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14–2C How is the concentration of a commodity defined? How is the concentration gradient defined? How is the diffusion rate of a commodity related to the concentration gradient
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14–3C Give examples for (a) liquid-to-gas, (b) solid-toliquid, (c) solid-to-gas, and (d) gas-to-liquid mass transfer
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14–4C Someone suggests that thermal (or heat) radiation can also be viewed as mass radiation since, according to Einstein’s formula, an energy transfer in the amount of E corresponds to a mass transfer in the amount of m E/c2. What do you think
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14–5C What is the driving force for (a) heat transfer, (b) electric current flow, (c) fluid flow, and (d) mass transfer
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14–6C What do (a) homogeneous reactions and (b) heterogeneous reactions represent in mass transfer? To what do they correspond in heat transfer?
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14–7C Both Fourier’s law of heat conduction and Fick’s law of mass diffusion can be expressed as Q · kA(dT/dx). What do the quantities Q · , k, A, and Trepresent in (a) heat conduction and (b) mass diffusion
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14–8C Mark these statements as being True or False for a binary mixture of substances A and B. (a) The density of a mixture is always equal to the sum of the densities of its constituents. (b) The ratio of the density of component A to the density of component B is equal to the mass fraction of component A. (c) If the mass fraction of component A is greater than 0.5, then at least half of the moles of the mixture are component A. (d) If the molar masses of A and B are equal to each other, then the mass fraction of A will be equal to the mole fraction of A. (e) If the mass fractions of A and B are both 0.5, then the molar mass of the mixture is simply the arithmetic average of the molar masses of A and B.
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14–9C Mark these statements as being True or False for a binary mixture of substances A and B. (a) The molar concentration of a mixture is always equal to the sum of the molar concentrations of its constituents. (b) The ratio of the molar concentration of A to the molar concentration of B is equal to the mole fraction of component A. (c) If the mole fraction of component A is greater than 0.5, then at least half of the mass of the mixture is component A. (d) If both Aand Bare ideal gases, then the pressure fraction of A is equal to its mole fraction. (e) If the mole fractions of A and B are both 0.5, then the molar mass of the mixture is simply the arithmetic average of the molar masses of A and B
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14–10C Fick’s law of diffusion is expressed on the mass and mole basis as m · diff, A = -pADAB(dwA/dx) and N · diff, A = -CADAB(dyA/dx), respectively. Are the diffusion coefficients DAB in the two relations the same or different
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14–11C How does the mass diffusivity of a gas mixture change with (a) temperature and (b) pressure
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14–12C At a given temperature and pressure, do you think the mass diffusivity of air in water vapor will be equal to the mass diffusivity of water vapor in air? Explain
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14–13C At a given temperature and pressure, do you think the mass diffusivity of copper in aluminum will be equal to the mass diffusivity of aluminum in copper? Explain
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14–14C In a mass production facility, steel components are to be hardened by carbon diffusion. Would you carry out the hardening process at room temperature or in a furnace at a high temperature, say 900°C? Why
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14–15C Someone claims that the mass and the mole fractions for a mixture of CO2 and N2O gases are identical. Do you agree? Explain
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14–16 The composition of moist air is given on a molar basis to be 78 percent N2, 20 percent O2, and 2 percent water vapor. Determine the mass fractions of the constituents of air.
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14–17E Agas mixture consists of 5 lbm of O2, 8 lbm of N2, and 10 lbm of CO2. Determine (a) the mass fraction of each component, (b) the mole fraction of each component, and (c) the average molar mass of the mixture
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14–18 Agas mixture consists of 8 kmol of H2 and 2 kmol of N2. Determine the mass of each gas and the apparent gas constant of the mixture.
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14–19 The molar analysis of a gas mixture at 290 K and 250 kPa is 65 percent N2, 20 percent O2, and 15 percent CO2. Determine the mass fraction and partial pressure of each gas
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14–20 Determine the binary diffusion coefficient of CO2 in air at (a) 200 K and 1 atm, (b) 400 K and 0.8 atm, and (c) 600 K and 3 atm
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14–21 Repeat Problem 14–20 for O2 in N2
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14–22E The relative humidity of air at 80°F and 14.7 psia is increased from 30 percent to 90 percent during a humidification process at constant temperature and pressure. Determine the percent error involved in assuming the density of air to have remained constant.
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14–23 The diffusion coefficient of hydrogen in steel is given as a function of temperature as DAB = 1.65 x 10-6 exp(–4630/T) (m 2/s) where T is in K. Determine the diffusion coefficients from 200 K to 1200 K in 200 K increments and plot the results
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14–24 Reconsider Problem 14–23. Using EES (or other) software, plot the diffusion coefficient as a function of the temperature in the range of 200 K to 1200 K.
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14–25C Write three boundary conditions for mass transfer (on a mass basis) for species A at x 0 that correspond to specified temperature, specified heat flux, and convection boundary conditions in heat transfer
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14–26C What is an impermeable surface in mass transfer? How is it expressed mathematically (on a mass basis)? To what does it correspond in heat transfer
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14–27C Consider the free surface of a lake exposed to the atmosphere. If the air at the lake surface is saturated, will the mole fraction of water vapor in air at the lake surface be the same as the mole fraction of water in the lake (which is nearly 1)
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14–28C When prescribing a boundary condition for mass transfer at a solid–gas interface, why do we need to specify the side of the surface (whether the solid or the gas side)? Why did we not do it in heat transfer
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14–29C Using properties of saturated water, explain how you would determine the mole fraction of water vapor at the surface of a lake when the temperature of the lake surface and the atmospheric pressure are specified
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14–30C Using solubility data of a solid in a specified liquid, explain how you would determine the mass fraction of the solid in the liquid at the interface at a specified temperature
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14–31C Using solubility data of a gas in a solid, explain how you would determine the molar concentration of the gas in the solid at the solid–gas interface at a specified temperature
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14–32C Using Henry’s constant data for a gas dissolved in a liquid, explain how you would determine the mole fraction of the gas dissolved in the liquid at the interface at a specified temperature
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14–33C What is permeability? How is the permeability of a gas in a solid related to the solubility of the gas in that solid
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14–34E Determine the mole fraction of the water vapor at the surface of a lake whose temperature at the surface is 60°F, and compare it to the mole fraction of water in the lake. Take the atmospheric pressure at lake level to be 13.8 psia
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14–35 Determine the mole fraction of dry air at the surface of a lake whose temperature is 15°C. Take the atmospheric pressure at lake level to be 100 kPa.
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14–36 Reconsider Problem 14–35. Using EES (or other) software, plot the mole fraction of dry air at the surface of the lake as a function of the lake temperature as the temperatue varies from 5°C to 25°C, and discuss the results
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14–37 Consider a rubber plate that is in contact with nitrogen gas at 298 K and 250 kPa. Determine the molar and mass densities of nitrogen in the rubber at the interface.
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14–38 A wall made of natural rubber separates O2 and N2 gases at 25°C and 500 kPa. Determine the molar concentrations of O2 and N2 in the wall
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14–39 Consider a glass of water in a room at 20°C and 97 kPa. If the relative humidity in the room is 100 percent and the water and the air are in thermal and phase equilibrium, determine (a) the mole fraction of the water vapor in the air and (b) the mole fraction of air in the water
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14–40E Water is sprayed into air at 80°F and 14.3 psia, and the falling water droplets are collected in a container on the floor. Determine the mass and mole fractions of air dissolved in the water
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14–41 Consider a carbonated drink in a bottle at 27°C and 130 kPa. Assuming the gas space above the liquid consists of a saturated mixture of CO2 and water vapor and treating the drink as water, determine (a) the mole fraction of the water vapor in the CO2 gas and (b) the mass of dissolved CO2 in a 200-ml drink.
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14–42C Write down the relations for steady one-dimensional heat conduction and mass diffusion through a plane wall, and identify the quantities in the two equations that correspond to each other
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14–43C Consider steady one-dimensional mass diffusion through a wall. Mark these statements as being True or False. (a) Other things being equal, the higher the density of the wall, the higher the rate of mass transfer. (b) Other things being equal, doubling the thickness of the wall will double the rate of mass transfer. (c) Other things being equal, the higher the temperature, the higher the rate of mass transfer. (d) Other things being equal, doubling the mass fraction of the diffusing species at the high concentration side will double the rate of mass transfer
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14–44C Consider one-dimensional mass diffusion of species A through a plane wall of thickness L. Under what conditions will the concentration profile of species A in the wall be a straight line
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14–45C Consider one-dimensional mass diffusion of species A through a plane wall. Does the species A content of the wall change during steady mass diffusion? How about during transient mass diffusion
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14–46 Helium gas is stored at 293 K in a 3-m-outer-diameter spherical container made of 5-cm-thick Pyrex. The molar concentration of helium in the Pyrex is 0.00073 kmol/m3 at the inner surface and negligible at the outer surface. Determine the mass flow rate of helium by diffusion through the Pyrex container.
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14–47 Athin plastic membrane separates hydrogen from air. The molar concentrations of hydrogen in the membrane at the inner and outer surfaces are determined to be 0.065 and 0.003 kmol/m3, respectively. The binary diffusion coefficient of hydrogen in plastic at the operation temperature is 5.3 x 10-10 m2/s. Determine the mass flow rate of hydrogen by diffusion through the membrane under steady conditions if the thickness of the membrane is (a) 2 mm and (b) 0.5 mm
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14–48 The solubility of hydrogen gas in steel in terms of its mass fraction is given as w = 2.09 x 10-4 exp(–3950/T) where is the partial pressure of hydrogen in bars and T is the temperature in K. If natural gas is transported in a 1-cmthick, 3-m-internal-diameter steel pipe at 500 kPa pressure and the mole fraction of hydrogen in the natural gas is 8 percent, determine the highest rate of hydrogen loss through a 100-mlong section of the pipe at steady conditions at a temperature of293 K if the pipe is exposed to air. Take the diffusivity of hydrogen in steel to be 2.9 x 10-13 m2/s.
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14–49 Reconsider Problem 14–48. Using EES (or other) software, plot the highest rate of hydrogen loss as a function of the mole fraction of hydrogen in natural gas as the mole fraction varies from 5 to 15 percent, and discuss the results
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14–50 Helium gas is stored at 293 K and 500 kPa in a 1-cmthick, 2-m-inner-diameter spherical tank made of fused silica (SiO2). The area where the container is located is well ventilated. Determine (a) the mass flow rate of helium by diffusion through the tank and (b) the pressure drop in the tank in one week as a result of the loss of helium gas
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14–51 You probably have noticed that balloons inflated with helium gas rise in the air the first day during a party but they fall down the next day and act like ordinary balloons filled with air. This is because the helium in the balloon slowly leaks out through the wall while air leaks in by diffusion. Consider a balloon that is made of 0.1-mm-thick soft rubber and has a diameter of 15 cm when inflated. The pressure and temperature inside the balloon are initially 110 kPa and 25°C. The permeability of rubber to helium, oxygen, and nitrogen at 25°C are 9.4 x 10-13, 7.05 x 10-13, and 2.6 x 10-13 kmol/m · s · bar, respectively. Determine the initial rates of diffusion of helium, oxygen, and nitrogen through the balloon wall and the mass fraction of helium that escapes the balloon during the first 5 h assuming the helium pressure inside the balloon remains nearly constant. Assume air to be 21 percent oxygen and 79 percent nitrogen by mole numbers and take the room conditions to be 100 kPa and 25°C.
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14–52 Reconsider the balloon discussed in Problem 14–51. Assuming the volume to remain constant and disregarding the diffusion of air into the balloon, obtain a relation for the variation of pressure in the balloon with time. Using the results obtained and the numerical values given in the problem, determine how long it will take for the pressure inside the balloon to drop to 100 kPa
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14–53 Pure N2 gas at 1 atm and 25°C is flowing through a 10-m-long, 3-cm-inner diameter pipe made of 1-mm-thick rubber. Determine the rate at which N2 leaks out of the pipe if the medium surrounding the pipe is (a) a vacuum and (b) atmospheric air at 1 atm and 25°C with 21 percent O2 and 79 percent N2.
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14–54C Consider a tank that contains moist air at 3 atm and whose walls are permeable to water vapor. The surrounding air at 1 atm pressure also contains some moisture. Is it possible for the water vapor to flow into the tank from surroundings? Explain
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14–55C Express the mass flow rate of water vapor through a wall of thickness L in terms of the partial pressure of water vapor on both sides of the wall and the permeability of the wall to the water vapor
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14–56C How does the condensation or freezing of water vapor in the wall affect the effectiveness of the insulation in the wall? How does the moisture content affect the effective thermal conductivity of soil
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14–57C Moisture migration in the walls, floors, and ceilings of buildings is controlled by vapor barriers or vapor retarders. Explain the difference between the two, and discuss which is more suitable for use in the walls of residential buildings
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14–58C What are the adverse effects of excess moisture on the wood and metal components of a house and the paint on the walls
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14–59C Why are the insulations on the chilled water lines always wrapped with vapor barrier jackets
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14–60C Explain how vapor pressure of the ambient air is determined when the temperature, total pressure, and relative humidity of the air are given
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14–61 The diffusion of water vapor through plaster boards and its condensation in the wall insulation in cold weather are of concern since they reduce the effectiveness of insulation. Consider a house that is maintained at 20°C and 60 percent relative humidity at a location where the atmospheric pressure is 97 kPa. The inside of the walls is finished with 9.5-mm-thick gypsum wallboard. Taking the vapor pressure at the outer side of the wallboard to be zero, determine the maximum amount of water vapor that will diffuse through a 3-m x 8-m section of a wall during a 24-h period. The permeance of the 9.5-mm-thick gypsum wallboard to water vapor is 2.86 x 10-9 kg/s · m2 · Pa
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14–62 Reconsider Problem 14–61. In order to reduce the migration of water vapor through the wall, it is proposed to use a 0.2-mm-thick polyethylene film with a permeance of 2.3 x 10-12 kg/s · m2 · Pa. Determine the amount of water vapor that will diffuse through the wall in this case during a 24-h period.
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14–63 The roof of a house is 15 m x 8 m and is made of a 20-cm-thick concrete layer. The interior of the house is maintained at 25°C and 50 percent relative humidity and the local atmospheric pressure is 100 kPa. Determine the amount of water vapor that will migrate through the roof in 24 h if the average outside conditions during that period are 3°C and 30 percent relative humidity. The permeability of concrete to water vapor is 24.7 x 10-12 kg/s · m · Pa
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14–64 Reconsider Problem 14–63. Using EES (or other) software, investigate the effects of temperature and relative humidity of air inside the house on the amount of water vapor that will migrate through the roo
f. Let the temperature vary from 15°C to 30°C and the relative humidity from 30 to 70 percent. Plot the amount of water vapor that will migrate as functions of the temperature and the relative humidity, and discuss the results
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14–65 Reconsider Problem 14–63. In order to reduce the migration of water vapor, the inner surface of the wall is painted with vapor retarder latex paint whose permeance is 26 x 10-12 kg/s · m2 · Pa. Determine the amount of water vapor that will diffuse through the roof in this case during a 24-h period
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14–66 Aglass of milk left on top of a counter in the kitchen at 25°C, 88 kPa, and 50 percent relative humidity is tightly sealed by a sheet of 0.009-mm-thick aluminum foil whose permeance is 2.9 x 10-12 kg/s · m2 · Pa. The inner diameter of the glass is 12 cm. Assuming the air in the glass to be saturated at all times, determine how much the level of the milk in the glass will recede in 12 h.
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14–67C In transient mass diffusion analysis, can we treat the diffusion of a solid into another solid of finite thickness (such as the diffusion of carbon into an ordinary steel component) as a diffusion process in a semi-infinite medium? Explain
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14–68C Define the penetration depth for mass transfer, and explain how it can be determined at a specified time when the diffusion coefficient is known
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14–69C When the density of a species A in a semi-infinite medium is known at the beginning and at the surface, explain how you would determine the concentration of the species A at a specified location and time
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14–70 A steel part whose initial carbon content is 0.12 percent by mass is to be case-hardened in a furnace at 1150 K by exposing it to a carburizing gas. The diffusion coefficient of carbon in steel is strongly temperature dependent, and at the furnace temperature it is given to be DAB = 7.2 x 10-12 m2/s. Also, the mass fraction of carbon at the exposed surface of the steel part is maintained at 0.011 by the carbon-rich environment in the furnace. If the hardening process is to continue until the mass fraction of carbon at a depth of 0.7 mm is raised to 0.32 percent, determine how long the part should be held in the furnace.
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14–71 Repeat Problem 14–70 for a furnace temperature of 500 K at which the diffusion coefficient of carbon in steel is DAB = 2.1 x 10-20 m2/s
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14–72 Apond with an initial oxygen content of zero is to be oxygenated by forming a tent over the water surface and filling the tent with oxygen gas at 25°C and 130 kPa. Determine the mole fraction of oxygen at a depth of 2 cm from the surface after 12 h.
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14–73 A long nickel bar with a diameter of 5 cm has been stored in a hydrogen-rich environment at 358 K and 300 kPa for a long time, and thus it contains hydrogen gas throughout uniformly. Now the bar is taken into a well-ventilated area so that the hydrogen concentration at the outer surface remains at almost zero at all times. Determine how long it will take for the hydrogen concentration at the center of the bar to drop by hal
f. The diffusion coefficient of hydrogen in the nickel bar at the room temperature of 298 K can be taken to be DAB = 1.2 x 10-12 m2/s.
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14–74C Define the following terms: mass-average velocity, diffusion velocity, stationary medium, and moving medium
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14–75C What is diffusion velocity? How does it affect the mass-average velocity? Can the velocity of a species in a moving medium relative to a fixed reference point be zero in a moving medium? Explain
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14–76C What is the difference between mass-average velocity and mole-average velocity during mass transfer in a moving medium? If one of these velocities is zero, will the other also necessarily be zero? Under what conditions will these two velocities be the same for a binary mixture
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14–77C Consider one-dimensional mass transfer in a moving medium that consists of species A and B with p= pA + pB = constant. Mark these statements as being True or False. (a) The rates of mass diffusion of species A and B are equal in magnitude and opposite in direction. (b) DAB = DBA. (c) During equimolar counterdiffusion through a tube, equal numbers of moles of A and B move in opposite directions, and thus a velocity measurement device placed in the tube will read zero. (d) The lid of a tank containing propane gas (which is heavier than air) is left open. If the surrounding air and the propane in the tank are at the same temperature and pressure, no propane will escape the tank and no air will enter
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14–78C What is Stefan flow? Write the expression for Stefan’s law and indicate what each variable represents
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14–79E The pressure in a pipeline that transports helium gas at a rate of 5 lbm/s is maintained at 14.5 psia by venting helium to the atmosphere through a -in. internal diameter tube that extends 30 ft into the air. Assuming both the helium and the atmospheric air to be at 80°F, determine (a) the mass flow rate of helium lost to the atmosphere through an individual tube, (b) the mass flow rate of air that infiltrates into the pipeline, and (c) the flow velocity at the bottom of the tube where it is attached to the pipeline that will be measured by an anemometer in steady operation.
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14–80E Repeat Problem 14–79E for a pipeline that transports carbon dioxide instead of helium
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14–81 Atank with a 2-cm thick shell contains hydrogen gas at the atmospheric conditions of 25°C and 90 kPa. The charging valve of the tank has an internal diameter of 3 cm and extends 8 cm above the tank. If the lid of the tank is left open so that hydrogen and air can undergo equimolar counterdiffusion through the 10-cm-long passageway, determine the mass flow rate of hydrogen lost to the atmosphere through the valve at the initial stages of the process.
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14–82 Reconsider Problem 14–81. Using EES (or other) software, plot the mass flow rate of hydrogen lost as a function of the diameter of the charging valve as the diameter varies from 1 cm to 5 cm, and discuss the results
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14–83E A1-in.-diameter Stefan tube is used to measure the binary diffusion coefficient of water vapor in air at 70°F and 13.8 psia. The tube is partially filled with water with a distance from the water surface to the open end of the tube of 10 in. Dry air is blown over the open end of the tube so that water vapor rising to the top is removed immediately and the concentration of vapor at the top of the tube is zero. During 10 days of continuous operation at constant pressure and temperature, the amount of water that has evaporated is measured to be 0.0015 lbm. Determine the diffusion coefficient of water vapor in air at 70°F and 13.8 psia
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14–84 An 8-cm-internal-diameter, 30-cm-high pitcher half filled with water is left in a dry room at 15°C and 87 kPa with its top open. If the water is maintained at 15°C at all times also, determine how long it will take for the water to evaporate completely.
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14–85 Alarge tank containing ammonia at 1 atm and 25°C is vented to the atmosphere through a 3-m-long tube whose internal diameter is 1 cm. Determine the rate of loss of ammonia and the rate of infiltration of air into the tank.
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14–86C Heat convection is expressed by Newton’s law of cooling as Q = hA(Ts - T∞). Express mass convection in an analogous manner on a mass basis, and identify all the quantities in the expression and state their units.
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14–87C What is a concentration boundary layer? How is it defined for flow over a plate
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14–88C What is the physical significance of the Schmidt number? How is it defined? To what dimensionless number does it correspond in heat transfer? What does a Schmidt number of 1 indicate
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14–89C What is the physical significance of the Sherwood number? How is it defined? To what dimensionless number does it correspond in heat transfer? What does a Sherwood number of 1 indicate for a plain fluid layer
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14–90C What is the physical significance of the Lewis number? How is it defined? What does a Lewis number of 1 indicate
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14–91C In natural convection mass transfer, the Grashof number is evaluated using density difference instead of temperature difference. Can the Grashof number evaluated this way be used in heat transfer calculations also
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14–92C Using the analogy between heat and mass transfer, explain how the mass transfer coefficient can be determined from the relations for the heat transfer coefficient
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14–93C It is well known that warm air in a cooler environment rises. Now consider a warm mixture of air and gasoline (C8H18) on top of an open gasoline can. Do you think this gas mixture will rise in a cooler environment
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14–94C Consider two identical cups of coffee, one with no sugar and the other with plenty of sugar at the bottom. Initially, both cups are at the same temperature. If left unattended, which cup of coffee will cool faster
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14–95C Under what conditions will the normalized velocity, thermal, and concentration boundary layers coincide during flow over a flat plate
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14–96C What is the relation ( f/2) Re = Nu = Sh known as? Under what conditions is it valid? What is the practical importance of it
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14–97C What is the name of the relation f/2 = St Pr2/3 = StmassSc2/3 and what are the names of the variables in it? Under what conditions is it valid? What is the importance of it in engineering
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14–98C What is the relation hheat =pCphmass known as? For what kind of mixtures is it valid? What is the practical importance of it
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14–99C What is the low mass flux approximation in mass transfer analysis? Can the evaporation of water from a lake be treated as a low mass flux process
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14–100E Consider a circular pipe of inner diameter D = 0.5 in. whose inner surface is covered with a thin layer of liquid water as a result of condensation. In order to dry the pipe, air at 540 R and 1 atm is forced to flow through it with an average velocity of 4 ft/s. Using the analogy between heat and mass transfer, determine the mass transfer coefficient inside the pipe for fully developed flow.
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14–101 The average heat transfer coefficient for air flow over an odd-shaped body is to be determined by mass transfer measurements and using the Chilton–Colburn analogy between heat and mass transfer. The experiment is conducted by blowing dry air at 1 atm at a free stream velocity of 2 m/s over a body covered with a layer of naphthalene. The surface area of the body is 0.75 m2, and it is observed that 100 g of naphthalene has sublimated in 45 min. During the experiment, both the body and the air were kept at 25°C, at which the vapor pressure and mass diffusivity of naphthalene are 11 Pa and DAB = 0.61 x 10-5 m2/s, respectively. Determine the heat transfer coefficient under the same flow conditions over the same geometry.
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14–102 Consider a 15-cm-internal-diameter, 10-m-long circular duct whose interior surface is wet. The duct is to be dried by forcing dry air at 1 atm and 15°C through it at an average velocity of 3 m/s. The duct passes through a chilled room, and it remains at an average temperature of 15°C at all times. Determine the mass transfer coefficient in the duct
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14–103 Reconsider Problem 14–102. Using EES (or other) software, plot the mass transfer coefficient as a function of the air velocity as the velocity varies from 1 m/s to 8 m/s, and discuss the results
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14–104 Dry air at 15°C and 92 kPa flows over a 2-m-long wet surface with a free stream velocity of 4 m/s. Determine the average mass transfer coefficient.
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14–105 Consider a 5-m x 5-m wet concrete patio with an average water film thickness of 0.3 mm. Now wind at 50 km/h is blowing over the surface. If the air is at 1 atm, 15°C, and 35 percent relative humidity, determine how long it will take for the patio to dry completely.
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14–106E A2-in.-diameter spherical naphthalene ball is suspended in a room at 1 atm and 80°F. Determine the average mass transfer coefficient between the naphthalene and the air if air is forced to flow over naphthalene with a free stream velocity of 15 ft/s. The Schmidt number of naphthalene in air at room temperature is 2.35.
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14–107 Consider a 3-mm-diameter raindrop that is falling freely in atmospheric air at 25°C. Taking the temperature of the raindrop to be 9°C, determine the terminal velocity of the raindrop at which the drag force equals the weight of the drop and the average mass transfer coefficient at that time
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14–108 In a manufacturing facility, wet brass plates coming out of a water bath are to be dried by passing them through a section where dry air at 1 atm and 25°C is blown parallel to their surfaces. If the plates are at 20°C and there are no dry spots, determine the rate of evaporation from both sides of a plate.
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14–109E Air at 80°F, 1 atm, and 30 percent relative humidity is blown over the surface of a 15-in. x 15-in. square pan filled with water at a free stream velocity of 10 ft/s. If the water is maintained at a uniform temperature of 80°F, determine the rate of evaporation of water and the amount of heat that needs to be supplied to the water to maintain its temperature constant
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14–110E Repeat Problem 14–109E for temperature of 60°F for both the air and water.
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14–111C Does a mass transfer process have to involve heat transfer? Describe a process that involves both heat and mass transfer
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14–112C Consider a shallow body of water. Is it possible for this water to freeze during a cold and dry night even when the ambient air and surrounding surface temperatures never drop to 0°C? Explain.
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14–113C During evaporation from a water body to air, under what conditions will the latent heat of vaporization be equal to convection heat transfer from the air
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14–114 Jugs made of porous clay were commonly used to cool water in the past. Asmall amount of water that leaks out keeps the outer surface of the jug wet at all times, and hot and relatively dry air flowing over the jug causes this water to evaporate. Part of the latent heat of evaporation comes from the water in the jug, and the water is cooled as a result. If the environment conditions are 1 atm, 30°C, and 35 percent relative humidity, determine the temperature of the water when steady conditions are reached.
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14–115 Reconsider Problem 14–114. Using EES (or other) software, plot the water temperature as a function of the relative humidity of air as the relative humidity varies from 10 to 100 percent, and discuss the results
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14–116E During a hot summer day, a 2-Lbottle drink is to be cooled by wrapping it in a cloth kept wet continually and blowing air to it with a fan. If the environment conditions are 1 atm, 80°F, and 30 percent relative humidity, determine the temperature of the drink when steady conditions are reached
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14–117 A glass bottle washing facility uses a wellagitated hot water bath at 55°C with an open top that is placed on the ground. The bathtub is 1 m high, 2 m wide, and 4 m long and is made of sheet metal so that the outer side surfaces are also at about 55°C. The bottles enter at a rate of 800 per minute at ambient temperature and leave at the water temperature. Each bottle has a mass of 150 g and removes 0.6 g of water as it leaves the bath wet. Makeup water is supplied at 15°C. If the average conditions in the plant are 1 atm, 25°C, and 50 percent relative humidity, and the average temperature of the surrounding surfaces is 15°C, determine (a) the amount of heat and water removed by the bottles themselves per second; (b) the rate of heat loss from the top surface of the water bath by radiation, natural convection, and evaporation; (c) the rate of heat loss from the side surfaces by natural convection and radiation; and (d) the rate at which heat and water must be supplied to maintain steady operating conditions. Disregard heatloss through the bottom surface of the bath and take the emissivities of sheet metal and water to be 0.61 and 0.95, respectively.
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14–118 Repeat Problem 14–117 for a water bath temperature of 50°C
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14–119 One way of increasing heat transfer from the head on a hot summer day is to wet it. This is especially effective in windy weather, as you may have noticed. Approximating the head as a 30-cm-diameter sphere at 30°C with an emissivity of 0.95, determine the total rate of heat loss from the head at ambient air conditions of 1 atm, 25°C, 40 percent relative humidity, and 25 km/h winds if the head is (a) dry and (b) wet. Take the surrounding temperature to be 25°C.
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14–120 A2-m-deep 20-m x 20-m heated swimming pool is maintained at a constant temperature of 30°C at a location where the atmospheric pressure is 1 atm. If the ambient air is at 20°C and 60 percent relative humidity and the effective sky temperature is 0°C, determine the rate of heat loss from the top surface of the pool by (a) radiation, (b) natural convection, and (c) evaporation. (d) Assuming the heat losses to the ground to be negligible, determine the size of the heater
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14–121 Repeat Problem 14–120 for a pool temperature of 25°C.
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14–122C Mark these statements as being True or False. (a) The units of mass diffusivity, heat diffusivity, and momentum diffusivity are all the same. (b) If the molar concentration (or molar density) C of a mixture is constant, then its density p must also be constant. (c) If the mass-average velocity of a binary mixture is zero, then the mole-average velocity of the mixture must also be zero. (d) If the mole fractions of A and B of a mixture are both 0.5, then the molar mass of the mixture is simply the arithmetic average of the molar masses of A and B
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14–123 Using Henry’s law, show that the dissolved gases in a liquid can be driven off by heating the liquid.
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14–124 Show that for an ideal gas mixture maintained at a constant temperature and pressure, the molar concentration C of the mixture remains constant but this is not necessarily the case for the density p of the mixture
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14–125E Agas mixture in a tank at 600 R and 20 psia consists of 1 lbm of CO2 and 3 lbm of CH4. Determine the volume of the tank and the partial pressure of each gas
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14–126 Dry air whose molar analysis is 78.1 percent N2, 20.9 percent O2, and 1 percent Ar flows over a water body until it is saturated. If the pressure and temperature of air remain constant at 1 atm and 25°C during the process, determine (a) the molar analysis of the saturated air and (b) the density of air before and after the process. What do you conclude from your results
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14–127 Consider a glass of water in a room at 25°C and 100 kPa. If the relative humidity in the room is 70 percent and the water and the air are at the same temperature, determine (a) the mole fraction of the water vapor in the room air, (b) the mole fraction of the water vapor in the air adjacent to the water surface, and (c) the mole fraction of air in the water near the surface.
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14–128 The diffusion coefficient of carbon in steel is given as DAB = 2.67 x 10-5 exp(–17,400/T)m 2/s where T is in K. Determine the diffusion coefficient from 300 K to 1500 K in 100 K increments and plot the results
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14–129 Acarbonated drink is fully charged with CO2 gas at 17°C and 600 kPa such that the entire bulk of the drink is in thermodynamic equilibrium with the CO2–water vapor mixture. Now consider a 2-Lsoda bottle. If the CO2 gas in that bottle were to be released and stored in a container at 25°C and 100 kPa, determine the volume of the container.
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14–130 Consider a brick house that is maintained at 20°C and 60 percent relative humidity at a location where the atmospheric pressure is 85 kPa. The walls of the house are made of 20-cm thick brick whose permeance is 23 x 10-9 kg/s · m2 · Pa. Taking the vapor pressure at the outer side of the wallboard to be zero, determine the maximum amount of water vapor that will diffuse through a 4-m x 7-m section of a wall during a 24-h period
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14–131E Consider a masonry cavity wall that is built around 6-in.-thick concrete blocks. The outside is finished with 4-in. face brick with -in. cement mortar between the bricks and concrete blocks. The inside finish consists of -in. gypsum wallboard separated from the concrete block by -in.-thick air space. The thermal and vapor resistances of various components for a unit wall area are as follows:
The indoor conditions are 70°F and 65 percent relative humidity while the outdoor conditions are 32°F and 40 percent relative humidity. Determine the rates of heat and water vapor transfer through a 9-ft x 25-ft section of the wall.
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14–132 The oxygen needs of fish in aquariums are usually met by forcing air to the bottom of the aquarium by a compressor. The air bubbles provide a large contact area between the water and the air, and as the bubbles rise, oxygen and nitrogen gases in the air dissolve in water while some water evaporates into the bubbles. Consider an aquarium that is maintained at room temperature of 25°C at all times. The air bubbles are observed to rise to the free surface of water in 2 s. If the air entering the aquarium is completely dry and the diameter of the air bubbles is 4 mm, determine the mole fraction of water vapor at the center of the bubble when it leaves the aquarium. Assume no fluid motion in the bubble so that water vapor propagates in the bubble by diffusion only.
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14–133 Oxygen gas is forced into an aquarium at 1 atm and 25°C, and the oxygen bubbles are observed to rise to the free surface in 2 s. Determine the penetration depth of oxygen into water from a bubble during this time period.
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14–134 Consider a 30-cm-diameter pan filled with water at 15°C in a room at 20°C, 1 atm, and 30 percent relative humidity. Determine (a) the rate of heat transfer by convection, (b) the rate of evaporation of water, and (c) the rate of heat transfer to the water needed to maintain its temperature at 15°C. Disregard any radiation effects
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14–135 Repeat Problem 14–134 assuming a fan blows air over the water surface at a velocity of 3 m/s. Take the radius of the pan to be the characteristic length
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14–136 Naphthalene is commonly used as a repellent against moths to protect clothing during storage. Consider a 1-cmdiameter spherical naphthalene ball hanging in a closet at 25°C and 1 atm. Considering the variation of diameter with time, determine how long it will take for the naphthalene to sublimate completely. The density and vapor pressure of naphthalene at 25°C are 0.11 Pa and 1100 kg/m3 and 11 Pa, respectively, and the mass diffusivity of naphthalene in air at 25°C is DAB = 0.61 x 10-5 m2/s.
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14–137E Aswimmer extends his wet arms into the windy air outside at 1 atm, 40°F, 50 percent relative humidity, and 20 mph. If the average skin temperature is 80°F, determine the rate at which water evaporates from both arms and the corresponding rate of heat transfer by evaporation. The arm can be modeled as a 2-ft-long and 3-in.-diameter cylinder with adiabatic ends
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14–138 Athick part made of nickel is put into a room filled with hydrogen at 3 atm and 85°C. Determine the hydrogen concentration at a depth of 2-mm from the surface after 24 h.
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14–139 Amembrane made of 0.1-mm-thick soft rubber separates pure O2 at 1 atm and 25°C from air at 1.2 atm pressure. Determine the mass flow rate of O2 through the membrane per unit area and the direction of flow
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14–140E The top section of an 8-ft-deep 100-ft x 100-ft heated solar pond is maintained at a constant temperature of 80°F at a location where the atmospheric pressure is 1 atm. If the ambient air is at 70°F and 100 percent relative humidity and wind is blowing at an average velocity of 40 mph, determine the rate of heat loss from the top surface of the pond by (a) forced convection, (b) radiation, and (c) evaporation. Take the average temperature of the surrounding surfaces to be 60°F
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14–141E Repeat Problem 14–140E for a solar pond surface temperature of 90°F.
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