8/10/2019 GATE 1990

1/12

GATE 1990

CHEMICAL ENGINEERING

Time All owed: 3 Hours Maximum Marks:

200

Instructions:

1.

For full credit, answer all questions. 2. There will be no negative marking.

------------------------------------------------------------------------------------------------------------

SECTION A

1)

(i). A mixture of Ethyl Acetate vapor and air has a relative saturation of 50 percent at

30 C and a total pressure of 100 kN / m2. If the vapor pressure of Ethyl Acetate at

30 C is 16 kN / m3,

(a). The percentage of air is

.

(b). The molal saturation is

..

(ii). The following data on heats of combustion at 25 C are given

Compound Heat of combustion at 25 C

--------------- -----------------------------------

n-Heptane C7H10 (g) - 4850 kJ / mol

Ethyl Alcohol C2H5OH (g) - 1410 kJ / mol

Heats of formation of CO2 (g) and H2O (l) are -380 kJ / mol and 280 kJ / mol

respectively.

(a). The heat of formation of gaseous n-Heptane at 25 C is

(b). The heat of formation of gaseous Ethyl Alcohol at 25 C is

2.

(i). The viscosity of CO at 1 bar and 27 C is 0.000015 Ns/m2. Estimate the viscosity of

CO at 1 bar and

327 C.

(ii). The hydraulic mean diameter of the annular space between pipes of diameter 0.4 m

and 0.6 m is

8/10/2019 GATE 1990

2/12

(iii). Bernoullis equation for steady frictionless flow states that, along a streamline,

(A) Total pressure is constant

(B) Total mechanical energy is constant

(C) Velocity head is constant

(D) None of the above

(iv). The pressure drop required for fluidizing a coal bed with a liquid petroleum fraction

of viscosity 0.015 Ns/m2is 103N/m3. The pressure drop is required for fluidizing the

same bed with an oil of viscosity 0.03

Ns/m2is

3.

(i). In a gyratory crusher size reduction is effected primarily by:

(A) Compression

(B) Impact

(C) Attrition

(D) Cutting action

(ii). In power correlations for agitated vessels the effect of Froude number appears:

(A) For baffled vessels and when Reynolds number is less than 300.

(B) For unbaffled vessels and Reynolds number is greater than 300.

(C) When there is no vortex formation.

(D) When Reynolds number is less than300.

(iii). Two very small silica particles are settling at their respective terminal velocities

through a highly viscous oil column. If one particle is twice as large as the other, the

larger particle will take the time taken by the smallest particle to fall through

the same height.

(iv). To increase the capacity of a commercial packed bed absorber, the volumetric flow

rate of gas entering is increased by 20%. The ratio of pressure drops (new to old) is

4.

(i). A water droplet at 25 C is suddenly introduced into an infinite gas medium at

100 saturated with water vapor. At steady state,

(A) The drop attains wet bulb temperature and vanishes.

(B) The dimensions of the drop remain unaltered and it attains a temperature of

100 C throughout.

(C) The drop increases in size and it attains a temperature of 100 C throughout.

(D) None of above.

(ii). In a finned tube heat exchanger:

8/10/2019 GATE 1990

3/12

(A) Only heat transfer area is augmented.

(B) Only film coefficient is augmented.

(C) Both heat transfer area and film coefficient are augmented.

(D) None of the above.

(iii). Grashof number is associated with,

(A) Buoyancy effects.

(B) Free convection.

(C) Forced convection.

(D) High temperature

difference.

(iv). A black body of finite dimension at 1000 K is inserted into an infinite medium at 300

K. Given Stefan Boltzman constant as 1.8x10-5W/m2K4, the radiative heat transfer

coefficient is

5.

(i). In the absorption of solute gas from a mixture containing inert in a solvent, it has

been found that the overall gas transfer coefficient is nearly equal to the individual gas

film transfer coefficient. It may therefore be concluded that,

(A) The process is liquid film controlled.

(B) The gas is sparingly soluble in the solvent.

(C) The transfer rate can be increased substantially by reducing the thickness ofthe liquid film.

(D) The transfer rate can be increased substantially by reducing the thickness of

the gas film.

(ii). At the bottom of a countercurrent cooling tower, where the water temperature is

below the dry bulb temperature of air, the sensible heat flows from .. to

. and the latent heatflows from . to (fill in the blanks in

the right order among interface , water, air, water and air).

(iii). Minimum number of ideal stages is required in a fractionating column when the

reflux ratio is equal to,

(A) Minimum reflux ratio.

(B) Optimum reflex ratio.

(C) Zero

(D) Infinity.

(iv). A batch of material is dried under constant drying conditions. When drying is taking

place from all the surfaces, the rate of drying during the constant rate period is,

(A) Directly proportional to the solid thickness.

8/10/2019 GATE 1990

4/12

(B) Independent of the solid thickness.

(C) Inversely proportional to the solid thickness.

(D) Directly proportional to the square of solid thickness.

(v). Lewis number = 1 signifies,

(A) Pr = Sc

(B) Pr = Re

(C) Sc = Re

(D) Nu = Sh

(vi). A binary hydrocarbon liquid mixture of A and B (K = 1.5) containing 60 mole

percent A in flash vaporized. The mole fraction of A in the liquid product is

6.

(i). Isothermal mixing of pure gases always results in a decrease in the . Hence

work has to be done the system for separating a mixture of gases into its

components.

(ii). A system of unite mass at equilibrium consists of two phases, and of extent x and

(1-x) respectively. Write down expressions for the pressure and the specific enthalpy

of the system as a whole in terms of the properties P , P .,h , h .

(iii) The maximum work obtainable from a closed system under isothermal operation isgiven by ; For one mole of an ideal gas expanding isothermally to twice its

volume , this is equal to..

(iv) The minimum work required for steady isothermal compression of a real gas is given

by .; For one mole of an ideal gas that is compressed isothermally from one to

two atmosphere , this is equal to

7.

(i) An exothermic gas phase reaction proceeds according to the equation

3A+2B2R. The equilibrium conversionfor this reaction

(a) increases with an increase in temperature

(b) decreases on dilation with an inert gas

(c) decreases with an increase in pressure

(d) is unaffected by the presence of catalyst

8/10/2019 GATE 1990

5/12

(ii) What is the exit conversion of reactant A for a zero order reaction taking place in a CSTR

with the following data (rate constant= 1 mol/min.L); feed concentration = 1 mol/L;

feed flow rate = 0.5 L/min and reactor volume = 1L

(A) 50% (B) 75% (c) 100% (d) 200%

(iii). In a homogeneous gas phase reaction A + 2BR+S what is the relationship between

rAand rB,

(A) 2 rA= rB

(B) rA= 2 rB

(C) rA= rB

(D) none of the above

(iv). Fill in the blanks:

A 10 m3 CSTR is used to decompose a dilute solution of A. the decomposition is

irreversible with a first order rate constant of 3.45 hr-1. If 95% decomposition of A is

desired. The required feed rate is

8.

(i). Choose the most appropriate combinations of words given below:

(A) Electrical.

(B) Mechanical.

(C) Chemical.(D) Thermal.

(E) Magnetic.

and fill in the following blanks

(a) A thermocouple is a sensor that converts a change in ..quantity to a change

in quantity.

(b)A strain gauge pressure transducer is a sensor that converts a change in .

quantity to a change in .. quantity.

(ii). The transfer function of a reactor is given by . What is the transfer functionof the system with two of these reactors if they are connected in,

(A) Series. ? (B) Parallel.?

(iii). What is the steady state output of the transfer function for a unit

slope ramp input?

8/10/2019 GATE 1990

6/12

9.

(i). For SO2/SO3 service at 400 C the recommended material of construction is,

(A) Stainless steel.

(B) Carbon steel.

(C) Cast steel.

(D) Monel.

(ii). For NH3reactors the material of construction is,

(A) Carbon steel.

(B) 5 Cr 1/8 Mo steel

(C) Cast steel.

(D) Stainless steel.

10. . Catalyst for platforming of petroleum feedstock is,

(A) Pt + Re

(B) Pt + Rh

(C) Pt

(D) Pt + CO

SECTIONB

11.(i). Pure propane (C5H8) is burnt in an excess of air to give following analysis of

combustion products in volume percent:

CO2 = 5.0, CO = 3.5, H2O = 11.4, O2= 7.0 and N2= 73.1

Calculate the percentage of excess air used.

(ii). For the reaction AB, the process flow diagram is shown in figure.1.The fresh feed

of A contents 0.5 % of inert by volume. 80% conversion per pass of A fed to the reactor is

obtained. The concentration of inert going into the reactor (after mixing with the recycle

stream) must be held at 2% by volume. All streams are ideal gases and the process is at

steady state. How many moles need to be recycled per mole of total feed to the reactor at (1).

8/10/2019 GATE 1990

7/12

12.

(i). Nikuradse developed a semitheoretical correlation for f vs. Re for steady turbulent

flow in smooth pipes (105 < Re < 107):

.Toluene ( = 866 kg/m3, = 0.0008 Ns/m2) is to be conveyed through a 100m pipeline of

diameter 0.2m. What is the maximum flow rate of toluene in kg/sec that can be maintained, if

the frictional pressure loss is not to exceed 10 kN/m2?

(ii). Water flowing at 1.5 L/s in a 0.05m diameter tube is metered by means of a simple

orifice of diameter 0.025m. If coefficient of discharge is 0.62, what will be the

reading on a mercury-under-water manometer connected to the meter? Density of

water = 1000 kg/m

3

; Viscosity of water = 0.001 Ns/m

2

; Density of mercury 13,600kg/m3.

13.

(i). A mixture of coal and sand particles having size smaller than 1x 10-4 m in diameter is

to be separated by screening and subsequent elutriation by water. Recommend a

screen aperture such that the oversize from the screen can be separated completely

into sand and coal particles by elutriation. Calculate also the required water velocity.

Assume that Stokes law is applicable. Density of sand = 2650 kg/m3; Density of coal

= 1350 kg/m3; Density of water = 1000 kg/m3; Viscosity of water = 1 x 10-3kg/m.s; g

= 9.81 m/s.

8/10/2019 GATE 1990

8/12

(ii). A filtration is carried out for 10 min at a constant rate in a leaf filter and there after it

is continued at constant pressure which is attained at the end of the constant rate

period. If one quarter of the total value of the filtrate is collected during the constant

rate period. What is the total filtration time? Assume that the cake is incompressible

and that the filter medium resistance is negligible.

14.

(i). In a 11 shell and tube heat exchanger, steam is condensing on the shell side at T S C,

and the cold fluid is being heated on the tube side from t1 C to t2 C. The following

equation relates t2 to the other variables.

Where U is the overall heat transfer coefficient, A is the heat transfer area, W is the

mass flow rate and CP is the heat capacity. The tube side coefficient is controlling and the

tube side fluid is in turbulent flow. TS= 130 C, t1= 30 C, t2= 80 C. If the mass flow rate of

the cold fluid is double while keeping all the other conditions it, find the new value of t2 at

steady state.

(ii). A hot fluid flows through a well-mixed stirred tank which is provided with a coolingjacket. The fluid in the cooling jacket can also be assumed to be well mixed. Calculate

the heat transfer area of the jacket required given the following data,

Hot fluid: Flow rate, Wh= 50 kg/s;

Tih= 205 C;

Cph= 2 kJ/kg C;

Cold fluid: Flow rate, WC= 100 kg/s;

tin= 25 C, tout= 45 C;

Cpc= 4 kJ/kg C;U = 2.5 kW/m2 C;

15.

(i). A continuous rectification column is used to separate a binary mixture of A and B.

Distillate in produced at 100 kgmol/hr containing 98 mole % A. The mole fractions of

A in the liquid and in the vapor, x and y respectively, from two adjacent ideal plates

in the enriching section are as follows,

x y

0.65 0.82

8/10/2019 GATE 1990

9/12

0.56 0.76

If the latent heat of vaporization is the same for all mixtures and if the feed is a

saturated liquid, calculate,

(a) The reflex ratio,

(b) Vapor rate in the striping section in kg moles /hr.

(ii). Drying of food is carried out in an insulated tray. The drying air has a partial pressure

of water equal to 2380 Pa and a wet bulb temperature of 30 C. The product has a

drying surface of 0.05 m2/kg dry solid. The material has a critical rate in the falling

rate period which is proportional to the moisture content and the mass transfer

coefficient is 5.34 x 10-4kg /m2hr Pa. Calculate,

(a) The drying rate in the constant rate period in kg /m2hr.

(b) The time required to dry the material from a moisture content of 0.22

to 0.06 (both on dry basis). Vapor pressure of water at 30 C =

4232Pa.

(iii). Consider a system in which component A is being transferred from a gas phase to a

liquid phase. The equilibrium relation is given by yA= 0.75 xA, where yAand xAare

mole fractions of A in gas and liquid respectively. At one point in the equipment, the

gas contains 10 mole % A and the liquid 2 mole % A. Gas film mass transfercoefficient ky at this point is 10 kg moles /(hr.m2 yA) and 80% of the resistance is

the gas film. Calculate,

(a) The overall mass transfer coefficient in kg moles /(hr.m2 yA).

(b) The mass flux of A in kg moles / hr.m2.

(c) The interfacial gas concentration of A in mole fraction.

16.

(i). Solid calcium oxalate dissociates at high temperature into solid calcium carbonate

and carbon monoxide,

CaC2O4(S) = CaCO3(S) + CO (g);

The equilibrium pressure of CO between 670 and 700 K is given by P (atm) = 14.4

9600 / T where T is in K. Assuming ideal behavior, calculate G , H and S at

675 K.

(ii). Benzene (1) and perfluoro-n-heptane (2) partially miscible below 113.4 C. At 100 C,

for example, a binary mixture of two separates into two liquid phases, a benzene rich

8/10/2019 GATE 1990

10/12

phase and a perfluoro-n-heptane rich phase . The excess Gibbs free energy for the

liquid mixture is well represented by Porters equation: gE / RT = 2.27.x1x2.

Calculate x1 and x1 at equilibrium.

17.

(i). For a unimolecular gas phase reaction AProducts, the reaction mechanism is

given by

What would be the order of this reaction at very high and very low pressures?

(ii). For an elementary reaction, A + BProducts, the reaction rate is 500 K is ten times

that at 400 K. Calculate the activation energy of this reaction.

(iii). An irreversible homogeneous liquid phase reaction AB+ C is carried out in two

isothermal flow reactors of 100 liters capacity each operating at 60 C. Find the exist

conversion if both the reactors are operated in series. When,

(a) Both the reactors are ideal plug flow reactors.

(b) An ideal plug flow reactor is followed by an ideal back mix reactor.

Additional data:Feed rate = 20 liters /min

Feed concentration = 1 mol /liter.

Rate constant = 0.5 min-

1.

18.

(i). A thermometer of time constant ten seconds, initially at 30 C, is suddenly immersed

into water at 100 C. How long it takes for the thermometer reading to reach 90 C?

(ii) The G(s) plot (the Nyquist plot) of an open loop transfer

function is given in fig2. Using these figures determine

for what range of values of a proportional controller gain K, the closed lopp system

will be stable?

8/10/2019 GATE 1990

11/12

19.

(i). For a 1-1 fixed tube sheet heat exchanger, the following data are given,

Design inside pressure: Shell side = 103kN /m2;

Tube side = 2 x 103kN /m2;

Design temperature; Shell side = 50 C;Tube side = 150 C;

Allowable stress value at both design temperatures is 1.2 x 103 kN /m2. Shell inside

diameter = 0.6m, corrosion allowance (for shell and headers) = 3 x10 -3 m and Joint

efficiency = 1. Find to the nearest mm,

(a) The shell thickness.

(b) The header shell thickness.

(ii) For a project having a life of ten years the following cash flow pattern is expected,End of years Net cash flow (Rs.)

0 -50,00,000

110 20,00,000

10 -1,50,00,000

If the expected interest rate is 20 percent, what is your recommendation about implementing

the project?

20. Give the main reasons for the following:

8/10/2019 GATE 1990

12/12

(i). While SO2+ O2SO3 is a low pressure process; N2 + 3H22NH3 is a high-

pressure process.

(ii). The dihydrate process is preferred to the hemihydrates process for the manufacture of

commercial grade ortho phosphoric acid from its ores and sulphuric acid.

(iii). Under Indian conditions caustic soda of 50% concentration can be best prepared by

the Mercury Cell Technology.