Ultimate Engineering Study Guide - Questions & Answers

What is the proper technique for anchoring?A.) From the bowB.) Over the port sideC.) Over the sternD.) From the starboard quarter
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A circle of diameter 46mm rolls on a straight line without slipping. Trace the locus of a point on the circumference of the circle as it makes 1 revolutions
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a string variable can hold digits such as account numbers and zip codes.
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A species A diffuses radially outwards from a sphere of radius ro. The following assumptions can be made. The mole fraction of species A at the surface of the sphere is XAO. Species A undergoes equimolar counter-diffusion with another species B. The diffusivity of A in B is denoted DAB. The total molar concentration of the system is c. The mole fraction of A at a radial distance of 10ro from the centre of the sphere is effectively zero. (a) Determine an expression for the molar flux of A at the surface of the sphere under these circumstances. Likewise determine an expression for the molar flow rate of A at the surface of the sphere. [12 marks] (b) Would one expect to see a large change in the molar flux of A if the distance at which the mole fraction had been considered to be effectively zero were located at 100ro from the centre of the sphere instead of 10ro from the centre? Explain your reasoning. [4 marks] (c) The situation described in (b) corresponds to a roughly tenfold increase in the length of the diffusion path. If one were to consider the case of 1-dimensional diffusion across a film rather than the case of radial diffusion from a sphere, how would a tenfold increase in the length of the diffusion path impact on the molar flux obtained in the 1-dimensional system? Hence comment on the differences between spherical radial diffusion and 1-dimensional diffusion in terms of the relative change in molar flux produced by a tenfold increase in the diffusion path.
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A process is described by the exact transfer function below. Gis) 5/(15518s 13s +10.55 - 1) (a) Using an appropriate method find an approximate first-order-plus-time-delay (FOPTD) transfer function method. State the method used |Methods FOPTD time constant and time delay calculated are [Taul, Theta (b) For a unit step change in Input x(), calculate the response yct) att 12 using the exact modely-exact-12) and the FOPTD model [y-FOPTD-12) (C) For a unit step change in input (t), calculate the response y(t) at 22 using the exact modelly-exact-22 and the FOPTD modely-FOPTD-22] For the toolbar, press ALT F10 (PC) or ALTEFN+F10 (Mac) B TOS Paragraph Open Sans 10pt : ...
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A species A diffuses radially outwards from a sphere of radius ro. The following assumptions can be made. The mole fraction of species A at the surface of the sphere is Xao. Species A undergoes equimolar counter-diffusion with another species B. The diffusivity of A in B is denoted DAB. The total molar concentration of the system is c. The mole fraction of A at a radial distance of 10ro from the centre of the sphere is effectively zero. (a) Determine an expression for the molar flux of A at the surface of the sphere under these circumstances. Likewise determine an expression for the molar flow rate of A at the surface of the sphere. [12 marks] (b) Would one expect to see a large change in the molar flux of A if the distance at which the mole fraction had been considered to be effectively zero were located at 100ro from the centre of the sphere instead of 10ro from the centre? Explain your reasoning. [4 marks] (c) The situation described in (b) corresponds to a roughly tenfold increase in the length of the diffusion path. If one were to consider the case of 1-dimensional diffusion across a film rather than the case of radial diffusion from a sphere, how would a tenfold increase in the length of the diffusion path impact on the molar flux obtained in the 1-dimensional system? Hence comment on the differences between spherical radial diffusion and 1-dimensional diffusion in terms of the relative change in molar flux produced by a tenfold increase in the diffusion path. [4 marks]
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A binary mixture of methanol and water is separated in a continuous-contact distillation column operating at a pressure of 1 atm. The height of a theoretical unit (based on the overall gas mass transfer coefficient), HGA, is 2.0 m. The feed to the column is liquid at its bubble point consisting of 50% methanol (on a molar basis). The mole fraction of methanol in the distillate, xa, is 0.92 and the reflux ratio is 1.5. For mole fractions of methanol in the liquid greater than x = 0.47, the equilibrium relationship for this binary system is approximately linear, y = 0.41x + 0.59. a) Derive an equation for the operating line in the rectification section of the column (i.e. the section above the feed). [4 marks] b) State the bulk compositions of the vapour and the liquid in the packed column at the feed location. You may assume that the feed is at its optimal location. [4 marks] c) Determine the height of the rectification section of the column. [8 marks] d) Explain the factors that would determine whether the reflux ratio mentioned above is the most suitable one for the process.
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An electrically heated stirred tank system of section 2.4.3 (page 23) of the Textbook is modeled by the following second order differential equation: 9 d 2T/dt 2 + 12 dT/dt + T = T;+ 0.05 Q where Ti and T are inlet and outlet temperatures of the liquid streams and Q is the heat input rate. At steady state Tiss = 100 C, T SS = 350 C, Q ss=5000 kcal/min (a) Obtain the transfer function T'(s)/Q'(s) for this process [Transfer_function] (b) Time constant 1 and damping coefficients in the transfer function are: (Tau], [Zeta] (c) At t= 0, if Q is suddenly changed from 5000 kcal/min to 6000 kcal/min, calculate the exit temperature T after 2 minutes. [T-2minutes] (d) Calculate the exit temperature T after 8 minutes. [T-8minutes)
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A system of adsorbed gas molecules can be treated as a mixture system formed by two species: one representing adsorbed molecules (occupied sites) and the other representing ghost particles (unoccupied sites). Let gi be the molecular partition of an adsorbed molecule (occupied site) and go be the molecular partition of the ghost particles (empty sites). Now consider at certain temperature an adsorbent surface that has a total number of M sites of which are occupied by molecules that can move around two dimensionally. Therefore, both the adsorbed molecules and the ghost particles are indistinguishable. (a) (15 pts) Formulate canonical partition function (N.V.T) for the system based on the given go a and qu N (b) (15 pts) Use your Q to obtain surface coverage, 0 = as a function of gas pressure. For your M information, the chemical potential of the molecules in gas phase is Mes = k 7In P+44 (c) (10 pts) Will increasing g increase or decrease adsorption (surface coverage)? Explain your answer based on your result of (b).
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A binary mixture of methanol and water is separated in a continuous-contact distillation column operating at a pressure of 1 atm. The height of a theoretical unit (based on the overall gas mass transfer coefficient), HGA, is 2.0 m. The feed to the column is liquid at its bubble point consisting of 50% methanol (on a molar basis). The mole fraction of methanol in the distillate, xd, is 0.92 and the reflux ratio is 1.5. = For mole fractions of methanol in the liquid greater than x = 0.47, the equilibrium relationship for this binary system is approximately linear, y = 0.41x + 0.59. = a) Derive an equation for the operating line in the rectification section of the column (i.e. the section above the feed). I [4 marks] b) State the bulk compositions of the vapour and the liquid in the packed column at the feed location. You may assume that the feed is at its optimal location. [4 marks] c) Determine the height of the rectification section of the column. [8 marks] d) Explain the factors that would determine whether the reflux ratio mentioned above is the most suitable one for the process.
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In a packed absorption column, hydrogen sulphide (H2S) is removed from natural gas by dissolution in an amine solvent. At a given location in the packed column, the mole fraction of H2S in the bulk of the liquid is 5 x 10-3, the mole fraction of H2S in the bulk of the gas is 3 x 10-2, and the molar flux of H2S across the gas- liquid interface is 2 x 10-5 mol s1 m2. The system can be considered dilute and is well approximated by the equilibrium relationship, YA' = 5xA a) Find the overall mass-transfer coefficients based on the gas-phase, Kga, and based on the liquid phase, KA [4 marks] KLA b) It is also known that the ratio of the film mass-transfer coefficients is 4. KGA Determine the mole fractions of H2S at the interface, both in the liquid and in the gas. [8 marks]
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A species A diffuses radially outwards from a sphere of radius ro. The following assumptions can be made. The mole fraction of species A at the surface of the sphere is XAO. Species A undergoes equimolar counter-diffusion with another species B. The diffusivity of A in B is denoted DAB. The total molar concentration of the system is c. The mole fraction of Aat a radial distance of 10ro from the centre of the sphere is effectively zero. (a) Determine an expression for the molar flux of A at the surface of the sphere under these circumstances. Likewise determine an expression for the molar flow rate of A at the surface of the sphere. [12 marks] (b) Would one expect to see a large change in the molar flux of A if the distance at which the mole fraction had been considered to be effectively zero were located at 100ro from the centre of the sphere instead of 10ro from the centre? Explain your reasoning. [4 marks] (c) The situation described in (b) corresponds to a roughly tenfold increase in the length of the diffusion path. If one were to consider the case of 1-dimensional diffusion across a film rather than the case of radial diffusion from a sphere, how would a tenfold increase in the length of the diffusion path impact on the molar flux obtained in the 1-dimensional system? Hence comment on the differences between spherical radial diffusion and 1-dimensional diffusion in terms of the relative change in molar flux produced by a tenfold increase in the diffusion path. 14 marks
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Please answer the following questions as succinctly as possible (5 points each): a) Explain why the convection term is non-zero when you have flux of A through Stagnant B. b) Explain what a diffusion coefficient (diffusivity) is. a c) Explain what a film mass transfer coefficient is. d) Give two reasons you might choose a packed column instead of an equilibrium stage column for an absorption process. e) Explain what concentration polarization is.
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Explain the connection between the viscous dissipation term and the second law of thermodynamics. You should refer to the derivation (of Couette flow) but more importantly, use physical arguments.
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A species A diffuses radially outwards from a sphere of radius ro. The following assumptions can be made. The mole fraction of species A at the surface of the sphere is XAO. Species A undergoes equimolar counter-diffusion with another species B: The diffusivity of A in B is denoted DAB. The total molar concentration of the system is c. The mole fraction of A at a radial distance of 10ro from the centre of the sphere is effectively zero. (a) Determine an expression for the molar flux of A at the surface of the sphere under these circumstances. Likewise determine an expression for the molar flow rate of A at the surface of the sphere. [12 marks] (b) Would one expect to see a large change in the molar flux of A if the distance at which the mole fraction had been considered to be effectively zero were located at 100ro from the centre of the sphere instead of 10ro from the centre? Explain your reasoning. (c) The situation described in (b) corresponds to a roughly tenfold increase in the length of the diffusion path. If one were to consider the case of 1-dimensional diffusion across a film rather than the case of radial diffusion from a sphere, how would a tenfold increase in the length of the diffusion path impact on the molar flux obtained in the 1-dimensional system? Hence comment on the differences between spherical radial diffusion and 1-dimensional diffusion in terms of the relative change in molar flux produced by a tenfold increase in the diffusion path.
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A sample of wet material weighs 20kg and weigns 12.3kg when completely dry. The equilibrium H2O content under the drying conditions of interest is 15,8 kg H20/10019 dry solid Q: Determine the actual moisture content and the free moisture content in units of kg H20/ kg dry solid.
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A species A diffuses radially outwards from a sphere of radius ro. The following assumptions can be made. The mole fraction of species A at the surface of the sphere is Xao. Species A undergoes equimolar counter-diffusion with another species B. The diffusivity of A in B is denoted DAB. The total molar concentration of the system is c. The mole fraction of A at a radial distance of 10ro from the centre of the sphere is effectively zero. (b) Would one expect to see a large change in the molar flux of A if the distance at which the mole fraction had been considered to be effectively zero were located at 100ro from the centre of the sphere instead of 10ro from the centre? Explain your reasoning. [4 marks]
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Calculate the molar volume of ethane at P bar and T oC using the Virial Equation of state truncated to 3 terms. The experimental values for B and C can be taken as 156.7 cm3 /mol and 9650 cm6 /mol2 . Use P=18 and T=52. [10 Marks]b) Redo part (a) using the Redlick Kwong Equation of state. [20 Marks]c) Comment on the difference in the molar volume you obtained in part (a) and part (b) and give your opinion on the most accurate answer between the two. [5 Marks
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A gas stream is placed into contact with an adsorbent material at temperature T. Sites are available within the material to adsorb up to nmax moles of gas, but the pressure P of the gas stream is such that, at equilibrium, half the adsorption sites in the material are occupied and half of them are empty. Heat (specifically in the form of isosteric heat of adsorption) is released during the adsorption process, although it can be assumed that such heat is conducted to the surroundings sufficiently quickly that any temperature rise is negligible. (b) Suppose now that the pressure Pin the gas is doubled, which causes the number of moles n of gas adsorbed to increase, thereby leading to additional heat release. Determine this additional heat of adsorption released, and comment on the significance of this answer in respect of additional heat release for yet further increases in pressure. [6 marks] (c) Is there an upper limit on the amount of heat released even in the case of arbitrarily large pressures? Explain your answer. [2 marks]
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Constants: ks = 1.3806x10-23 J/particle-K; NA=6.022x102): 1 atm =101325 Pa 1. Nitrogen molecules have a molecular mass of 28 g/mol and the following characteristic properties measured: 0,2 = 2.88 K. 0,6 = 3374 K, 0), = 1, and D. = 955.63 kJ/mol. Its normal (1 atm.) boiling point is Tnb=-195.85 C (77.3 K). (a) (25 pts) Estimate the thermal de Broglie wavelength and molar entropy of N; vapor at its T. (b) (20 pts) Liquid N2 has a density of 0.8064 g/cm' at its Tob. If it is treated by the same method as (a) for vapor and assuming the intramolecular energy modes to be un affected, calculate the resultant Agup and AP = TAS (C) (15 pts) The experimental value of Na's A** at its Tos is 6.53 kJ/mol. What correction(s) would be needed for (b) to produce the actual ?
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In a packed absorption column, hydrogen sulphide (H2S) is removed from natural gas by dissolution in an amine solvent. At a given location in the packed column, the mole fraction of H2S in the bulk of the liquid is 6 103 , the mole fraction of H2S in the bulk of the gas is 2 102 , and the molar flux of H2S across the gas-liquid interface is 1 105 mol s -1 m-2 . The system can be considered dilute and is well approximated by the equilibrium relationship, y = 5x .a) Find the overall mass-transfer coefficients based on the gas-phase, K, and based on the liquid phase, K.b) It is also known that the ratio of the film mass-transfer coefficients is = 4. Determine the mole fractions of H2S at the interface, both in the liquid and in the gas.c) In another absorption column with a superior packing material there is a location with the same bulk mole fractions as stated above. The molar flux has a higher value of 3 105 mol s -1 m-2 . The ratio of film mass-transfer coefficients remains, = 4. The same equilibrium relationship also applies. Explain how you would expect the overall mass-transfer coefficients and the interfacial mole fractions to compare to those calculated in parts a) and b).d) In the previous parts of this problem you have considered the thin-film model of diffusion across a gas-liquid interface. Explain what you would expect to be the ratio of the widths of the thin-films in the gas and liquid phases for this system if the diffusion coefficient is 105 times higher in the gas than in the liquid, but the overall molar concentration is 103 times higher in the liquid than in the gas.
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Considering that air is being compressed in a polytropic process having an initial pressure and temperature of 200 kPa and 355 K respectively to 400 kPa and 700 K. a) Calculate the specific volume for both initially and final state. (5) b) Determine the exponent (n) of the polytropic process. (5) c) Calculate the specific work of the process. (5) Question 2 [15] A gas initially at a pressure of 40 kPa and a volume of 100 mL is compressed until the final pressure of 200 kPa and its volume is being reduced to half. During the process, the internal energy of the gas has increases by 2.1 KJ. Determine the heat transfer in the process. (15) Question 3 [20] A cylindrical having a frictionless piston contains 3.45 moles of nitrogen (N2) at 300 C having an initial volume of 4 liters (L). Determine the work done by the nitrogen gas if it undergoes a reversible isothermal expansion process until the volume doubles. (20)
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Considering that air is being compressed in a polytropic process having an initial pressure and temperature of 200 kPa and 355 K respectively to 400 kPa and 700 K. a) Calculate the specific volume for both initially and final state. b) Determine the exponent (n) of the polytropic process. c) Calculate the specific work of the process. (5) (5) (5)
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A cylindrical having a frictionless piston contains 3.45 moles of nitrogen (N2) at 300 C having an initial volume of 4 liters (L). Determine the work done by the nitrogen gas if it undergoes a reversible isothermal expansion process until the volume doubles. (20)
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