Questions and Answers of Fundamentals Of Chemical Engineering Thermodynamics

Water is heated in a double-pipe heat exchanger from \(15^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\). Oil \(\left(C_{p}=2500 \mathrm{~J} / \mathrm{kg}{ }^{\circ} \mathrm{C}\right)\) with a
A small-steam condenser is designed to condense \(1 \mathrm{~kg} / \mathrm{min}\) of steam at \(90 \mathrm{kPa}\) with cooling water at \(10^{\circ} \mathrm{C}\). The exit water is not to exceed
In Section 11.8 we discussed the ability to use a heat exchanger simultaneously as a chemical reactor. In that example, we were running an exothermic reaction. Suppose we were interested in running
In Section 11.8, suppose the exchanger is made of copper. The exothermic reaction has a rate constant, \(k^{\prime \prime}=0.1\) and a heat of reaction \(\Delta H_{r}=60 \mathrm{~kJ} /
The analog of a shell-and-tube heat exchanger, or our double-pipe configuration, is a membrane system used for hemodialysis. Here, instead of a solid pipe wall passing heat, we have a porous membrane
Assume that the analogy discussed in Problem 11.31 holds. That means that we would have an overall mass transfer coefficient that serves as the replacement for the overall heat transfer coefficient.
A stirred tank has a capacity of \(V \mathrm{~m}^{3}\). Before time \(t=0\) the concentration of salt within the tank is \(c_{i}\) moles \(/ \mathrm{m}^{3}\). At time \(=0\), pure water is run in at
The liquid phase reaction \(2 \mathrm{~A} \rightarrow \mathrm{B}\), is to be carried out in a 500 liter well-mixed reactor. Pure \(\mathrm{A}\) is to be fed to the reactor at a rate of \(20
A continuous, stirred tank reactor is initially filled with solvent. At \(t=0\), reactant, A, is fed into the tank at a rate of \(\dot{v}_{a o}\left(\mathrm{~m}^{3} / \mathrm{min}\right)\). The
A tubular reactor is running a second-order addition reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}\) in the liquid phase. The rate law is first order in the concentrations of \(\mathrm{A}\)
A radial flow reactor is often used for highly exothermic reactions. The high radial velocities at the reactor inlet compensate for any hot spots that might form in the reactor there. Consider the
Often one absorbs a component from the gas phase into a liquid where a reaction occurs. The presence of the reaction increases the mass transfer and the loading the liquid can take. A prime example
Water is being used to absorb acetone in a packed tower whose cross-sectional area is \(0.2 \mathrm{~m}^{2}\). The inlet air contains 3 mole \% acetone and the outlet contains \(0.6 \%\). The gas
Chromatography is a process by which a separation of chemical species is accomplished by selective adsorption on a solid medium. Consider the simple case of a packed column of cross-sectional area,
Often in the theory of chromatography we assume local equilibrium at all points in the column between the adsorbent particles and the adjacent fluid. Under these conditions, we can express \(c_{p
The pressure in a container is related to the change in momentum of particles as they smash into the walls of the container. We derived an expression for it in equation (3.2). We also determined the
We defined an overall collision frequency between particles, \(\Omega_{c}\), in equation (3.8) and the mean free path, \(\lambda_{f}\) in equation (3.12). If we assume that all the particles are the
Calculate the mean-square, root mean square, and mean velocity for \(\mathrm{H}_{2}, \mathrm{CO}_{2}, \mathrm{CH}_{4}\) and \(\mathrm{SF}_{6}\).
Escape velocity from Earth's atmosphere is \(10.8 \mathrm{~km} / \mathrm{s}\).a. Based on that number, to what temperature would \(\mathrm{He}, \mathrm{O}_{2}, \mathrm{CO}_{2}\) need to be heated so
Compare predictions for the viscosity of \(\mathrm{He}, \mathrm{CCl}_{4}\), and \(\mathrm{C}_{6} \mathrm{H}_{14}\) at \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\) using the kinetic theory of gases and
Using the results of Free Volume theory for calculating the viscosity of liquids, determine \(\Delta G^{\dagger}\) for the following liquids \(\left(20^{\circ} \mathrm{C})\) : water, ethylene glycol,
The speed of sound in dry air at \(20^{\circ} \mathrm{C}\) is about \(343 \mathrm{~m} / \mathrm{s}\).a. Calculate the average speed of individual air molecules using the Maxwell-Boltzmann velocity
The viscosity of suspensions has been the subject of much study. Knowing its value is critical to the processing of items such as paints, ketchup, cosmetics, concrete, and pharmaceuticals. One of the
Thermoplastic polymers are used often in 3-D printing. Polylactic acid (PLA) is a commonly used material. In general, temperatures within a range of can be programmed into the machines and successful
Compare predictions for the thermal conductivity of \(\mathrm{He}, \mathrm{C}_{5} \mathrm{H}_{12}\), and \(\mathrm{C}_{6} \mathrm{H}_{6}\) at \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\). using the
Liquid thermal conductivities may be calculated using the following equation from Weber [43]:\[k=\frac{3.59 \times 10^{-8} C_{p} ho^{4 / 3}}{M_{w}^{1 / 3}} \text { Weber equation }\]where \(k\) has
A key aspect of conductors for integrated circuits is their ability to remove heat. Several materials are commonly used including aluminum, copper, and tungsten. Lately, silver is also being
Diamond has an extraordinarily high thermal conductivity given the fact that it is an excellent insulator. With reference to the derivation in Section 3.9, can you say something about diamond that
The steady-state heat flux through the \(1.9 \mathrm{~cm}\) argon gap in an insulated window is to be measured. Assuming pure conduction through the gas and windowpane temperatures of \(20^{\circ}
Composite materials offer the possibility of engineering materials with properties that cannot be achieved using a single material. One such class of materials are metal-filled epoxies that can be
Composite materials are a very common and important class of substances. Many theories have been developed to help explain how their properties depend upon their composition. One class of models are
Cellular solids are materials that are highly porous with very thin, solid walls. Examples include metal foams, coral, cork, aerogels, styrofoam, etc. Because they are so porous, their thermal
Compare predictions for the diffusivity of \(\mathrm{He}, \mathrm{C}_{6} \mathrm{H}_{14}\), and \(\mathrm{H}_{2} \mathrm{O}\) in air at \(298 \mathrm{~K}\) and \(1 \mathrm{~atm}\). using the kinetic
Compare experimental and calculated values of the diffusivity (at \(298 \mathrm{~K}\) ) for the following compounds in water at infinite dilution: methanol, propane, oxygen, helium, and hemoglobin.
An empirical correlation for diffusion coefficients was developed by Wilke and Chang [47]. For water as the solvent this formula is:\[D=\frac{5.06 \times 10^{-16} T}{\mu_{w} \bar{V}_{s}^{0.6}}
Another empirical correlation for predicting the diffusion coefficient of large molecules and polymers was given by Polson and later used to look at biopolymers by Young et al.\[D=\frac{9.4 \times
Mass diffusion of gases in confined spaces or at very low pressures, called Knudsen diffusion, is quite different from diffusion at atmospheric pressure. The motion of the gas is governed by
If we look at the kinetic theory expressions for the viscosity, thermal conductivity, and diffusivity, we can express them in the following form:The product of velocity and mean free path has the
We have talked about the diffusivity in liquids and how the Stokes-Einstein formulation works reasonably well. Ionic liquids are a relatively recent class of liquids useful as replacements for many
In Section 3.4, we discussed briefly the idea of surface diffusion. We can use an expression very similar to equation (3.30) derived from kinetic theory to look at surface diffusion of gases adsorbed
The concentration profile of algae across a large body of water measured as a function of distance, \(x\), is given as:\[C(x)=4 x^{2}+x\]With \(C(x)\) in units of \(\mathrm{kg} / \mathrm{m}^{3}\). If
The Hirschfelder-Bird-Spotz equation is commonly used in predicting binary bas diffusivities by using its theoretical foundations. A more recent correlation has been developed by Fuller and is given
What is the ionic conductivity of a \(0.01 \mathrm{M}\) sulfuric acid solution at \(25^{\circ} \mathrm{C}\) ? What is the mobility of the \(\mathrm{H}^{+}\)ion? The \(\mathrm{SO}_{4}^{2-}\) ion? If
The solubility product constant for magnesium hydroxide, \(\operatorname{Mg}(\mathrm{OH})_{2}\), in water is \(K_{s p}=1.2 \times 10^{-11}(\mathrm{kmol} / \mathrm{m})^{3}\). If \(5 \mathrm{~g}\) of
In a solid, like \(\mathrm{Si}\), the mobile charge carriers are in constant motion due to their thermal energy. This energy, a classic kinetic energy, is \(3 k_{b} T / 2\).a. What is the thermal
In general, the mobility of a charge carrier, like an electron, is directly proportional to the electric field it experiences. However, this velocity cannot increase indefinitely and at some point,
In a one-dimensional transport situation where we only have In and Out terms, does the maximum value of velocity, temperature, concentration, or charge always occur on a boundary? Why?
Is the overall or equivalent resistance for a set of resistances in parallel always less than the smallest resistance in the set? Why?
In a one-dimensional, steady-state, transport situation, if the heat flow rate is a constant throughout the medium, does the heat flux also have to be constant? Why?
In steady-state, one-dimensional mass transport, if we change our transport assumption from dilute solutions to diffusion through a stagnant medium and then calculate the resulting mass flow rate,
The space between two very long concentric cylinders is filled with water as shown in Figure P4.5. The inner cylinder is stationary while the outer cylinder is pulled along axially with a velocity
A Newtonian fluid of viscosity, \(\mu\), and density, \(ho\), fills the gap between two very long concentric cylinders. The inner cylinder \(\left(r=r_{i}\right)\) is stationary while the outer
The Ostwald-deWaele equation is often used to correlate the shear stress and shear rate relationship of shear-thickening fluids such as a cornstarch suspension. Here:\[\tau_{x y}=K\left(-\frac{d
Plate glass is made by the float process. A molten glass slab rides on a pool of liquid metal. The other side of the glass is exposed to the air. To produce a striated, textured plate glass, the
An engineer is attempting to measure the force needed to shear two plates past one another when the fluid inside is a slurry. The slurry is relatively dilute and obeys the
A slurry is contained between the walls of the concentric cylinder in problem 5.The slurry is dilute and so obeys the linear form of the Einstein relation \(\left(\mu=\mu_{0}(1+2.5 \phi)\right)\).
A Bingham fluid sits between two parallel plates that are separated by a distance of \(0.5 \mathrm{~cm}\). The plate area is \(0.25 \mathrm{~m}^{2}\). If the stress-strain relationship for the fluid
A stratified layer of oil on water is placed between parallel plates. The plates are separated by a distance of \(1 \mathrm{~cm}\) and the oil layer is \(0.4 \mathrm{~cm}\) thick. The water has a
Consider fully developed, laminar flow between infinite parallel plates separated by a gap width, \(h\). The upper plate \((y=h)\) moves to the right (positive \(x\)-direction) with a velocity of
Calculate the steady-state heat loss from the cup of cappuccino shown in Figure P4.14. You may assume that the cappuccino (not the foam) is held at a constant temperature of \(91.67^{\circ}
Wind chill, the phenomenon experienced on a cold, windy day, is related to the increased heat transfer from exposed human skin to the surrounding atmosphere. Consider a layer of skin, \(3
As a building contractor, you are designing the walls of a house. Each wall is a threecomponent (minimum) composite of plasterboard, insulation, and plywood shown in Figure P4.16. You are to design
Please use the resistance diagram in Figure P4.17 to construct the heat transfer situation. The diagram represents a composite plane wall. Assume steady-state operation and no generation. Draw the
Tempered glass substrates for high-speed compact disks and disk drives are made by healing surface cracks that form during manufacture. The disks are \(10 \mathrm{~cm}\) in diameter, \(3
Water boils in a paper cup over an open flame.a. Ignoring radiative heat transfer, determine a numerical value for the maximum thickness of the bottom of the cup.Data: Paper burns at \(250^{\circ}
Consider a hollow sphere designed to hold a cryogenic fluid. The fluid inside the sphere is at a uniform temperature, \(T_{i}\). Insulation with thermal conductivity, \(k\), is added to the outer
Many forms of insulation, especially for pipes, are formed as periodic structures consisting of layers of insulation separated by air gaps. For the structure in Figure P4.21, calculate the thermal
A fired heater is designed to produce superheated steam at a temperature of \(300^{\circ} \mathrm{C}\) and a pressure of \(15 \mathrm{~atm}\). The steam is carried in tubes ( \(4 \mathrm{~cm}\)
In example 4.4 we considered a thermal interface resistance in rectangular coordinates. Consider the cylindrical coordinate version shown in Figure P4.23.a. Derive an expression for the temperature
In the test example we considered a thermal interface resistance in rectangular coordinates. Consider the spherical coordinate version shown in Figure P4.24.a. Derive an expression for the
On a hot day, the temperature of a race track is higher than that of the surrounding air. The track temperature is highly influential in determining the rate of tire degradation for a race car.
Space shuttles are exposed to temperatures of up to \(1600^{\circ} \mathrm{C}\) during reentry. However, the aluminum shell of the spacecraft cannot withstand temperatures higher than \(175^{\circ}
A tubular furnace must be designed so that it can treat materials at an inner surface temperature of \(1200^{\circ} \mathrm{C}\) yet have its outer surface be at a temperature no more than
The rear window of a car is defrosted by having a transparent film heater attached to the glass. The heater provides a uniform heat flux on the surface that depends on the amount of current passing
Compuconc Inc. has developed a new bottle that it claims will store volatile materials for a long time without a cover (Figure P4.29). The key is that the cross sectional area of the device is
Oxygen transfer from the atmosphere to the interior regions of the eye depends enormously on whether one wears contact lenses. Treating the eye as a composite spherical system, determine the mass
A timed-release drug is dissolving in the intestine of a modern humanoid. As a steady-state approximation, we may assume that the drug is a rod of overall radius \(r_{o}(\mathrm{~m})\) and length of
Oxygen diffuses through the wall of drug containers and oxidizes many drugs rendering them inactive. It is the oxygen diffusion/reaction scenario that limits the shelf-life of many pharmaceutical
You detect the smell of gas in your house. Following the odor you discover a small gas leak in your furnace. Assuming a steady-state concentration profile of gas, diffusion of the gas through air,
Ion exchange in glasses is one method for producing optical waveguides and gradient index lenses. Relatively high concentrations of dopant ions are required to produce a gradient index lens and the
A nicotine patch is designed to deliver \(24 \mathrm{mg}\) of nicotine over a \(24 \mathrm{hr}\) period. The patch is \(5 \mathrm{~cm}\) in diameter as shown in Figure P4.35. The steady-state
Consider the continuous adsorption situation shown in the Figure P4.37. The adsorbate is present in the gas phase at a concentration, \(c_{a o}\). It adsorbs uniformly on the surface of the adsorbent
Diffusion of dopants into solids under the application of an electric field often requires the introduction of a composition-dependent diffusivity to account for the phenomenon of "elastic drift"
Performance fabrics, like that shown in Figure P4.39, are known to allow only a one-way direction of water vapors, created from sweat, to move away from the body. Taking a microscopic view, assume
Pure hydrogen gas is stored at \(400^{\circ} \mathrm{C}\) and 9 atm in a steel tank with a wall thickness of \(1 \mathrm{~mm}\). At \(400^{\circ} \mathrm{C}\) the diffusion coefficient of atomic
A new type of battery uses a gel electrolyte. Ions move through the gel via diffusion and drift through the electric field but the gel remains stagnant. Determine the maximum current through such a
A physiologist is looking to quantify the charge transfer coefficient, \(S_{k}\), about a nerve bundle that is being tested for a myelin sheath growth hormone. The nerve bundle itself is 1 micron in
Does the maximum value of velocity, temperature, concentration, or charge need to occur on a boundary if a generation term is added to a differential equation?
In a system where diffusion and chemical reaction are occurring simultaneously, what is the role of the Damkohler number?
In a system where diffusion and chemical reaction occur simultaneously, what does it mean to be mass transfer controlled? To be reaction rate controlled?
Does the sum-of-resistance concept we used in Chapter 4 for composite media apply if one of those media has generation occurring within it?
A thin film of a silicon oil, \(3 \mathrm{~mm}\) thick, sits on a long plate that is partially heated. The plate has a linear temperature distribution imposed on it. At \(x=0\), on the left-hand side
A fluid flows between two plates separated by a distance, \(d\). The velocity profile is measured, and the data can be fit to the following function. The fluid viscosity is a constant, \(\mu\), and
Two immiscible fluids are flowing between parallel plates separated by a distance, \(d\). Each fluid occupies \(50 \%\) by volume of the pipe. For the pressure drop given in Figure P5.7, determine
An incompressible, Newtonian fluid is in steady, laminar flow within the annular region between two concentric cylinders of radii \(r_{i}\) and \(r_{o}\). The cylinders are inclined at an angle of
A fluid of density, \(ho\), and viscosity, \(\mu\), drains from between very long parallel flat plates oriented vertically with respect to gravity. One plate is held stationary and the other travels
A Bingham fluid of viscosity, \(\mu\), and yield stress, \(\tau_{0}\), flows through a horizontal pipe of radius, \(R\), and length, \(L\). The flow is driven by a pressure drop, \(\Delta P / L\)
A fluid is sheared between two parallel plates as we saw in Chapter 4.If the gap between the plates is small and the shearing rate is high, friction between the fluid molecules will generate heat.
Consider the flow of water at \(20^{\circ} \mathrm{C}\) between two very large horizontal plates. The lower plate is stationary and the upper plate moves to the right at a velocity of \(0.25
Water is flowing between two parallel plates separated by a distance, \(H\), that are inclined at an angle of \(\theta\) degrees from the vertical.a. Find the velocity profile of the water between

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