Gate 1990

GATE – 1990 CHEMICAL ENGINEERING Time Allowed: 3 Hours 200

Maximum Marks:

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 2

30 C and a total pressure of 100 kN / m . If the vapor pressure of Ethyl Acetate at 3

30 C is 16 kN / m , (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

The

heat

of

formation

of

gaseous

n-Heptane

at

25 C

is

25 C

is

………… (b).

of

formation

of

gaseous

Ethyl

Alcohol

at

……… 2. (i).

2

The viscosity of CO at 1 bar and 27 C is 0.000015 Ns/m . 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 ………

(iii).

Bernoulli’s 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 abo

(iv).

The pressure drop required for fluidizing a coal bed with a liquid petroleum fraction 2

3

3

of viscosity 0.015 Ns/m is 10 N/m . The pressure drop is required for fluidizing the same bed with an oil of viscosity 0.03 2

Ns/m is ……… 3. (i).

(ii).

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

Compression

(B)

Impact

(C)

Attrition

(D)

Cutting action

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 than 300. (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)

(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)

(ii).

(iii).

The drop attains wet bulb temperature and vanishes.

None of above.

In a finned tube heat exchanger: (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.

Grashof number is associated with,

(iv).

(A)

Buoyancy effects.

(B)

Free convection.

(A)

Forced convection.

High temperature difference

A black body of finite dimension at 1000 K is inserted into an infinite medium at 300 -5

2

4

K. Given Stefan Boltzman constant as 1.8x10 W/m K , 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) (B)

The process is liquid film controlled. The gas is sparingly soluble in the solvent.

(C)

The transfer rate can be increased substantially by reducing the thickness of the liquid film.

(D)

The transfer rate can be increased substantially by reducing the thickness of the gas film. 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

(ii).

…………. and the latent heat flows from …….…… to ………… (fill in the blanks in the right order among interface , water, air, water and air). (iii).

(iv).

(v).

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.

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.

(B)

Independent of the solid thickness.

(C)

Inversely proportional to the solid thickness.

(D)

Directly proportional to the square of solid thickness.

Lewis number = 1 signifies, (A)

Pr = Sc

(B)

Pr = Re

(C)

Sc = Re

(D) (vi).

Nu = Sh

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 (1x) 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 is given 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+2B 2R. The equilibrium conversion for this reaction (a) ncreases with an increase in temperature (b) decreases on dilation with an inert gas (c) ecreases with an increase in pressure (d) is unaffected by the presence of catalyst (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% (iii). (A) (B) (C)

(D)

(B) 75%

(c) 100%

(d) 200%

In a homogeneous gas phase reaction A + 2BR+S what is the relationship between rA and rB, 2 rA = rB rA = 2 rB rA = rB none of the abov

(iv).

Fill in the blanks: 3

A 10 m CSTR is used to decompose a dilute solution of A. the decomposition is -1

irreversible with a first order rate constant of 3.45 hr . 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 function

of the system with two of these reactors if they are connected in,

(iii).

(A) Series. ? (B) Parallel.? What is the steady state output of the transfer function

for a unit

slope ramp input? 9. (i).

(ii).

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

Stainless steel.

(B)

Carbon steel.

(C)

Cast steel.

(D)

Monel.

For NH3 reactors 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

SECTION – ‘B’ 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, H2 O = 11.4, O2 = 7.0 and N2 = 73.1 Calculate the percentage of excess air used. (ii).

For the reaction A B, 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).

12 . (i). Nikuradse developed a semitheoretical correlation for f vs. Re for steady turbulent flow in smooth pipes (105 < Re < 107): . 3

2

Toluene ( = 866 kg/m , = 0.0008 Ns/m ) 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, 2

if the frictional pressure loss is not to exceed 10 kN/m ? (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

3

2

of water = 1000 kg/m ; Viscosity of water = 0.001 Ns/m ; Density of mercury 3

13,600kg/m

13. (i).

-4

A mixture of coal and sand particles having size smaller than 1x 10 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. 3

Assume that Stokes law is applicable. Density of sand = 2650 kg/m ; Density of coal 3

3

-3

= 1350 kg/m ; Density of water = 1000 kg/m ; Viscosity of water = 1 x 10 kg/m.s; g = 9.81 m/s. (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 1–1 shell and tube heat exchanger, steam is condensing on the shell side at TS 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 cooling jacket. 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:

Cold fluid: kg/s;

Flow rate,

Wh = 50 kg/s;

Flow rate,

Tih = 205 C; Cph = 2 kJ/kg C; WC = 100 tin = 25 C, tout = 45 C; Cpc = 4 kJ/kg C; 2

U = 2.5 kW/m 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

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 2

has a drying surface of 0.05 m /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 -4

2

coefficient is 5.34 x 10 kg /m hr Pa. Calculate, (a) (b)

(iii).

2

The drying rate in the constant rate period in kg /m hr.

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. 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 xA are 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 2

transfer coefficient ky at this point is 10 kg moles /(hr.m yA ) and 80% of the resistance is the gas film. Calculate, 2

(a)

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

(b)

The mass flux of A in kg moles / hr.m .

(c)

The interfacial gas concentration of A in mole fraction.

2

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 phase and a perfluoro-n-heptane rich phase . The excess Gibbs free energy for the liquid mixture is well represented by Porter’s equation: E

g / RT = 2.27.x1x2. Calculate x1 and x1at equilibrium.

17. (i). is

For a unimolecular gas phase reaction A Products, the reaction mechanism given by

What would be the order of this reaction at very high and very low pressures? (ii).

For an elementary reaction, A + B Products, 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 A B+ 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)

(b)

Both the reactors are ideal plug flow reactors.

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. Rat constant

-

=0.5min 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?

19. (i).

For a 1-1 fixed tube sheet heat exchanger, the following data are given, 3

2

Design inside pressure: Shell side = 10 kN /m ; 3

2

Tube side = 2 x 10 kN /m ; Design temperature;

Shell side = 50 C; Tube side = 150 C; 2

Allowable stress value at both design temperatures is 1.2 x 103 kN /m . Shell inside diameter = 0.6m, corrosion allowance (for shell and headers) = 3 x10 efficiency = 1. Find to the nearest mm, (a) The shell thickness. (b) (ii)

-3

m and Joint

The header shell thickness.

For a project having a life of ten years the following cash flow pattern is expected, End of years 0 1 – 10 10

Net cash flow (Rs.) -50,00,000 20,00,000 -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:

(i).

While SO2 + ½ O2 SO3 is a low pressure process; N2 + 3H2 2NH3 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 it’s ores and sulphuric acid.

(iii).

Under Indian conditions caustic soda of 50% concentration can be best prepared by the Mercury Cell Technology.