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engineering
heat and mass transfer fundamentals and applications

Questions and Answers of Heat And Mass Transfer Fundamentals And Applications

Consider the diffusion of urea in an agar gel discussed in Example 1.26. In this case the gel, containing a uniform initial urea concentration of \(50 \mathrm{~g} / \mathrm{L}\), is molded in the
Consider the ternary mixture of Example 6.2 and Problem 6.3. It is desired to recover in the vapor \(75 \%\) of the benzene in the feed, and to recover in the liquid \(70 \%\) of the \(o\)-xylene in
Consider the binary batch distillation of Example 6.3. For this system, \(n\)-heptane with \(n\)-octane at \(1 \mathrm{~atm}\), the average relative volatility is \(\alpha=2.16\) (Treybal, 1980).
Consider the differential distillation of Example (6.3. For this system, \(n\)-heptane with \(n\)-octane at \(1 \mathrm{~atm}\), the average relative volatility is \(\alpha=2.16\) (Treybal, 1980).
Consider the extraction process of Problem 7.3. Calculate the total amount of solvent required if the extraction is done in a crosscurrent cascade consisting of 5 ideal stages. Use equation (3-89)
Larson (1964) measured the diffusivity of chloroform in air at \(298 \mathrm{~K}\) and a pressure of \(1 \mathrm{~atm}\) and reported its value as \(0.093 \mathrm{~cm}^{2} / \mathrm{s}\). Estimate
If one or both components of a binary gas mixture are polar, a modified Lennard-Jones relation is often used. Brokaw (equation (1969) has suggested an alternative method for this case. 1-49) is used,
A wetted-wall experimental setup consists of a glass pipe, \(50 \mathrm{~mm}\) in diameter and \(1.0 \mathrm{~m}\) long. Water at \(300 \mathrm{~K}\) flows down the inner wall. Dry air enters the
(a) In studying rates of diffusion of naphthalene into air, an investigator replaced a \(30.5-\mathrm{cm}\) section of the inner pipe of an annulus with a naphthalene rod. The annulus was composed of
During the experiment described in Problem 2.3, the air velocity was measured at \(6 \mathrm{~m} / \mathrm{s}\), parallel to the longest side of the pan. Estimate the mass-transfer coefficient
During the experiment described in Problem 2.2, the air velocity was measured at \(10 \mathrm{~m} / \mathrm{s}\). Estimate the mass-transfer coefficient predicted by equation (2-64) and compare it to
Water flows through a thin tube, the walls of which are lightly coated with benzoic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2}\right)\). The water flows slowly, at \(298 \mathrm{~K}\)
In studying the sublimation of naphthalene into an airstream, an investigator constructed a 3-m-long annular duct. The inner pipe was made from a \(25-\mathrm{mm}-\mathrm{OD}\), solid naphthalene
The interfacial surface area per unit volume, \(a\), in many types of packing materials used in industrial towers is virtually impossible to measure. Both \(a\) and the mass-transfer coefficient
Cavatorta et al. (1999) studied the electrochemical reduction of ferricyanide ions, \(\left\{\mathrm{Fe}(\mathrm{CN})_{6}\right\}^{-3}\), to ferrocyanide,
Design a packed-bed air humidifier to process \(9.12 \mathrm{~kg} / \mathrm{h}\) of dry air. Assume that conditions are like those of Example 2.13. The packing will consist of spherical glass beads
At a different point in the packed distillation column of Example 3.10, the methanol content of the bulk of the gas phase \(76.2 \mathrm{~mol} \%\); that of the bulk of the liquid phase is \(60
Consider a countercurrent mass-transfer device for which the equilibrium distribution relation consists of a set of discrete values \(\left\{X_{i D}, Y_{i D}\right\}\) instead of a continuous model
The drying and liquid–liquid extraction operations described in Problems 3.20 and 3.21, respectively, are examples of a flow configuration called a cross-flow cascade. Figure 3.30 is a schematic
Repeat the calculations of Examples 4.6, 4.7, 4.8, and 4.9 for a column diameter corresponding to \(50 \%\) of flooding.Data From Example 4.6:-Design a sieve-tray column for the ethanol absorber of
Repeat the calculations of Example 9.5, but for a total solution normality of 0.5.Data From Example 9.5:-For the Cu2+/Na+ exchange with a strong-acid resin, show how the fraction CuR2 in the resin
In the benzene adsorber of Example 9.7, the flow rate is increased to \(0.25 \mathrm{~m}^{3} / \mathrm{s}\). Calculate the breakthrough time and the fraction of the bed adsorption capacity that has
Redesign the VOCs adsorber of Example 9.15 for a breakthrough time of \(4.0 \mathrm{~h}\). The pressure drop through the bed [calculated using the Ergun equation (2-95)] should not exceed \(1.0
Thermal regeneration of a fixed-bed adsorber is based on the fact that the adsorption process is exothermic; therefore, heating the saturated adsorbent will result in desorption. The dynamics of the
Repeat the calculations of Example 6.3, but for \(80 \mathrm{~mol} \%\) of the liquid distilled.Data From Example 6.3:-Suppose the liquid of Example 6.1 [50 mol% n-heptane (A), 50 mol% n-octane (B)]
Redesign the fractionator of Example 6.8 using a random packing. The column is to be packed with 50-mm metal Pall rings. Determine the diameter of the tower, the height of packing in the stripping
Redesign the fractionator of Example 6.8 for a reflux ratio that is twice the minimum. Determine the diameter of the tower, the height of packing in the stripping and rectifying sections, and the
Repeat Example 7.3 using \(10 \mathrm{~kg} / \mathrm{h}\) of solvent in each stage.Data From Example 7.3:-The feed of Example 7.2 is extracted three times with pure chloroform at 298 K, using 8 kg/h
Determine the number of ideal stages required in Example 7.4 if the solvent rate used is twice the minimum.Data From Example 7.4:-A solution of acetic acid (C) in water (A) is to be extracted using
This is a special case of countercurrent gas-liquid contact in which the liquid enters the equipment at the adiabatic-saturation temperature of the entering gas. This can be achieved by continuously
A bed of ion-exchange beads \(1.5 \mathrm{~mm}\) in diameter is used to deionize water at \(293 \mathrm{~K}\) with a superficial velocity of \(0.6 \mathrm{~cm} / \mathrm{s}\). The feed concentration
Calculate the ideal break time for the ion exchanger of Problem 9.11.Data From Problem 9.11:-A bed of ion-exchange beads \(1.5 \mathrm{~mm}\) in diameter is used to deionize water at \(293
Ultrafiltration of a protein solution at constant volume is achieved by the addition of water or buffer to the feed in an operation called diafiltration. Consider a protein diafiltration system where
Modify the Mathcad program of Figure 6.3 for ternary mixtures. Test your program with the data presented in Example 6.2 for a mixture of benzene (A), toluene (B), and \(o\)-xylene (C). Critical
The cooling water flow rate to the condensers of a big coal-fired power plant is \(8970 \mathrm{~kg} / \mathrm{s}\). The water enters the condensers at \(29^{\circ} \mathrm{C}\) and leaves at
Since its introduction in the market in 1995, numerous mass-transfer columns have been packed with Raschig Super-Rings-a new fourth-generation packing shown in Figure 4.8-in various chemical
The latent heat of vaporization per unit mass of a pure substance at a given temperature, \(\lambda\), is defined as the difference in enthalpy between the saturated vapor and saturated liquid at the
Air at \(345 \mathrm{~K}\) has a dew-point temperature of \(312 \mathrm{~K}\). Calculate the absolute and relative humidity, and the enthalpy of the mixture relative to liquid water and air at \(273
Calculate the absolute humidity, relative saturation, and dew-point temperature of a mixture of benzene-nitrogen at a pressure of \(1.5 \mathrm{bar}\) and temperature of \(320 \mathrm{~K}\) if the
In a plant for the recovery of acetone which has been used as a solvent, the acetone is evaporated into a stream of nitrogen gas. A mixture of acetone vapor and nitrogen flows through a duct, 0.3 by
A drier requires \(1.5 \mathrm{~m}^{3} / \mathrm{s}\) of air at \(338 \mathrm{~K}, 1 \mathrm{~atm}\), and \(20 \%\) relative humidity. This is to be prepared from air at \(300 \mathrm{~K}\) dry-bulb,
Modify the Mathcad program developed in Problem 3.16 to estimate the minimum gas flow rate in strippers so that it can be used to estimate the minimum air flow required for water cooling. Test your
In the cooling tower of Example 8.7, to what temperature would the water be cooled if, after the tower was built and operated at the design water and air rates, the air entered at a dry-bulb
A recently installed induced-draft cooling tower (with the fan located at the top) was guaranteed by the manufacturer to cool \(450 \mathrm{~m}^{3} / \mathrm{h}\) of water from \(316 \mathrm{~K}\) to
Water is to be cooled at the rate of \(10 \mathrm{~kg} / \mathrm{s}\) from \(317 \mathrm{~K}\) to \(300 \mathrm{~K}\) in a countercurrent cooling tower under conditions such that \(H_{t O G}=2.5
A cooling tower cools \(227 \mathrm{~m}^{3} / \mathrm{h}\) of water from \(314 \mathrm{~K}\) to \(306 \mathrm{~K}\) using a countercurrent forced draft of air entering at \(317 \mathrm{~K}\) and
A nuclear power plant produces 1000 megawatts of electricity with a power cycle thermodynamic efficiency of \(30 \%\). The heat rejected is removed by cooling water that enters the condenser at \(293
It is desired to dehumidify \(1.2 \mathrm{~m}^{3} / \mathrm{s}\) of air, available at \(311 \mathrm{~K}\) with a wet-bulb temperature of \(303 \mathrm{~K}\), to a wet-bulb temperature of \(288
Demonstrate equation (9-76). For dilute solutions of solute \(B\) in solvent \(\mathrm{A}, x_{B} \approx n_{B} / n_{A}\).Data From Equation 9-76:- RTx (1) B VAL RTCB MB (9-76)
The membrane in Example 9.1 is replaced with another of the same thickness, but with a permeability of 300 barrer for solute A. Calculate the transmembrane flux of solute A if the film coefficients
Repeat Example 9.2, but with a feed pressure of 5.0 MPa. Compare your results to those obtained at a feed pressure of 1.0 \(\mathrm{MPa}\).Data From Example 9.2:-Air can be separated into
Repeat Example 9.3, but with a feed pressure of 5.0 MPa. Compare your results to those obtained at a feed pressure of \(1.0 \mathrm{MPa}\).Data From Example 9.3:-Consider the air separation problem
Laboratory tests of a membrane for \(\mathrm{H}_{2} / \mathrm{CH}_{4}\) separation gave a permeate composition of \(80 \% \mathrm{H}_{2}\) and a \(20 \%\) cut when the feed was \(50 \%
The following data have been reported for equilibrium adsorption of benzene on certain activated carbon at \(306 \mathrm{~K}\).(a) Fit a Langmuir-type isotherm to these data.(b) Fit a Freundlich-type
The equilibrium adsorption of methane on a given activated carbon was studied by Grant et al. (1962). They proposed a Langmuir-type adsorption isotherm with parameters \(q_{m}=48 \mathrm{~g}
In the benzene adsorber of Example 9.6, the flow rate is increased to \(0.25 \mathrm{~m}^{3} / \mathrm{s}\). Calculate the breakthrough time and the fraction of the bed adsorption capacity that has
If the aqueous solution of Example 9.10 also contained \(2 \mathrm{~g} / \mathrm{cm}^{3}\) of sucrose ( \(K_{c} a=0.0429 \mathrm{~s}^{-1}, \kappa=0.9 \mathrm{~cm}^{3} / \mathrm{g}\) ), generate the
Eastern European farmers produce a variety of fruit juices, which they wish to dehydrate to prolong shelf-life and facilitate transportation. One very simple dehydration method is to put the juice in
Pervaporation (PV) is a membrane-separation process in which one or more components of a liquid mixture diffuse through a selective membrane, evaporate under low pressure on the downstream side, and
Repeat the calculations of Example 9.13, but for an initial protein concentration of the whey of \(30 \mathrm{~g} / \mathrm{L}\).Data From Example 9.13:-The coagulation process to produce cheese out
The Bohart-Adams model is an exact analytic solution for fixed-bed adsorbers when the adsorption isotherm is irreversible, \(q=q_{m}\) (see Figure 9.5). The sorbate concentration in the solution is
Consider a tray absorber with a constant Murphree efficiency \(\mathbf{E}_{M G E}=0.75\), and an average absorption factor \(A=1.25\).(a) Estimate the overall tray efficiency.(b) If the absorber
Derive equation (5-5). Start with the definition of \(\mathbf{E}_{M G E}\) and locate the pseudoequilibrium line which could be used together with the operating line for graphically constructing
A tray tower providing six equilibrium stages is used for stripping ammonia from a wastewater stream by means of countercurrent air at \(1 \mathrm{~atm}\) and \(300 \mathrm{~K}\). Calculate the
The Murphree plate efficiency for the ammonia stripper of Problem 5.3 is constant at \(53.5 \%\). Estimate the number of real trays required.Data From Problem 5.3:-A tray tower providing six
If the air flow rate to the absorber of Problems 5.3 and 5.4 is reduced to 1.0 standard \(\mathrm{m}^{3} / \mathrm{kg}\) of water, calculate concentration of ammonia in the exit water if 8 real trays
A heavy-oil stream at \(320 \mathrm{~K}\) is used in an absorber to remove dilute quantities of pollutant A from an air stream. The heavy oil is then recycled back to the process where A is stripped.
An absorption column for laboratory use has been carefully constructed so that it has exactly 4 equilibrium stages and is being used to measure equilibrium data. Water is used as the solvent to
A process for making small amounts of hydrogen by cracking ammonia is being considered and residual, uncracked ammonia is to be removed from the resulting gas. The gas will consist of
A plant manufacturing dry ice will burn coke in air to produce a flue gas which, when cleaned and cooled, will contain \(15 \% \mathrm{CO}_{2}, 6 \% \mathrm{O}_{2}\), and \(79 \% \mathrm{~N}_{2}\).
Example 2.14 introduced the design equation for a countercurrent hollowfiber boiler feed water deaerator when all the resistance to mass transfer resides on the liquid phase and the entering gas
Carbon disulfide, \(\mathrm{CS}_{2}\), used as a solvent in a chemical plant, is evaporated from the product in a dryer into an inert gas (essentially \(\mathrm{N}_{2}\) ) in order to avoid an
Repeat Problem 5.11, but design for a liquid rate 2.0 times the minimum and \(60 \%\) of the flooding velocity.Data From Problem 5.11:-Carbon disulfide, \(\mathrm{CS}_{2}\), used as a solvent in a
With the help of the Kremser equation (5-3) and equation (5-24), derive the relation between \(N\) and \(N_{t O G}\) for constant absorption factor. Establish the condition for which \(N=N_{t O
Design a tower packed with \(50-\mathrm{mm}\) ceramic Hiflow rings for the carbon disulfide scrubber of Problem 5.11. Assume isothermal operation and use a liquid rate of 1.5 times the minimum and a
It is desired to remove \(90 \%\) of the sulfur dioxide in a flue gas stream at \(298 \mathrm{~K}\) and \(1 \mathrm{~atm}\) by countercurrent absorption with pure water at the same temperature, using
Benzene vapor in the gaseous effluent of an industrial process is scrubbed with a wash oil in a countercurrent packed absorber. The resulting benzene-wash oil solution is then heated to \(398
For dilute mixtures and when Henry's law applies, prove that the number of overall transfer units for cocurrent gas absorption in packed towers is given bywhere subscript 1 indicates the top (where
Germanium tetrachloride \(\left(\mathrm{GeCl}_{4}\right)\) and silicon tetrachloride \(\left(\mathrm{SiCl}_{4}\right)\) are used in the production of optical fibers. Both chlorides are oxidized at
Redesign the absorber of Problem 5.15 using metal Montz B2-300 structured packing. The characteristics of this packing are (Billet and Schultes, 1999)Data From Problem 5.15:-Design a tower packed
It is desired to reduce the ammonia content of \(0.05 \mathrm{~m}^{3} / \mathrm{s}\) of an ammonia-air mixture ( \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\) ) from \(5.0 \%\) to \(0.04 \%\) by volume
A tower packed with metal Montz B2-300 structured packing is to be designed to absorb \(\mathrm{SO}_{2}\) from air by scrubbing with water. The entering gas, at an \(\mathrm{SO}_{2}\)-free flow rate
Repeat Problem 5.22 using \(50-\mathrm{mm}\) ceramic Pall rings as packing material. Compare your results to those of Problem 5.22.Data From Problem 5.22:-A tower packed with metal Montz B2-300
A system for recovering methanol from a solid product wet with methanol involves evaporation of the alcohol into a stream of inert gas, essentially nitrogen. In order to recover the methanol from the
A tower \(0.6 \mathrm{~m}\) in diameter, packed with \(50-\mathrm{mm}\) ceramic Raschig rings to a depth of \(1.2 \mathrm{~m}\), is to be used for producing a solution of oxygen in water for certain
Air at \(300 \mathrm{~K}\) is used to dry a plastic sheet. The solvent wetting the plastic is acetone. At the end of the dryer, the air leaves containing \(2.0 \mathrm{~mol} \%\) acetone. The acetone
You are asked to design a packed column to recover acetone from air continuously by absorption with pure water at \(289 \mathrm{~K}\). The air contains \(3.0 \mathrm{~mol} \%\) acetone, and a \(97
A liquid mixture containing \(50 \mathrm{~mol} \%\)-heptane (A) and \(50 \mathrm{~mol} \%\)-octane (B), at \(303 \mathrm{~K}\), is to be continuously flash-vaporized at a pressure of \(1
A liquid mixture containing \(50 \mathrm{~mol} \%\)-heptane (A) and \(50 \mathrm{~mol} \%\)-octane (B), at \(303 \mathrm{~K}\), is to be continuously flash-vaporized at a temperature of \(350
Consider the ternary mixture of Example 6.2 and Problem 6.3. Estimate the temperature, and composition of the liquid and vapor phases when \(60 \%\) of the mixture has been vaporized at a constant
If equation (6-40) describes the equilibrium relation at constant pressure by use of some average relative volatility \(\alpha\) over the concentration range involved, show that equation (6-11)
Because of the complex concentration functionality of the \(m\)-values, VLE calculations in general require iterative procedures suited only to computer solutions. However, in the case of mixtures of
A solution has the following composition, expressed as mol percentage: ethane, \(0.25 \%\); propane, \(25 \%\); isobutane, \(18.5 \%\); \(n\)-butane, \(56 \%\); isopentane, \(0.25 \%\). In the
An open kettle contains \(50 \mathrm{kmol}\) of a dilute aqueous solution of methanol ( \(2 \mathrm{~mol} \%\) of methanol), at the bubble point, into which steam is continuously sparged. The
For continuous distillation of a binary mixture of constant relative volatility, Fenske equation (6-58) can be used to estimate the minimum number of equilibrium stages required for the given
For continuous distillation of a binary mixture of constant relative volatility, the minimum reflux ratio can be determined analytically from the following equation (Treybal, 1980):Use (6-108) to
When the equilibrium curve is always concave downward, the minimum reflux ratio can be calculated algebraically. The required relationship can be developed by solving simultaneously equations (6-18),
a) Show that the problem of flash vaporization of a multicomponent ideal mixture can be reformulated as suggested by Rachford and Rice (Doherty and Malone, 2001):Equation (6-109) is solved
A water-isopropanol mixture at its bubble point containing \(10 \mathrm{~mol} \%\) isopropanol is to be continuously rectified at atmospheric pressure to produce a distillate containing \(67.5
A distillation column is separating \(1000 \mathrm{~mol} / \mathrm{h}\) of a \(32 \mathrm{~mol} \%\) ethanol, \(68 \mathrm{~mol} \%\) water mixture at atmospheric pressure. The feed enters as a

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