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Questions and Answers of Chemical Engineering

Transient thermal behavior of a chromatographic device (Fig. 15B.7), you are a consultant to an industrial concern that is experimenting, among other things, with transient thermal phenomena in gas
Derivation of the macroscopic energy balance, show how to integrate Eq. (N) of Table 11.4-1 over the entire volume V of a flow system, which, because of moving parts, may be a function of time. With
The classical Bernoulli equation, below Eq. 15.2-5 we have emphasized that the mechanical energy balance and the total energy balance contain different information, since the first is a consequence
Approximation of a black body by a hole in a sphere, a thin sphere of copper, with its internal surface highly oxidized, has a diameter of 6 in. How small a hole must be made in the sphere to make an
Efficiency of a solar engine, a device for utilizing solar energy, developed by Abbot,’ consists of a parabolic mirror that focuses the impinging sunlight onto a Pyrex tube containing a
Radiant heating requirement, a shed is rectangular in shape, with the floor 15 ft by 30 ft and the roof 7.5 ft above the floor. The floor is heated by hot water running through coils. On cold winter
Steady-state temperature of a roof, estimate the maximum temperature attained by a level roof at 45° north latitude on June 21 in clear weather. Radiation from sources other than the sun may be
Radiation errors in temperature measurements The temperature of an air stream in a duct is being measured by means of a thermocouple. The thermocouple wires and junction are cylindrical, 0.05
Surface temperatures on the Earth's moon(a) Estimate the surface temperature of our moon at the point nearest the sun by a quasi-steady-state radiant energy balance, regarding the lunar surface as
Reference temperature for effective emissivity show that, if the emissivity increases linearly with the temperature, Eq. 16.5-3 may be written as in which eo1 is the emissivity of surface 1 evaluated
Radiation across an annular gap, Develop an expression for the radiant heat transfer between two long gray coaxial cylinders 1 and 2. Show that where A1 is the surface area of the innercylinder.
Multiple radiation shields (a) Develop an equation for the rate of radiant heat transfer through a series of n very thin, fiat, parallel metal sheets, each having a different emissivity e, when the
Radiation and conduction through absorbing media a glass slab, bounded by planes z = 0 and z = δ, is of infinite extent in the x and y directions. The temperatures of the surfaces at z = 0 and z =
Cooling of a black body in vacuo a thin black body of very high thermal conductivity has a volume V, surface area A, density p, and heat capacity Cp. At time t = 0, this body at temperature T1 is
Prediction of a low-density binary diffusivity estimate DAB for the system methane-ethane at 293K and 1atm by the following methods: (a) Equation 17.2-1. (b) The corresponding-states chart
Extrapolation of binary diffusivity to a very high temperature, a value of DAB = 0.151 cm2/s has been reported1 for the system CO2-air at 293K and 1 atm. Extrapolate DAB to 1500K by the following
Self-diffusion in liquid mercury, the diffusivity of Hg203 in normal liquid Hg has been measured2 along with viscosity and volume per unit mass. Compare the experimentally measured DAA, with the
Schmidt numbers for binary gas mixtures at low density, use Eq. 17.3-11 and the data given in Problem 1A.4 to compute Sc = µ/pDAB for binary mixtures of hydrogen and Freon 12 at xA = 0.00, 0.25,
Estimation of diffusivity for a binary mixture at high density, Predict CDAB for an equimolar mixture of N2 and C2H6 at 288.2K and 40atm (a) Use the value of DAB at 1atm from Table 17.1-1, along
Diffusivity and Schmidt number for chlorine-air mixtures (a) Predict DAB for chlorine-air mixtures at 75°F and 1atm. Treat air as a single substance with Lennard-Jones parameters as given in
The Schmidt number for self-diffusion at high density (a) Use Eqs. 1.3-1b and 17.2-2 to predict the self-diffusion Schmidt number Sc = µ/pDAA ∙ at the critical point for a system with MA ≈
Corrcection of high-density diffusivity for temperature, the measured value3 of CDAB for a mixture of 80 mole% CH4 and 20 mole% C2H6 at 313K and 136 atm is 6.0 x 10-6 g-mol/cm ∙ s (see Example
Estimation of liquid diffusivities (a) Estimate the diffusivity for a dilute aqueous solution of acetic acid at 12.5°C, using the Wilke-Chang equation, the density of pure acetic acid is 0.937
Relations among fluxes in multi component systems, verify Eqs. (K), (O), (T), and (X) Table 17.8-1 using only the definitions of concentrations, velocities, and fluxes.
Interrelation of composition variables in mixtures(a) Using the basic definitions in Eqs. (A) to (G) of Table 17.7-1, verify the algebraic relations in Eqs. (H) to (O).(b) Verify that, in Table
Relations between fluxes in binary systems, the following equation is useful for interrelating expressions in mass units and those in molar units in two-component systems: Verify the correctness of
Equivalence of various forms of Fick's law for binary mixtures (a) Starting with Eq. (A) of Table 17.8-2, derive Eqs. (B), (D), and (F). (b) Starting with Eq. (A) of Table 17.8-2, derive
Mass flux with respect to the solvent velocity (a) In a system with N chemical species, choose component N to be the solvent. Then define jNa = pa (va – VN) (17C.2-1) to be the mass flux with
Determination of Lennard-Jones potential parameters from diffusivity data of a binary, gas mixture(a) Use the following data5 for the system H2O-O2 at 1atm pressure to determine σAB and εAB/k:One
Evaporation rate for the system shown in Fig. 18.2-1, what is the evaporation rate in g/hr of CC13NO2 (chloropicrin) into air at 25°C Make the customary assumption that air is a "pure
Sub-limitation of small iodine spheres in still air. A sphere of iodine, 1 cm in diameter, is placed in still air at 40°C and 747 mm Hg pressure. At this temperature the vapor pressure of iodine is
Estimating the error in calculating the absorption rate, what is the maximum possible error in computing the absorption rate from Eq. 18.5-18, if the solubility of A in B is known within + 5% and the
Chlorine absorption in a falling film (Fig. 18A.4), chlorine is being absorbed from a gas in a small experimental wetted-wall tower as shown in the figure. The absorbing fluid is water, which is
Measurement of diffusivity by the poinbsource method (Fig. 18C.1)1, we wish to design a flow system to utilize the results of Problem 18C.1 for the measure of DAB. The approaching stream of pure B
Determination of diffusivity for ether-air system the following data on the evaporation of ethyl ether (C2H5OC2H5) have been tabulated by Jost. 2 The data are for a tube of 6.16 mm diameter, a total
Mass flux from a circulating bubble (a) Use Eq. 18.5-20 to estimate the rate of absorption of CO2 (component A) from a carbon dioxide bubble 0.5 cm in diameter rising through pure water
Error in neglecting the convection term in evaporation(a) Rework the problem in the text in S18.2 by neglecting the term xA (NA + NB) in Eq. 18.0-1. Show that this leads to this is a useful
Effect of mass transfer rate on the concentration profiles (a) Combine the result in Eq. 18.2-11 with that in Eq. 18.2-14 to get(b) Obtain the same result by integrating Eq. 18.2-1 directly
Absorption with chernical reaction (a) Rework the problem discussed in the text in S18.4, but take z = 0 to be the bottom of the beaker and z = L at the gas-liquid interface. (b) In solving
Method for separating helium from natural gas (Fig. 18B.8), Pyrex glass is almost impermeable to all gases but helium. For example, the diffusivity of He through Pyrex is about 25 times the
Effect of temperature and pressure on evaporation rate (a) In S18.2 what is the effect of a change of temperature and pressure on the quantity xA1? (b) If the pressure is doubled, how is
Evaporation rate for small mole fraction of the volatile liquid, in Eq 18.2-15, expand in a Taylor series appropriate for small mole fractions of A. First rewrite the logarithm of the quotient as the
Effectiveness factors for long cylinder so derive the expression for ηA for long cylinders analogous to Eq. 18.7-16. Neglect the diffusion through the ends of the cylinders.
Gas absorption in a falling film with chemical reaction, rework the problem discussed in S18.5 and described in Fig. 18.5-1, when gas A reacts with liquid B by a first-order irreversible chemical
Diffusion through a stagnant film--alternate derivation in S18.2 an expression for the evaporation rate was obtained in Eq. 18.2-14 by differentiating the concentration profile found a few lines
Dehumidification of air (Fig. 19.4-1) for the system of Example 19.4-1 let the vapor is H20 and the stagnant gas is air. Assume the following conditions (which are representative in air
Steady-state evaporation (Fig. 18.2-1), rework the problem solved in S18.2, dealing with the evaporation of liquid A into gas B, starting from Eq. 19.1-17. (a) First obtain an expression for v*,
Gas absorption with chemical reaction (Fig. 18.4-1), rework the problem solved in S18.4, by starting with Eq. 19.1-16. What assumptions do you have to make in order to get Eq. 18.4-4?
The Maxwell-Stefan equations for multicomponent gas mixtures. In Eq. 17.9-1 the Maxwell-Stefan equations for the mass fluxes in a multicomponent gas system are given. Show that these equations
Various forms of the species continuity equation(a) In this chapter the species equation of continuity is given in three different forms: Eq. 19.1-7, Eq. (A) of Table 19.2-1, and Eq. (B) in Table
Alternate form of the binary diffusion equation, in the absence of chemical reactions, Eq. 19.1-17 can be written in terms of v rather than v* by using a different measure of concentration namely,
Derivation of the equation of continuity, in S19.1 the species equation of continuity is derived by making a mass balance on a small rectangular volume ∆x ∆y ∆z fixed in space. (a) Repeat the
Measurement of diffusivity by unsteady-state evaporation, use the following data to determine the diffusivity of ethyl propionate (species A) into a mixture of 20 mole% air and 80 mole% hydrogen
Absorption of oxygen from a growing bubble (Fig. 20A.2), oxygen is being injected into pure water from a capillary tube. The system is virtually isothermal and isobaric at 25°C and 1 atm. The
Rate of evaporation of n-octane, at 20°C, how many grams of liquid n-octane will evaporate into N2 in 24.5 hr in a system such as that studied in Example 20.1-1 at system pressures of (a) 1atm,
Absorption with rapid second-order reaction (Fig. 20.1-2), make the following calculations for the reacting system depicted in the figure: (a) Verify the location of the reaction zone, using Eq.
Rapid forced-convection mass transfer into a laminar boundary layer, calculate the evaporation rate nA0(x) for the system described under Eq. 20.2-52, given that wA0 = 0.9, wA∞ = 0.1, and Sc = 2.0.
Slow forced convection mass transfer into a laminar boundary layer, this problem illustrates the use of Eqs. 20.2-55 and 57 and tests their accuracy. (a) Estimate the local evaporation rate,
Extension of the Arnold problem to account for interphase transfer of both species, show how to obtain Eqs. 20.1-23, 24, and 25 starting with the equations of continuity for species A and B (in molar
Stoichiometric boundary condition for rapid irreversible reaction, example 20.1-2 must satisfy the stoichiometric relation the reactant fluxes in which vR = dzR/dt. Show that this relation leads to
Taylor dispersion in slit flow (Fig. 2B.3), show that, for laminar flow in a plane slit of width 2B and length L, the Taylor dispersion coefficient is
Diffusion from an instantaneous point source, at time t = 0, a mass mA of species A is injected into a large body of fluid B. Take the point of injection to be the origin of coordinates. The material
Simultaneous momentum, heat, and mass transfer: alternate boundary conditions (Fig. 20B.7). The dimensionless profiles II (η, Λ, K) in Eq. 20.2-43 are applicable to a variety of situations. Use
Absorption from a pulsating bubble, use the results of Example 20.1-4 to calculate δ(t) and NA0(t) for a bubble whose radius undergoes a square-wave pulsation: Here w is a characteristic frequency,
Design of fluid control circuits, it is desired to control a reactor via continuous analysis of a side stream. Calculate the maximum frequency of concentration changes that can be detected as a
Dissociation of a gas caused by a temperature gradient, a dissociating gas (for example, Na2 → 2Na) is enclosed in a tube, sealed at both ends, and the two ends are maintained at different
Two-bulb experiment for measuring gas diffusivitiesmanalytical solution (Fig. 18B.6) this experiment, described in Problem 18B.6, is analyzed there by a quasi-steady-state method. The method of
Determination of eddy diffusivity (Figs. 18C.1 and 21A.1), in Problem 18C.1 we gave the formula for the concentration profiles in diffusion from a point source in a moving stream. In isotropic highly
Heat and mass transfer analogy write the mass transfer analog of Eq. 13.4-19, what are the limitations of the resulting equation?
Wall mass flux for turbulent flow with no chemical reactions use the diffusional analog of Eq. 13.3-7 for turbulent flow in circular tubes, and the Blasius formula for the friction factor, to obtain
Deposition of silver from a turbulent stream (Fig. 21B.3), an approximately 0.1 N solution of KNO3 containing 1.00 x 10-6 g-equiv. AgNO3 per liter is flowing between parallel Ag plates, as shown in
Prediction of mass transfer coefficients in closed channels, estimate the gas-phase mass transfer coefficients for water vapor evaporating into air at 2 atm and 25°C, and a mass flow rate of 1570
Calculation of gas composition from psychometric data, a stream of moist air has a wet bulb temperature of 80°F and a dry-bulb temperature of 130°F, measured at 800 mm Hg total pressure and high
Calculating the air temperature for drying in a fixed bed, a shallow bed of water-saturated granular solids is to be dried by blowing dry air through it at 1.1atm pressure and a superficial velocity
Rate of drying of granular solids in a fixed bed calculate the initial rate of water removal in the drying operation described in Problem 22A.3, if the solids are cylinders with a = 180 ft-1.
Evaporation of a freely falling drop a drop of water, 1.00 mm in diameter, is falling freely through dry, still air at pressure of 1atm and a temperature of 100°F with no internal circulation.
Effect of radiation on psychometric measurements, suppose that a wet-bulb and dry-bulb thermometer are installed in a long duct with constant inside surface temperature Ts and that the gas velocity
Film theory with variable transport properties (a) Show that for systems in which the transport properties are functions of y, Eqs. 19.4-12 and 13 may be integrated to give for y
An evaporative ice maker, consider a circular shallow dish of water 0.5 m in diameter and filled to the brim, resting on an insulating layer, such as loose straw, and in a windless area. At what air
Oxygen stripping, calculate the rate at which oxygen transfers from quiescent oxygen saturated water at 20°C to a bubble of pure nitrogen 1 mm in diameter, if the bubble acts as a rigid sphere. It
Controlling diffusional resistance water drops 2 mm in diameter are being oxygenated by falling freely through pure oxygen at 20°C and a pressure of 1 atm. Do you need to know the gas-phase
Determination of diffusivity (Fig. 22B.7) the diffusivity of water vapor in nitrogen is to be determined at a pressure of 1 atm over the temperature range from 0°C to 100°C by means of the "Arnold
Marangoni effects in condensation of vapors. In many situations the heat transfer coefficient for condensing vapors is given as h = k/& where k is the thermal conductivity of the condensate film,
Film model for spheres derive the results that correspond to Eqs. 22.8-3, 4 for simultaneous heat and mass transfer in a system with spherical symmetry that is, assume a spherical mass transfer
Film model for cylinders derive the results that correspond to Eqs. 22.8-3, 4 for a system with cylindrical symmetry, that is, assume a cylindrical mass transfer surface and assume that T and XA
Expansion of a gas mixture very slow reaction rate, estimate the temperature and velocity of the water-gas mixture at the discharge end of the nozzle in Example 23.5-3 if the reaction rate is very
Height of a packed-tower absorber a packed tower of the type described in Example 23.5-2 is to be used for removing 90% of the cyclohexane from a cyclohexane-air mixture by absorption into a
Effective average driving forces in a gas absorber consider a packed-tower gas absorber of the type discussed in Example 23.5-2. Assume that the solute concentration is always low and that the
Irreversible first-order reaction in a continuous reactor, a well-stirred reactor of volume V is initially completely filled with a solution of solute A in a solvent S at concentration CAO. At time t
Isotope separation and the value function, you wish to compare an existing isotope fractionators that processes 50 moles/hr of a feed containing 1.0 mole% of the desired isotope to a product of 90%
Irreversible second-order reaction in an agitated tank consider a system similar to that discussed in Problem 23B.4, except that the solute disappears according to a second-order reaction; that is,
Start-up of a chemical reactor rework Example 23.6-1 by use of Laplace transforms of Eqs. 23.6-2 and 3
Transient behavior of N reactors in series2 there are N identical chemical reactors of volume V connected in series, each equipped with a perfect stirrer. Initially, each tank is filled with pure
Thermal diffusion(a) Estimate the steady-state separation of H2 and D2 occurring in the simple thermal diffusion apparatus shown in Fig. 24.3-1 under the following conditions: T1 is 200K, T2 is 600K
Ultracentrifugation of proteins estimate the steady-state concentration profile when a typical albumin solution is subjected to a centrifugal field 50,000 times the force of gravity under the
The dimensions of the Lorentz force. Show how the Lorentz force on a charge moving through a magnetic field corresponds to the first term added to the linear da of Eq. 25.4-51 and gives a consistent
Junction potentials, consider two well-mixed reservoirs of aqueous salt at 25°C, as in Fig. 24.4-2, separated by a stagnant region. Salt concentrations are 1.0 N on the left (1) and 0.1 N on the
Osmotic pressure, typical sea water, containing 3.45% by weight of dissolved salts, has a vapor pressure 1.84% below that of pure water. Estimate the minimum possible trans-membrane pressure required
Permeability of a perfectly selective filtration membrane develops an expression for the hydraulic permeability of the perfectly selective membrane described in Example 22.8-5 in terms of the
Expressions for the mass flux (a) Show how to transform the left side of Eq. 24.2-8 into the left side of Eq. 24.2-9. First rewrite the former as follows: Rewrite the second term as a sum

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