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engineering
heat and mass transfer fundamentals and applications

Questions and Answers of Heat And Mass Transfer Fundamentals And Applications

Generate the Janecke diagram and the distribution curve for the system cottonseed oil (A)-propane (B)-oleic acid (C) at \(372 \mathrm{~K}\) and \(42.5 \mathrm{~atm}\).
If \(100 \mathrm{~kg}\) of a cottonseed oil-oleic acid solution containing \(25 \mathrm{wt} \%\) acid is extracted twice in crosscurrent fashion, each time with \(1000 \mathrm{~kg}\) of pure propane,
If \(1000 \mathrm{~kg} / \mathrm{h}\) of a cottonseed oil-oleic acid solution containing \(25 \mathrm{wt} \%\) acid is to be continuously separated into two products containing 2 and \(90 \mathrm{wt}
Acetic acid is to be extracted from a dilute aqueous solution with isopropyl ether at \(298 \mathrm{~K}\) in a countercurrent cascade of mixer-settler units. In one of the units, the following
Estimate the diameter and height of an RDC column to extract acetic acid from water using isopropyl ether for the conditions and data of Problem 7.21. For the desired degree of separation, 15
Estimate the diameter and the HETS of a Karr column to extract acetic acid from water using isopropyl ether for the conditions and data of Problem 7.21.Data From Problem 7.21:-Acetic acid is to be
A monoacidic sugar extracted from water into hexanol has partition coefficients of 4.5 and 2.0 at \(\mathrm{pH} 4.0\) and 5.5, respectively, both at the same temperature. Estimate the value of
Phase-distribution measurements were made for the PEG 3400 - dextran T40 - water system at \(4{ }^{\circ} \mathrm{C}\) by Diamond and Hsu (1989). The following table gives the equilibrium
Alcohol dehydrogenase (ADH) is an enzyme that occurs in many organisms and facilitates the interconversion between alcohols and aldehydes or ketones with the reduction of nicotinamide adenine
A mixture of noble gases (helium, argon, krypton, and xenon) is at a total pressure of \(150 \mathrm{kPa}\) and a temperature of \(500 \mathrm{~K}\). If the mixture has equal mole fractions of each
A solution of carbon tetrachloride and carbon disulfide containing \(50 \%\) by weight of each is to be continuously distilled at the rate of \(5000 \mathrm{~kg} / \mathrm{h}\).(a) Determine the
A sample of liquefied natural gas, LNG, from Alaska has the following molar composition: \(93.5 \% \mathrm{CH}_{4}, 4.6 \% \mathrm{C}_{2} \mathrm{H}_{6}, 1.2 \% \mathrm{C}_{3} \mathrm{H}_{8}\), and
A flue gas consists of carbon dioxide, oxygen, water vapor, and nitrogen. The molar fractions of \(\mathrm{CO}_{2}\) and \(\mathrm{O}_{2}\) in a sample of the gas are \(12 \%\) and \(6 \%\),
A gas stream flows at the rate of \(10.0 \mathrm{~m}^{3} / \mathrm{s}\) at \(300 \mathrm{~K}\) and \(102 \mathrm{kPa}\). It consists of an equimolar mixture of ammonia and air. The gas enters through
A gas mixture at a total pressure of \(150 \mathrm{kPa}\) and \(295 \mathrm{~K}\) contains \(20 \% \mathrm{H}_{2}, 40 \%\) \(\mathrm{O}_{2}\), and \(40 \% \mathrm{H}_{2} \mathrm{O}\) by volume. The
Air, stored in a \(30-\mathrm{m}^{3}\) container at \(340 \mathrm{~K}\) and \(150 \mathrm{kPa}\), is saturated with water vapor. Determine the following properties of the gas mixture:(a) Mol fraction
It is desired to dry \(10 \mathrm{~kg} / \mathrm{min}\) of soap continuously from \(20 \%\) moisture by weight to \(4 \%\) moisture in a countercurrent stream of hot air. The air enters the dryer at
A waste gas contains \(0.5 \%\) toluene in air and occupies a volume of \(2500 \mathrm{~m}^{3}\) at \(298 \mathrm{~K}\) and \(101.3 \mathrm{kPa}\). To reduce the toluene content of this gas, it is
It is desired to adsorb \(99.8 \%\) of the toluene originally present in the waste gas of Problem 1.10. Estimate how much activated carbon should be used if the system is allowed to reach equilibrium
(a) Estimate the diffusivity of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) in air at \(303 \mathrm{~K}\) and 1 bar. Compare it with the experimental value of \(0.087 \mathrm{~cm}^{2}
Evaluate the diffusion coefficient of hydrogen sulfide in sulfur dioxide at a temperature of \(298 \mathrm{~K}\) and a pressure of 1.5 bar. The data required to use Brokaw's relation are shown below
Evaluate the diffusion coefficient of hydrogen sulfide in sulfur dioxide at a temperature of \(298 \mathrm{~K}\) and a pressure of 1.5 bar. The data required to use Brokaw's relation are shown below
Calculate the effective diffusivity of nitrogen through a stagnant gas mixture at \(400 \mathrm{~K}\) and 1.5 bar. The mixture composition is 02 CO2 888 15 mol% 30% 35% N2 20%
Mercury is considered for possible regulation in the electric power industry under Title III of the 1990 Clean Air Act Amendments. One promising approach for removing mercury from fossil-fired flue
When a salt dissociates in solution, ions rather than molecules diffuse. In the absence of an electric potential, the diffusion of a single salt may be treated as molecular diffusion. For dilute
Estimate the diffusion coefficient of oxygen in liquid water at \(298 \mathrm{~K}\). Use the Hayduk and Minhas correlation for solutes in aqueous solutions. At this temperature, the viscosity of
Estimate the diffusivity of carbon tetrachloride in a dilute solution in \(n\)-hexane at \(298 \mathrm{~K}\) using the Hayduk and Minhas correlation for nonaqueous solutions. Compare the estimate to
The diffusivity of allyl alcohol \(\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right)\) in a very dilute aqueous solution at \(288 \mathrm{~K}\) is \(0.9 \times 10^{-5} \mathrm{~cm}^{2} /
(a) Estimate the diffusivity of ethanol in water at \(298 \mathrm{~K}\) when the mol fraction of ethanol in solution is 40\%. Under these conditions (Hammond and Stokes, 1953),The experimental value
A flat plate of solid carbon is being burned in the presence of pure oxygen according to the reactionMolecular diffusion of gaseous reactant and products takes place through a gas film adjacent to
A crystal of Glauber's salt \(\left(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\right)\) dissolves in a large tank of pure water at \(288 \mathrm{~K}\). Estimate the rate at
A mixture of ethanol and water vapor is being rectified in an adiabatic distillation column. The alcohol is vaporized and transferred from the liquid to the vapor phase. Water vapor condenses-enough
It has been observed that for the system air-water vapor at near-ambient conditions, Le \(=1.0\) (Treybal, 1980). This observation, called the Lewis relation, has profound implications in
Water evaporating from a pond at \(298 \mathrm{~K}\) does so by molecular diffusion across an air film \(1.5 \mathrm{~mm}\) thick. If the relative humidity of the air at the outer edge of the film is
Calculate the fluxes and concentration profiles for the ternary system hydrogen (1), nitrogen (2), and carbon dioxide (3) under the following conditions. The temperature is \(308 \mathrm{~K}\) and
One of the oldest membrane materials used for dialysis is porous cellophane, a thin transparent sheet made of regenerated cellulose. Typical values of parameters for commercial cellophane membranes
Porous silica gel is used to adsorb propane from helium at \(373 \mathrm{~K}\) and \(1 \mathrm{~atm}\). Typical values of parameters for porous silica gel are as follows: porosity \(=0.486\),
It is desired to increase by \(50 \%\) the oxygen flux in the process described in Example 1.22 by changing the pore size while maintaining all the other conditions unchanged. Calculate the required
An unglazed porcelain plate \(5 \mathrm{~mm}\) thick has an average pore diameter of \(0.2 \mu \mathrm{m}\). Pure oxygen gas at an absolute pressure of \(20 \mathrm{~mm} \mathrm{Hg}, 400
Consider the hydrodynamic flow of nitrogen at \(400 \mathrm{~K}\) through the porous diaphragm described in Example 1.24. It is desired to achieve a superficial gas velocity through the diaphragm of
Oxygen uptake by the blood is faster than oxygen uptake by water because of the reaction of oxygen with hemoglobin. Many chemists have dreamed of inventing a new compound capable of fast, selective
Consider the Krogh cylinder model for oxygen transport in skeletal muscles described in Example 1.28.(a) At what radial position in the tissue surrounding the capillary entrance is the oxygen partial
As discussed in Example equation (1.28, zero-order kinetics is a good approximation to the Michaelis-Menten model if \(p_{A}\) is much larger than \(p_{0}\). However, when \(p_{A}\) and \(p_{0}\) are
A slab of clay \(50 \mathrm{~mm}\) thick was dried from both flat surfaces-with the four thin edges sealed-by exposure to dry air. The initial uniform moisture content was \(15 \%\). The drying took
To illustrate the slowness of molecular diffusion, an environmental engineering professor claims that one could place a droplet of water containing \(100 \mu \mathrm{g}\) of \(n\)-hexadecane into the
Ammonia, \(\mathrm{NH}_{3}\), is being selectively removed from an air \(-\mathrm{NH}_{3}\) mixture by absorption into water. In this steady-state process, ammonia is transferred by molecular
A gas absorber is used to remove benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) vapors from air by scrubbing the gas mixture with a nonvolatile oil at \(300 \mathrm{~K}\) and \(1
In a laboratory experiment, air at \(347 \mathrm{~K}\) and \(1 \mathrm{~atm}\) is blown at high speed around a single naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) sphere, which
In a laboratory experiment, air at \(300 \mathrm{~K}\) and 1 atm is blown at high speed parallel to the surface of a rectangular shallow pan that contains liquid acetone \(\left(\mathrm{C}_{3}
Aeration is a common industrial process and yet one in which there is often serious disagreement about correlations (Cussler, 1997). This is especially true for deep-bed fermentors and for sewage
In the artificial kidney, blood flowing inside a tubular membrane is dialyzed against well-stirred saline solution. Toxins in the blood diffuse across the membrane into the saline solution, thus
Winding and Cheney (1948) passed air at \(310 \mathrm{~K}\) and \(1 \mathrm{~atm}\) through a bank of rods of naphthalene. The rods were in a staggered arrangement, with the air flowing at right
A 1-m square thin plate of solid naphthalene is oriented parallel to a stream of air flowing at \(20 \mathrm{~m} / \mathrm{s}\). The air is at \(330 \mathrm{~K}\) and \(101.3 \mathrm{kPa}\). The
A thin plate of solid salt, \(\mathrm{NaCl}\), measuring 15 by \(15 \mathrm{~cm}\), is to be dragged through seawater at a velocity of \(0.6 \mathrm{~m} / \mathrm{s}\). The \(291 \mathrm{~K}\)
Repeat Example 2.9 for a drop of water which is originally \(2 \mathrm{~mm}\) in diameter.Data From Example 2.9:-Estimate the distance a spherical drop of water, originally 1.0 mm in diameter,must
Estimate the mass-transfer coefficient for the dissolution of sodium chloride from a cast sphere, \(1.5 \mathrm{~cm}\) in diameter, if placed in a flowing water stream. The velocity of the \(291
The crystal of Problem 1.25 is a sphere \(2 \mathrm{~cm}\) in diameter. It is falling at terminal velocity under the influence of gravity into a big tank of water at \(288 \mathrm{~K}\). The density
Water flows down the inside wall of a 25-mm-ID wetted-wall tower of the design of Figure 2.4, while air flows upward through the core. Dry air enters at the rate of \(7 \mathrm{~kg} / \mathrm{m}^{2}
Benzene is evaporating at \(20 \mathrm{~kg} / \mathrm{h}\) over the surface of a porous \(10-\mathrm{cm}\)-diameter cylinder. Dry air at \(325 \mathrm{~K}\) and \(1 \mathrm{~atm}\) flows at right
Wilke and Hougan (1945) reported the mass transfer in beds of granular solids. Air was blown through a bed of porous celite pellets wetted with water, and by evaporating this water under adiabatic
Air at \(373 \mathrm{~K}\) and \(2 \mathrm{~atm}\) is passed through a bed \(10 \mathrm{~cm}\) in diameter composed of iodine spheres \(0.7 \mathrm{~cm}\) in diameter. The air flows at a rate of \(2
An air-water vapor mixture flows upward through a vertical copper tube \(25.4-\mathrm{mm}\) OD, \(1.65-\mathrm{mm}\) wall thickness, which is surrounded by flowing cold water. As a result, water
Equation (2-76) can also be used for calculations of transpiration cooling, a method of cooling porous surfaces which are exposed to extremely hot gases by forcing a cold gas or evaporating liquid
Consider the hollow-fiber BFW deaerator described in Example 2.14. If the water flow rate increases to \(60,000 \mathrm{~kg} / \mathrm{h}\) while everything else remains constant, calculate the
(a) Consider the hollow-fiber BFW deaerator described in Example 2.14. If only oxygen diffuses across the membrane, calculate the gas volume flow rate and composition at the lumen outlet. The water
Because of intravascular resistance to oxygen diffusion, the oxygen partial pressure at the blood-tissue interface may be less than the average oxygen partial pressure in the blood. This effect can
Isopropanol (1) and water (2) are condensing in the presence of nitrogen (3) inside a vertical tube of \(2.54 \mathrm{~cm}\) inside diameter. At the vapor inlet, the bulk composition of the gas phase
A hollow, porous cylinder \(25 \mathrm{~mm}\) in OD, \(15 \mathrm{~mm}\) in ID, is fed internally with liquid diethyl ether at \(293 \mathrm{~K}\). The ether flows radially outward and evaporates on
The occurrence of mass transfer to and from droplets driven by buoyancy can be found in applications such as liquid-liquid extraction, and during environmental accidents such as deep water oil
The volumetric mass-transfer coefficient, \(k_{L} a\), is one of the most important transport characteristics used in the design of mechanically agitated gas-liquid contactors. These apparatuses are
Air and water are the two most important fluids on Earth. The physical processes at the surfaces of oceans, estuaries, rivers, and lakes relevant to the exchange of chemicals between the two phases
Repeat Example 3.1, but for a liquid concentration of $0.5 \mathrm{~mol}$ fraction of benzene and a temperature of $310 \mathrm{~K}$.Data From Example 3.1:-Raoult’s law may be used to determine
(a) Determine the composition of the liquid in equilibrium with a vapor containing 70 mol%70 mol% benzene, 30 mol%30 mol% toluene if the system exists in a vessel under a pressure
Normal heptane, n−C7H16n−C7H16, and normal octane, n−C8H18n−C8H18, form ideal solutions. At 373 K373 K, normal heptane has a vapor pressure of 106kPa106kPa and normal octane of
A solution with oxygen dissolved in water containing $0.5 \mathrm{mg} \mathrm{\textrm {O } _ { 2 }} / 100 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O}$ is brought in contact with a large volume of
Repeat Example 3.3, but assume that the ammonia, air, and water are brought into contact in a closed container. There is $10.0 \mathrm{~m}^{3}$ of gas space over the liquid. Assuming that the
Consider the behavior of the amino acid alanine as a function of $\mathrm{pH}$ shown in the following sequence of reactions.The sequence shown starts at low $\mathrm{pH}$ (high hydrogen ion
Serine $\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NO}_{3}\right)$ is a nonessential amino acid that plays an important role in the catalytic function of many enzymes. The dissociation constants for
In the absorption of component A (molecular weight $=60$ ) from an airstream into an aqueous solution, the bulk compositions of the two adjacent streams at a point in the apparatus were analyzed to
For a system in which component $\mathrm{A}$ is transferring from the gas phase to the liquid phase, the equilibrium relation is given by $p_{A, i}=0.80 x_{A, i}$ where $p_{A, i}$ is the equilibrium
Modify the Mathcad program in Figure 3.6 to repeat Example 3.9, but with $y_{A, G}=0.70$ and $x_{A, L}=0.10$. Everything else remains constant.Data From Example 3.9:-A wetted-wall absorption tower is
Modify the Mathcad program in Figure 3.6 to repeat Example 3.9, but with $F_{L}=5.0 \mathrm{~mol} / \mathrm{m}^{2}$-s. Everything else remains constant.Data From Example 3.9:-A wetted-wall absorption
In the absorption of ammonia into water from an air-ammonia mixture at 300 K300 K and 1 atm1 atm, the individual film coefficients were estimated to be
For mass transfer across the hollow-fiber membrane contactors described in Example 2.14, the overall mass-transfer coefficient based on the liquid concentration, $K_{L}$, is given by (Yang and
During absorption of low-solubility gases, mass transfer from a highly concentrated gas mixture to a very dilute liquid solution frequently takes place. In that case, although it is appropriate to
Activated carbon is used to recover benzene from a nitrogen-benzene vapor mixture. The mixture, at $306 \mathrm{~K}$ and $1 \mathrm{~atm}$ containing $1.0 \%$ benzene by volume, is to be passed
The activated carbon leaving the adsorber of Problem 3.17 is regenerated by countercurrent contact with steam at $380 \mathrm{~K}$ and $1 \mathrm{~atm}$. The regenerated carbon is returned to the
If the adsorption process described in Problem 3.17 took place cocurrently, calculate the minimum flow rate of activated carbon required.Data From Problem 3.17:-Activated carbon is used to recover
It is desired to dry $10 \mathrm{~kg}$ of soap from $20 \%$ moisture by weight to no more than $6 \%$ moisture by contact with hot air. The wet soap is placed in a vessel containing $8.06
Nicotine in a water solution containing $2 \%$ nicotine is to be extracted with kerosene at $293 \mathrm{~K}$. Water and kerosene are essentially insoluble in each other. Determine the percentage
Consider the nicotine extraction of Problems 3.21 and 3.22. Calculate the number of ideal stages required to achieve at least $95 \%$ extraction efficiency.Data From Problem 3.21:-Nicotine in a water
A scheme for the removal of $\mathrm{H}_{2} \mathrm{~S}$ from a flow of $1.0 \mathrm{std} \mathrm{m}^{3} / \mathrm{s}$ of natural gas by scrubbing with water at $298 \mathrm{~K}$ and 10 atm is being
As shown in Problem 3.24, scrubbing of hydrogen sulfide from natural gas using water is not practical since it requires large amounts of water due to the low solubility of $\mathrm{H}_{2}
A flue gas flows at the rate of 10kmol/s10kmol/s at 298 K298 K and 1 atm1 atm with a SO2SO2 content of 0.15 mol%0.15 mol%. Ninety percent of the sulfur dioxide is to be
An absorber is available to treat the flue gas of Problem 3.26, which is equivalent to 8.5 equilibrium stages.Data From Problem 3.26:-A flue gas flows at the rate of $10 \mathrm{kmol} / \mathrm{s}$
An aqueous acetic acid solution flows at the rate of $1000 \mathrm{~kg} / \mathrm{h}$. The solution is $1.1 \mathrm{wt} \%$ acetic acid. It is desired to reduce the concentration of this solution to
A 1-butanol acid solution is to be extracted with pure water. The butanol solution contains 4.5wt%4.5wt% of acetic acid and flows at the rate of 400 kg/h400 kg/h. A total water flow rate of
Ching and Ruthven (1985) found that the equilibrium of glucose on an ionexchange resin in the calcium form was linear for concentrations below 50 g/L50 g/L. Their equilibrium expression at
Consider a cylindrical vessel with a diameter of $610 \mathrm{~mm}$ packed with solid spheres with a diameter of $50 \mathrm{~mm}$.(a) From equation (4-1), calculate the asymptotic porosity of the
Because of the oscillatory nature of the void-fraction radial variation of packed beds, there are a number of locations close to the wall where the local void fraction is exactly equal to the

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