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1 Pre GATE-018 Chemical Engineering CH 1 Pre-GATE 018 Duration : 180 minutes Total Marks : 100 CODE: GATE18-1B Classroom Postal Course Test Series (Add : 61C, Kalusarai Near HauzKhas Metro, Delhi )

2 Pre GATE-018 Chemical Engineering CH Q. 1-Q.30 carry one mark each 1. Which one of the following cost does not come under working capital cost (a) Salaries and wages (b) Tax payable (c) Insulation and instrument cost (d) Raw material cost. It is desired to borrow some amount to meet a financial obligation. Money has borrowed from a loan agency at a interest rate of % compounded monthly. The effective interest rate in % 3. Consider an ideal gas in a frictionless piston cylinder assembly. The weightless piston is initially loaded with a large number of small weights. How would you carry out a reversible isothermal expansion process? Assume that a large number of very small weights, and an arrangement for reversible heat transfer are available. (a) Without adding or removing weights on the piston, transfer heat to the system (b) Without adding or removing weights on the piston, transfer heat from the system (c) Adding weights on the piston, transfer heat to the system (d) Removing weights from the piston, transfer heat to the system 4. Match items in Group I with those in Group II Group I P. Critical point Q. Dry saturated vapour R. Superheated vapour Group II 1. Quality = 1.0. v f vg 3. T Tsat 4. T Tsat

3 Pre GATE-018 Chemical Engineering CH 3 (a) P-1 Q- R-3 (b) P-1 Q-3 R- (c) P- Q-1 R-3 (d) P- Q-1 R-4 5. Consider the cycles given below and state which one of the following statements is true (a) In both (a) and (b) net work done is + 1 units. (b) In (b) net work done is more since in (a) no work is produced by the constant volume process (c) Magnitudes of net work produced in both (a) and (b) are 1 units but their signs are opposite (d) Magnitudes of net work produced in both (a) and (b) are different 6. The ideal gas law is valid for (a) Inert gases (b) Gases at high pressure and high temperature (c) Gases at low pressure and low temperature (d) Gases at low pressure and high temperature 7. During the adiabatic saturations process (a) The relative humidity increase but the specific humidity remains constant (b) Both the relative humidity and the specific humidity constant (c) Both the relative humidity and the specific humidity increase (d) The relative humidity decreases but the specific humidity increases 8. For an ideal gas undergoing a throttling process 1-, which of the following relationships holds?

4 Pre GATE-018 Chemical Engineering CH 4 9. An ideal gas undergoes expansion according to the process PV 0.5 = constant. The temperature of the gas during the expansion process (a) does not change (b) increases (c) decreases (d) changes depending on the initial condition 10. On a T-s diagram, the slope of the constant volume line for an ideal gas is (a) Less than that of constant pressure line (b) More than that of constant pressure line (c) Less than that of constant enthalpy line (d) Equal to that of constant enthalpy line 11. An evacuated, rigid, adiabatic tank is filled slowly with air from a supply line supplying air at a constant pressure, p L and temperature, T L. The temperature of air in the tank at the end of the filling process will be (a) greater than T L (b) equal to T L (c) less than T L (d) the average of ambient temperature and T L 1. Laplace transforms of given input signals will be 13. Which of the following statements are true? 1. Feedback and feedforward control both require a measured variable.. The process variable to be controlled is measured in feedback control. 3. Feedforward control can be perfect in the theoretical sense that the controller can take action via the manipulated variable even while the controlled variable remains equal to its desired value. 4. Feedforward control can provide perfect control; that is, the output can be kept at its desired value, even with an imperfect process model. 5. Feedback control will always take action regardless of the accuracy of any process model that was used to design it and the source of a disturbance. (a) 1,, 4 (b) 1,, 3 and 5 (c), 3 and 4 (d) none of these

5 Pre GATE-018 Chemical Engineering CH Which of the following points is correct for N F > 0, where N F is degree of freedom 1. Number of variables are more than number of equation. Presses model is underspecified 3. Infinite number of solution Presses model is over specified Sufficient number of input variables have not been assigned numerical value (a) 1,, 3 & 5 (b) 1, 3 & 5 (c) 3, 4 & 5 (d) 1, 4 & The input -3e t u(t), where u(t) is the unit step function, is applied to a system with s transfer function. If the initial value of the output is -, then the value of the s 3 output at steady state is. 16. A system described by the following differential equation initially at rest. For input x(t) = u(t), the output y(t) is (a) (1 )() e t e t u t (b) (1 )() e t e t u t (c) ( )() t t e e u t (d) (0.5 )() t t e e u t d y dy 3 () y x t is dt dt 17. For the asymptotic bode magnitude plot shown below, the system transfer function can be (a) 10 s 1 0.1s 1 (b) 100 s 1 0.1s 1 (c) 100s 10s 1 (d) 0.1 s 1 10s A plant is controlled by a proportional controller. If the time delay element is introduced in the loop, its (a) (b) (c) (d) Phase margin remains the same Phase margin increase Phase margin decreases Gain margin decrease

6 Pre GATE-018 Chemical Engineering CH A second order system is described by the equation d x dx 5 7x 7y dt dt The frequency and damping ratio respectively are (a) 1 rad/sec and 5 (b) 5 rad/sec and 7 (c) 1 rad/sec and 7 (d) 7 rad/sec and The unit step response of a second order system is Consider the following statements: 1. The undamped natural frequency is 5 rad/s.. The damping ratio is 1. 5t 3. The impulse response is 5 t e. Which of the statements given above are correct? (a) Only 1 and (b) Only and 3 (c) Only 1 and 3 (d) 1, and 3 1 e 5t e 5t 5t 1. For which kinetic situation, A or B would a PFR require a lower volume for 60% conversion? (a) A (c) Volume would be essentially the same (b) B (d) Not enough information to tell

7 Pre GATE-018 Chemical Engineering CH 7. What batch time is required to achieve 80% mole conversion for the following kinetics, if the beginning concentration of the limiting reactant A is 10 mol/dm 3? (a) 8 h (b) 16 h (c) 4 h (d) 3 h 3. Consider the two isothermal reactions and their equilibrium constants Reaction 1: R + S P K Reaction : R + N Q K 78 For a feed to an isothermal reaction that contains R, S and N in equimolar amounts, which conclusion is correct? (a) Reaction 1 reaches equilibrium first. (b) Reaction reaches equilibrium first. (c) Reaction has a higher conversion at equilibrium. (d) None of these 4. Choose the correct answer: For multiple reaction, A R R S The number of moles of S present when the number of moles of A and R is 0.3 and 0.5 respectively (initially moles of A are only present) is (a) 0.15 (b) (c) (d) 0.350

8 Pre GATE-018 Chemical Engineering CH 8 5. Which plot represents the rate of reaction vs. time for the batch isothermal, 1 st order reaction S P? (a) (b) (c) (d) 6. For a heterogeneous catalytic reaction A B C, with equimolal feed of A and R, the initial rate rao is invariant with total pressure. The rate controlling step is (a) surface reaction between adsorbed A and B in the gas phase. (b) surface reaction between adsorbed A and adsorbed B. (c) surface reaction between A in the gas phase and adsorbed B. (d) Desorption of C.

9 Pre GATE-018 Chemical Engineering CH 9 7. Consider the following scheme of elementary reaction: For which of the product increasing temperature and PFR is required for the above reaction scheme (a) R (b) S (c) T (d) U 8. The number equal volume of ideal tanks of mean residence time min required to model the real reactor having variance 100 sec is 9. A liquid macrofluid reacts according to A R as it flows through a vessel. Find the conversion of A for the flow patterns of figure kinetics as shown 30. For following parallel reaction A R () Desired A S () Desired For pure A (C A0 = 1 mol / l) the mol of R produced at 100% conversion of reactant A in mol /liter is

10 Pre GATE-018 Chemical Engineering CH 10 Q. 31-Q.68 carry two marks each 31. A rough rule of thumb for the chemical industry is that Rs.1 of annual sales requires Rs. of fixed-capital investment. In a chemical processing plant where this rule applies, the total capital investment is Rs , and the working capital is 0 percent of the total capital investment. The annual total product cost amounts to Rs If the income tax rates on gross earnings total 35 percent, determine the percent of total capital investment returned annually as net profit 3. The purchased cost of a shell-and-tube heat exchanger with 10 m of heating surface was 5 Rs in If the purchased cost capacity exponent is 0.60 for surface areas ranging from 10 to 40 m and is 0.81 for surface areas ranging from 40 to 00 m, if cost index in 000 is 1098 and in 1990 is 930. What will be the purchased cost (in rupees) of a heat exchanger with 100 m of heating surface in 000? 33. The original value of a piece of equipment is Rs Its salvage value is estimated to be Rs. 000 at the end of service life of 10 year. Book value of equipment at the end of 5 year by text book declining balance method is (a) Rs (b) Rs (c) Rs (d) Rs An investigation of a proposed investment has been made. The following result has been presented to management. The payback period is 5 years. Annual depreciation is 10 percent per year of the fixed-capital investment; and fixed-capital investment is 85 percent of total capital investment. Using this information, the rate of return on the investment is (a) 5.5 % (b) 30 % (c) 6.5% (d) 3.3 % 35. Methanol is produced from carbon mono oxide and hydrogen as per reaction CO H CH OH 3 Feed composition (in mole %) is given in figure The product Methanol is separated out from separator and untreated reactant are recycled along with the purge and per pass conversion of CO in reactor is 0%. For 100 kmol of fresh feed the ratio of Recycled (R) to Purge (P) is

11 Pre GATE-018 Chemical Engineering CH The orsat analysis flue gas from a furnace using a hydrocarbon fuel oil as follows by volume. CO 16.5%, CO 0.%, O 1.5%, N rest. (C/H) ratio by weight of fuel is 37. The orsat analysis flue gas from a furnace using a hydrocarbon fuel oil as follows by volume. CO 16.5%, CO 0.%, O 1.5%, N rest. The percentage excess air used 38. Carbon monoxide (CO) is burnt in presence of 00% excess pure oxygen. The inlet streams are at 5ºC. The standard heat of formation (at 5ºC) of CO and CO are 110 kj mol 1 and 390 kj mol 1 respectively. The heat capacities (in J mol 1 K 1 ) of the components are C Po T C Pco Where, T is the temperature in K. If the heat loss (in kj) per mole of CO burnt is 34.6 then flame temperature in K is 39. A rigid tank is connected through a valve to steam mains supplying steam at 1 MPa, 400ºC. Heat is transferred from the tank to the surroundings, and the valve is closed when the total amount of cooling is 000 kj. The energy contained in the tank is the same before and after the process. Neglecting potential and kinetic energy changes the mass of the steam that enters the tank is MPa and 400ºC v = m 3 / kg u = kj/kg h = kj/kg (a) kg (b) 6.76 kg (c) 0.61 kg (d) 6.1 kg 40. The conditions of steam at inlet and exit of a perfectly insulated steam turbine running under steady-state conditions is as follows: At inlet: specific enthalpy = 330 kj/kg; velocity = 160 m/s At exit: specific enthalpy = 660 kj/kg; velocity = 100 m/s Neglecting change in potential energy, the work done by the steam turbine is approximately (a) 570 kj/kg (b) 578 kj/kg (c) 630 kj/kg (d) 638 kj/kg 3 T

Pre GATE-018 Chemical Engineering CH 1 41.

12 Pre GATE-018 Chemical Engineering CH Given for water Using Clapeyron equation, the enthalpy of vaporization (kj/kg) of water at 00ºC is approximately (a) 1857 (b) 194 (c) 1947 (d) 05 Linked Answer Question 4 to 43 Carry Tow marks each: Statement for Linked Answer Question 4 to 43: An ideal gas undergoes a cyclic process consisting of the following three processes: Process 1-: Compression process with pv = constant Process -3: Constant pressure Process 3-1: Constant volume; U3 U kj Changes in kinetic and potential energies are neglected. 4. The work done (kj) during the process -3 is (a) 110 (b) 10 (c) 130 (d) The heat transferred (kj) during the process -3 is (a) 469 (b) 4469 (c) 4569 (d) The vapour pressure of liquid ammonia (in atmosphere) in the vicinity of the triple point can be expressed as 3063 ln p T where temperature T is expressed in K. In a similar manner, the vapour pressure of solid ammonia can be expressed as 3754 ln p 18.7 T Take the molecular mass of ammonia to be 17 kg / kmol. The temperature and pressure at the triple point are (a) 95. K, 0.69 atm (b) 95. K, 0.59 atm (c) 195. K, 0.69 atm (d) 195. K, 0.59 atm

13 Pre GATE-018 Chemical Engineering CH For the system methanol (1)/methyl acetate (), the following equations provide a reasonable correlation for the activity coefficients: In addition, the following Antoine equations provide vapour pressures of methanol (1)/methyl acetate () at temperature K are kp a and kpa respectively. The bubble point pressure (in kpa) and temperature K and x 1 = 0.5 is 46. At 318 K and 4.4 kpa, the composition of the system ethanol (1) and toluene () at equilibrium is x1 0.3 & y The saturation pressure at the given temperature S for the pure components are P kpa & P kpa, respectively. The E value of G / RT for the liquid phase 47. Ammonia synthesis reaction is represented by N 3H NH3 The reactant stream consists of 1 mol N, 3 mol H and mol argon. The temperature and pressure of the reaction are 675 K and 0 bar. The equilibrium constant for the reaction is Find the % conversion of nitrogen is 48. One kilogram of a perfect gas at 15ºC and 100 kpa is heated to 45ºC by (i) a constant pressure process and (ii) a constant volume process, c p of the gas = 1.04 kj/kg.k and R = kj/kg.k. Heat added in the constant pressure (Q P ) and constant volume (Q V ) processes are (a) Q 31.6 kj, Q.35 kj P (b) Q.35 kj, Q 31.6 kj P (c) Q 31.6 kj, Q 31.6 kj P (d) Q.35 kj, Q 0 kj P V V V V 49. If the input Y m to a PI controller changes stepwise (Y(s) m = /s) and the controller output changes initially as in figure. the values of the controller gain and integral time in min S

Pre GATE-018 Chemical Engineering CH 14 50. A liquid-level control system can be configured in following way with a control valve manipulating flow of liquid into the holding as show in the figure.

14 Pre GATE-018 Chemical Engineering CH A liquid-level control system can be configured in following way with a control valve manipulating flow of liquid into the holding as show in the figure. Assuming that the liquid level transmitter always is direct acting, what control action should a proportional pneumatic controller have if the control valve is air-to-open and air-to closed respectively (a) Direct acting and reverse acting (b) Reverse acting and reverse acting (c) Reverse acting and Direct acting (d) Direct acting and Direct acting 51. The following two possible ways to design a feedback control loop to obtain a desired rate of liquid flow. Assume that in both systems I and II, the flow transmitter is direct acting (i.e., the output increases as the actual flow rate increases). However, the control valve in system I is air-to-open, meaning that an increasing pressure signal from the controller will open the valve more, thus increasing the flow rate. On the other hand the control valve in system II is air-to-close. The dynamics for both of the valves are negligible. If K c and K v is the gain of controller and control valve respectively then which one of the following is correct

15 Pre GATE-018 Chemical Engineering CH In the feedback system shown below G() s ( s ) s The step response of the closed-loop system should have minimum settling time and have no overshoot. The required value of gain to achieve this is 53. The unit step response of an under-damped second order system has steady state value of. Which one of the following transfer functions has these properties? (a) (b) s.59s 1.1 s 1.91s (c) s.59s (d) s 1.91s Step responses of a set of three second-order under damped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of three systems? (a) (b) (c) (d)

16 Pre GATE-018 Chemical Engineering CH The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as The range of K for which the system is stable is (a).0 <K< 0.5 (b) 0 <K< 0.5 (c) 0 <K< (d) 0.5 < K < 56. The characteristic equation of an LTI system is given by F() s s s 3 s 6 s 4 s 8 0. The number of roots that lie strictly in the left half s-plane is 57. Two pumps are being considered for pumping water from a reservoir. Installed cost and salvage value for the two pumps are given below: Pump A has a service life of 4 years. If the annual effective interest rate is 15 percent. The service life of pump B at which the two pumps are competitive is (a) 6.5 year (b) 5.3 year (c) 5 year (d) 8. year 58. Consider a transfer function G () s p ps 3ps with p a positive real s (3)() p s p parameter. The maximum value of p until which G p remains stable is. 59. The open loop transfer function of a unity feedback system is given by The gain and phase crossover frequencies in rad/sec are, respectively (a) 0.63 and 1.6 (b) 0.63 and (c) and 0.63 (d) 1.6 and A proposed chemical plant will require a fixed-capital investment of Rs. G() s s 3e s( s ) 8 Rs It is estimated that the working capital will be 5 percent of the total investment. Annual depreciation costs are estimated to be 10 percent of the fixed-capital investment. If the annual profit will be year. 61. The first-order reversible liquid reaction A R, C 0.5 mol/liter, C 0 8 Rs , determine the payout period A0 R0 Takes place in a batch reactor. After 8 minutes, conversion of A is 33.3% while equilibrium conversion is 66.7%. the rate constants K 1 (in min 1 ) and K (in min 1 ) equation for this reaction.

17 Pre GATE-018 Chemical Engineering CH First-order reaction for the disappearance of A in the gas reaction A R if, on holding the pressure constant, the volume of the reaction mixture, starting with 80% A, decreases by 0% in 3 min, the rate constant K in min Group-I lists a set of four transfer functions. Group-II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions. Group-I 5 P = s 5 1. Group II 36 Q = s 0s R = s 1s S= s 7s (a) P-3 Q-1 R-4 S- (b) P-3 Q- R-4 S-1 (c) P- Q-1 R-4 S-3 (d) P-3 Q-4 R-1 S-

18 Pre GATE-018 Chemical Engineering CH A liquid phase reversible reaction A B is carried out in an adiabatic CSTR operating under steady state conditions. The reaction is elementary and follows the first order rate law. For this reaction, the figure below shows the conversion (X A ) of A as a function of temperature ( T) for different values of the rate of reaction ( r A in -1-1 mole lit min ) denoted by the numbers to the left of each curve. This figure can be used to determine the rate of the reaction at a particular temperature, for a given conversion of A. The inlet stream does not contain B and the concentration of A in the inlet stream is 5 mol/m 3. The molar feed rate of A is 100 mol/s. A steady state energy balance for this CSTR results in the following relation: T = X A where T is the temperature (in K) of the exit stream and X A is the conversion of A in the CSTR. For an exit conversion of 50 % of A, the volume (in m 3, rounded off to the first decimal place) of CSTR required is

19 Pre GATE-018 Chemical Engineering CH For a reversible exothermic elementary catalytic reaction of the type k1 A R k Data: k1 exp( /) T k exp( /) T Maximum allowable temperature = 300 K. At a conversion level, X =0.8 find the optimum operating reaction temperature in K A 66. For the reaction A B+C r A A kp (1) K P K P A A C C from which mechanism is consistent with the rate law (a) A S A S A S B S C B S B S (b) A S A S A S B S C C S C S (c) A S A S A S A() g B S C (d) C S C S A S A S A S A S B S C S C S C S

20 Pre GATE-018 Chemical Engineering CH The first order, exothermic, irreversible, liquid phase reaction A +B is to be conducted in an adiabatic CSTR. The desired conversion is 70% and the reactor is to be operated at 353 K. for the data give below, Data: The rate constant at 353 K = 0.0 s 1 Inlet volumetric flow rate = 0.01 m 3 /s Density of inlet stream = 1000 kg/m 3 Inlet concentration of A =.0 Kmol/m 3 Heat of reaction (independent of temp) = 50,000 kj/kmol of A reacting Average heat capacity of inlet and outlet streams = kj/kg.k. The feed temperature in K 68. The liquid phase parallel reaction: A R : r k C : k 0.3s R 1 A 1 A S : r k : k 0.3 Kmol / m. s S is conducted in an isothermal plug flow reactor. The inlet concentration of A is.0 Kmol/m 3. No products are present in the feed. If conversion of A is 80%, then determine the exit concentration of R (Kmol/m 3 ) 1 3 Space for Rough Work BEST OF LUCK!!!!

Thermal Energy Final Exam Fall 2002

16.050 Thermal Energy Final Exam Fall 2002 Do all eight problems. All problems count the same. 1. A system undergoes a reversible cycle while exchanging heat with three thermal reservoirs, as shown below.