Gate - 2006 PDF
Gate - 2006 PDF
Gate - 2006 PDF
CHEMICAL ENGINEERING
ONE MARKS QUESTIONS (1-20) fraction of the heat supplied that is
converted to work is
a. 0.2
1. The ordinary differential equation dy/dt =
b. 0.3
f(Y) is solved using the approximation Y(t
c. 0.4
+ Δt) = Y(t) + f[Y(t)] Δt. The numerical
d. 0.6
en-or introduced by the approximation at
7. For the isentropic expansion of an ideal
each step is
gas from the initial conditions P1, T1 to the
a. proportional to Δt final conditions P2, T2, which ONE of the
b. proportional to (Δt)2 following relations is valid ? (γ = Cp/Cv)
c. independent of Δt γ
⎛ P ⎞ ⎛T ⎞
d. proportional to (1/Δt) a. ⎜ 1 ⎟ = ⎜ 2 ⎟
2. The trapezoidal rule of integration when ⎝ P2 ⎠ ⎝ T1 ⎠
b γ
applied to ∫ f ( x)dx
a
will give the exact ⎛ P ⎞ ⎛ T ⎞ γ −1
b. ⎜ 1 ⎟ = ⎜ 1 ⎟
value of the integral ⎝ P2 ⎠ ⎝ T2 ⎠
a. if f(x) is a linear function of x ⎛ P ⎞ ⎛T ⎞
c. ⎜ 1 ⎟ = ⎜ 1 ⎟
b. if f(x) is a quadratic function of x
⎝ P2 ⎠ ⎝ T2 ⎠
c. for any f(x) γ −1
d. for no f(x) ⎛ P ⎞ ⎛T ⎞ γ
3. The value of α for which the following d. ⎜ 1 ⎟ = ⎜ 1 ⎟
three vectors are coplanar is ⎝ P2 ⎠ ⎝ T2 ⎠
a = i + 2j + k 8. Match the following for a centrifugal
b = 3j + k pump with impeller speed n
c = 2i + αj List I
a. 4 A. Capacity
b. zero B. Head
c. –2 List II
d. –10 1. proportional to n
4. The derivative of |x| with respect to x 2. proportional to n2
3. proportional to n3
when x≠0 is
A B
a. |x|/x
a. 2 1
b. –1
b. 1 3
c. 1
c. 2 3
d. Undefined
d. 1 2
5. At a given temperature and pressure, a
liquid mixture of benzene and toluene is in 9. The magnitude of the force (in N) required
equilibrium with its vapor. The available to hold a body of volume 0.05 m3 and
degree(s) of freedom is (are) mass 40kg in water (density 1000 kg/m3)
a. Zero at a depth of 0.1 m is (g = 9.81 m/s2)
a. Zero
b. 1
c. 2 b. 98.1
d. 3 c. 490.5
6. A heat engine operates at 75% of the d. 882.9
maximum possible efficiency. The ratio of 10. A stagnant liquid film of 0.4 mm thickness
the heat source temperature (in K) to the is held between two parallel plates. The
heat sink temperature (in K) is 5/3. The top plate is maintained at 40°C and the
bottom plate is maintained at 30°C. If the
thermal conductivity of the liquid is 0.14
2 of 12
W/(m K), then the steady state heat flux 15. An irreversible gas phase reaction A → 5B
(in W/m2) assuming one dimensional heat is conducted in an isothermal batch reactor
transfer is at constant pressure in the presence of an
a. 3.5 inert. The feed contains no B. If the
b. 350 volume of the gas at complete conversion
c. 3500 must not exceed three times the initial
d. 7000 volume, the minimum mole percent of the
11. Let dh be the hydrodynamic entrance inert in the feed must be
length for mercury in laminar flow in a a. 0
pipe under isothermal conditions. Let dt, b. 20
be its thermal entrance length under fully c. 33
developed hydrodynamic conditions. d. 50
Which ONE of the following is TRUE? 16. A first order reversible reaction
a. dh > dt
b. dh < dt
c. dh = dt
d. dh < dt only if the pipe is vertical occurs in a batch reactor. The exponential
12. The Boussinesq approximation for the decay of the concentration of A has the
fluid density in the gravitational force term time constant
is given by ONE of the following (ρref is 1
a.
the fluid density at the reference k1
temperature Tref , and β is the thermal 1
coefficient of volume expansion at Tref) b.
k2
a. ρ = ρ ref + Tref β ( ρ − ρ ref ) 1
c.
b. ρ = ρ ref − Tref β ( ρ − ρ ref ) k1 − k2
c. ρ = ρ ref − Tref β (T − Tref ) d.
1
k1 + k2
d. ρ = ρ ref − Tref ( ρ − ρ ref ) + ρ ref (T − Tref ) / Tref
17. If the absolute error in the measurement of
13. The reaction 2A + B → 2C occurs on a A is ΔA and the absolute error in the
catalyst surface. The reactants A and B measurement of B is ΔB, then the absolute
diffuse to the catalyst surface and get error in the estimate of A – B is
converted completely to the product C, a. ΔA+ΔB
which diffuses back. The steady state b. ΔA − ΔB
molar fluxes of A, B and C are related by ΔA ΔB
a. NA = 2NB = NC c. +
A B
b. NA = –(1/2) NB = –NC
ΔA ΔB
c. NA = 2NB – NC d. −
d. NA = (1/2) NB = NC A B
14. An ideal single stage extraction process is 18. The oxo reaction is used for converting
used to treat 100 molls of an organic feed a. alcohol to aldehyde
solution. The solution concentration in this b. paraffin to olefin
solution is to be reduced from 0.5 mol% to c. olefin to aldehyde
0.1 mol%. A pure solvent S is used. To d. aldehyde to alcohol
reduce the solvent requirement by half for 19. In a fluid catalytic cracking unit, the nature
the same separation, of the reactions occurring in the reactor
a. add one more ideal co-current stage and the regenerator is
b. use another pure solvent S* whose a. Reactor-Exothermic, Regenerator-
partition coefficient is twice that of S Exothermic
c. use solvent S containing 0.02 mole b. Reactor-Exothermic, Regenerator-
fraction of the solute Endothermic
d. double the residence time of the c. Reactor-Endothermic, Regenerator-
solvent S in the contactor Exothermic
3 of 12
d. Reactor-Endothermic, Regenerator- d. 2
Endothermic 24. Determine the following integral
20. The control valve characteristics for three I = ∫ r.dS
types of control valves (P. Q and R) are S
given in the figure below : Match the where r is the position vector field (r = ix +
control valve with its characteristics. jy + kz) and S is the surface of a sphere of
radius R
a. 4πR2
3 2
b. πR
4
c. πR2
d. 4πR3
25. The liquid surface in a cylindrical bucket
of radius R rotating about its axis acquires
a. P – Quick opening, Q – Linear, R – a parabolic profile given by the equation y
Equal percentage = a + br2, where y is the height of the
b. P – Linear, Q – Square root, R – Equal liquid surface from the bottom of the
percentage bucket at a radial distance r from the
c. P – Equal percentage, Q – Linear, R – bucket axis. If the liquid has density ρ.
Quick opening then the mass of the liquid in the bucket is
d. P – Square root, Q – Quick opening, R ⎛ a + bR 2 ⎞
– Linear a. πρ R 2 ⎜ ⎟
⎝ 2 ⎠
⎛ bR 2 ⎞
TWO MARKS QUESTIONS (21-75) b. πρ R 2 ⎜ a + ⎟
⎝ 2 ⎠
21. If the following represents the equation of c. πρ R 2 a
a line d. πρ R 2 ( a + bR 2 )
x 2 4
26. The solution to the following equation is
y 8 0 =0
d3y d2y dy
1 1 1 x2 3 + 2x 2 − 2 = 0
dx dx dx
then the line passes through the point is given by
a. (0, 0) a. y = C1x + C2x–2 + C3
b. (3, 4) b. y = C1x2 + C2x–2 + C3
c. (4, 3) c. y = C1x2 + C2x–1 + C3
d. (4, 4) d. y = C1x + C2x–1 + C3
⎡ 2 1⎤ 27. The value of the contour integral
22. If A = ⎢ ⎥ , then the eigenvalues of A3 where C is the circle |z| = 2 is
⎣ 2 3⎦
1
are a.
a. 27 and 8 2e
b. 64 and 1 1⎛1 1 ⎞
b. ⎜ − ⎟
c. 12 and 3 2 ⎝ e e3 ⎠
d. 4 and 1 c. zero
23. With y = eax, if the sum 1
d.
S=
dy d 2 y
+ 2 + ... + n
dny ( 2π i ) e3
dx dx dx 28. The Newton-Raphson method is used to
approaches 2y as n → ∞, then the value of
solve the equation, ( x − 1) + x − 3 = 0 . The
2
a is
a. 1/3 method will fail in the very first iteration if
b. 1/2 the initial guess is
c. 2/3 a. Zero
4 of 12
b. 0.5 d. 2 1 2 1
c. 1 32. For a reversible exothermic gas phase
d. 3 reaction, A + B U C, the equilibrium
29. A pair of fair dice is rolled three times. conversion will increase with
What is the probability that 10(sum of the a. increase in pressure and increase in
numbers on the two faces) will show up temperature
exactly once ? b. decrease in pressure and increase in
121 temperature
a.
1728 c. increase in pressure and decrease in
363 temperature
b. d. decrease in pressure and decrease in
1728
121 temperature
c. 33. For a binary mixture of A and B at 400 K
576 and 1 atm, which ONE of the following
363 equilibrium states deviates significantly
d.
576 from ideality?
30. A company purchased components from Given:
three firms P, Q, and R as shown in the
ln ( PAsat ) = 6.2 −
2758
table below : T
Firm Total number Number of where
of components components PAsat = vapor pressure of A, atm; T =
purchased likely to be temperature, K
defective PA = partial pressure of A, atm
P 1000 5 xA = mole fraction of A in liquid; yA =
Q 2500 5 mole fraction of A in vapor
a. xA = 0.5; yA = 0.25
R 500 2
b. xA = 0.5; pA = 0.25
The components are stored together. One c. xA = 0.5; pA = 0.5
of the components is selected at random d. xA = 0.6; yA = 0.3
and found to be defective. What is the 34. Pure A at 200°C is fed to a steady slate
probability that it was supplied by Firm R? adiabatic continuous reactor at the rate of
1 100 kg/hr where it undergoes an
a.
250 exothermic reaction to give its isomer B.
1 The product stream is at temperature
b.
12 500°C. The heat of reaction is 21 kJ/mol
1 of A and the specific heat of the reaction
c. mixture is constant at 35 J/(mol °C). The
8
conversion in the reactor is
1
d. a. 25%
6 b. 50%
31. Match the following: c. 75%
List I d. 100%
A. Heat 35. The molar density of water vapor at the
B. Internal energy normal boiling point of water is 33
C. Work mol/m3. The compressibility factor under
D. Entropy these conditions is close to which ONE of
List II the following? R = 8.314 J/(mol K)
1. State Function a. 0.75
2. Path Function b. 1
A B C D c. 1.25
a. 2 1 1 1 d. 1.5
b. 2 1 2 2 36. A liquid is pumped at the flow rate Q
c. 2 2 1 1 through a pipe of length L. The pressure
5 of 12
drop of the fluid across the pipe is Δ P. unit length is directly proportional to the
Now a leak develops at the mid-point of fluid velocity
the length of the pipe and the fluid leaks at a. 0.70
the rate of Q/2. Assuming that the friction b. 0.90
factor in the pipe remains unchanged, the c. 1.00
new pressure drop across the pipe for the d. 1.46
same inlet flow rate (Q) will be 40. Two spherical particles have the same
a. (1/2) ΔP outer diameter but are made of different
b. (5/8) ΔP materials The first one (with material
c. (3/4) ΔP density ρ1) is solid, whereas the second
d. ΔP (with material density ρ2) is a hollow
37. In a laminar flow through a pipe of radius sphere with the inner shell diameter equal
R, the fraction of the total fluid flowing to half the outer diameter. If both the
through a circular cross-section of radius spheres have the same terminal velocity in
R/2 centered at the pipe axis is any fluid, then the ratio of their material
a. 3/8 densities, ρ2/ρ1 , is
b. 7/16 a. 1
c. 1/2 b. 8/7
d. 3/4 c. 2
38. A fluid obeying the constitutive equation d. 8
1 41. A filtration is conducted at constant
⎛ dv ⎞ 2 pressure to recover solids from dilute
τ = τ 0 + K ⎜ x ⎟ ,τ > τ 0
⎝ dy ⎠ slurry. To reduce the time of filtration, the
is held between two parallel plates a solids concentration in the feed slurry is
distance d apart. If the stress applied to the increased by evaporating half the solvent.
top plate is 3τ0, then the velocity with If the resistance of the filter medium is
which the top plate moves relative to the negligible, the filtration time will be
bottom plate would be reduced by a factor of
a. 1
⎛τ ⎞
2
a. 2 ⎜ 0 ⎟ d b. 2
⎝K⎠ c. 4
⎛τ ⎞ d. 8
2