining

Q. Hydrocracking 2. Petrochemicals

R. Condensation 3. Polymers

4. Soaps and detergents

(A) P - 1, Q - 2, R - 3 (B) P - 2, Q - 3, R - 3

Common Data for Questions 51 and 52:

An ideal gas with molar heat capacity C_p = R (where R = 8.314 J/mol×K) is compressed adiabatically from 1 bar and 300 K to pressure P₂ in a closed system. The final temperature after compression is 600 K and the mechanically efficient of compression is 50%.

51. The work required for compression (in kJ/mol) is

(A) 3.74 (B) 6.24 (C) 7.48 (D) 12.48

52. The final pressure P₂ (in bar) is

(A) 2^3/4(B) 2^5/4(C) 2^3/2(D) 2^5/2

Common Data for Questions 53 and 54:

A slab of thickness L with one side (x = 0) insulated and the other side (x = L) maintained at a constant temperature T₀ is shown below.

A uniformly distributed internal heat source produces heat in the slab at the rate of SW/m³. Assume the heat conduction to be steady and 1-D along the x-direction.

53. The maximum temperature in the slab occurs at x equal to

(A) 0 (B) L/4 (C) L/2 (D) L

54. The heat flux at x = L is

(A) 0 (B) S L/4 (C) S L/2 (D) S L

Common Data for Questions 55 and 56:

A flash distillation drum (see figure below) is used to separate a methanol-water mixture. The mole fraction of methanol in the feed is 0.5, and the feed flow rate is 1000 kmol/hr. The feed is preheated in a heater with heat duty Q_h and is subsequently flashed in the drum. The flash drum can be assumed to be an equilibrium stage, operating adiabatically. The equilibrium relation between the mole fractions of methanol in the vapor and liquid phases is = 4x. The ratio of distillate to feed flow rate is 0.5.

55. The mole fraction of methanol in the distillate is

(A) 0.2 (B) 0.7 (C) 0.8 (D) 0.9

56. If the enthalpy of the distillate with reference to the feed is 3000 kJ/kmol, and the enthalpy of the bottoms with reference to the feed is -1000 kJ/kmol, the heat duty of the preheater (Q_h in kJ/hr) is

(A) -2 ´ 10⁶ (B) -1 ´ 10⁶(C) 1 ´ 10⁶ (D) 2 ´ 10⁶

Linked Answer Questions

Statement for Linked Answer Questions 57 and 58:

A free jet of water is emerging from a nozzle (diameter 75 mm) attached to a pipe (diameter 225 mm) as shown below.

The velocity of water at point A is 18 m/s. Neglect frition in the pipe and nozzle. Use g = 9.81 m/s² and density of water = 1000 kg/m³.

57. The velocity of water at the tip of the nozzle (in m/s) is

(A) 13.4 (B) 18.0 (C) 23.2 (D) 27.1

58. The gauge pressure (in kPa) at point B is

(A) 80.0 (B) 100.0 (C) 239.3 (D) 367.6

Statement for Linked Answer Questions 59 and 60.

The liquid-phase reaction A ® B + C is conducted isothermally at 50°C in a continuous stirred tank reactor (CSTR). The inlet concentration of A is 8.0 gmol/liter. At a space time of 5 minutes, the concentration of A at the exit of CSTR is 4.0 gmol/liter. The kinetics of the reaction is