Questions and Answers of Fundamentals Of Chemical Engineering Thermodynamics

Consider flow between infinite, parallel plates. The upper plate moves to the right ( $+x$ direction) at $v_{x}=3 \mathrm{~mm} / \mathrm{s}$. There is no pressure variation in the
A liquid flows within an annular region between the two cylinders under the action of a pressure gradient, $d P / d z$ as shown in Figure P5.15. The inner cylinder is heated such that the viscosity
Acrylic latex paint can be described as a Bingham plastic with a yield stress of $20 \mathrm{~N} / \mathrm{m}^{2}$, a limiting viscosity of $0.05 \mathrm{Ns} / \mathrm{m}^{2}$, and a density of
A Bakelite $(k=1.4 \mathrm{~W} / \mathrm{mK})$ coating is to be used with a $10 \mathrm{~mm}$ diameter conducting rod whose surface is maintained at $200^{\circ} \mathrm{C}$ by passage of an
An electronic device that dissipates (generates) $30 \mathrm{~W}$ is used infrequently. Its maximum allowable operating temperature is limited to $75^{\circ} \mathrm{C}$; as soon as \(75^{\circ}
A hollow sphere of wall thickness $1 \mathrm{~mm}$ and inner diameter of $20 \mathrm{~mm}$ is exposed to an environment where the inner surface of the sphere is held at a temperature of
Consider the case of steady-state, simultaneous heat and mass transfer with chemical reaction as discussed in Section 5.5.1. The reaction is autocatalytic (self-catalyzed) and takes off at a
A truncated solid cone is of circular cross-section with a diameter that varies along its length according to $d(x)=a e^{x}$ where $a=0.8 \mathrm{~m}$ and $x$ is in meters. The cone has a
Consider the composite wall shown in Figure P5.22 exhibiting an interfacial resistance due to the roughness of the interface. Derive the steady-state temperature distributions in both walls and based
One way of cooling off integrated circuits efficiently is by having a film of liquid evaporating from the surface of the chip. Figure P5.23 shows the general situation. Evaporation takes place at the
A solid rod is manufactured from a new superconducting material, Coldmet, and is shown in Figure P5.24. The material has the property that when a current is passed through it, it actually gets
The exposed surface $(x=0)$ of a plane wall of thermal conductivity, $k$, is subjected to microwave radiation that causes the heat generation rate within the wall to vary
A cylindrical nuclear fuel rod contains a core of active, fissionable material and a cladding formed from a high-temperature metal (Figure P5.26). The heat generation rate within this core is a
Consider natural convection between two infinite parallel plates like the system discussed in section 5.5.2. Instead of using a Newtonian fluid between the heated walls, what would happen if a
New generations of safer nuclear reactors including the pebble bed reactor use spherical nuclear fuel pellets that consist of a fissionable core of radius, $r_{\text {core }}$, and thermal
Oxygen is consumed by living cells at a rate that is often independent of $\mathrm{O}_{2}$ concentration. As a model for a living cell, consider a steady state $\mathrm{O}_{2}$ diffusion in a
Infections are often accompanied by a biofilm that is very resistant to antibiotics and hard to kill. We can model the situation as a thin film of material atop an inert substrate. The antibiotic
In the production of superconducting wire tube, the alloy is reacted with oxygen to produce the appropriate ceramic phase. Oxygen at a concentration $c_{o}$ flows through the inner tube and
Mitochondria are the centers for energy conversion in the body. Enzymes attached to the internal membranes oxidize sugars to produce energy. To get an idea about mitochondria performance, the system
A semiconductor photodiode consists of a light sensitive layer of thickness, $d$, coupled to electronic circuitry that measures the current produced in that layer (Figure P5.33). Electrons are
The speed of semiconductor photodetectors is increased by applying a bias voltage. We can investigate this effect by assuming a constant electric field, $E_{o}$, is applied across the light
Avalanche photodiodes work on a bit different mechanism from that discussed in problem 5.33. Here a thin photosensitive layer is used as the source of electrons (Figure P5.35). Those electrons enter
A membrane separates two fluids. One of the fluids is well mixed and the other is unmixed as shown in Figure P5.36. On the side of the membrane adjacent to the unmixed fluid, an enzyme is attached
You are working for a contract research firm, DATATEC, and your first job is to determine the diffusion coefficient and reaction rate constant for a decomposition reaction $(A \rightarrow C)$. You
Reconsider the first example in the text a final time. However, in this instance let's assume we have a first-order chemical reaction $a \xrightarrow{k_{a}^{\prime \prime}} b$ occurring in the
The simple analysis of the junction diode shows that if the Damkohler number, $D a=0$, no current will flow and so recombination is the main source of current flow (equation (5.136)). However, if
A similarity variable is generally used for which class of problems?a. Lumped capacitanceb. Moving frontc. Semi-infinite
What two characteristics of a system does the decay constant in the lumped capacitance formulation represent?
The Biot number represents the ratio of which two resistances?
How are the error function (erf) and complementary error function $(e r f c)$ related?
If we have temperature as a function of space, $x$, and time, $t$, express the total differential of the temperature, $d T$, in terms of changes of temperature with respect to changes in $x$
Consider the operation of the lava lamp. Polymer is heated at the base and due to buoyant forces, begins to rise through a colored liquid in the form of small spheres \(\left(r_{o}=1.5
A polymer manufacturer is looking to cut cost. An engineer has the idea of changing the geometry of their "pellets" from spherical to cubes while keeping the "pellet" volume the same. This would
A somewhat sadistic yet decidedly normal child, James decides to pull out his magnifying glass and torture an ant. The ignition temperature of an ant is roughly $300^{\circ} \mathrm{C}$. James' low
The lumped capacitance formulation can be used when a system is being cooled by thermal radiation, too. Consider a spherical object of radius $1 \mathrm{~m}$ in low Earth orbit at an initial
The makers of rapid beverage coolers, like the Cooper Cooler ${ }^{\mathrm{TM}}$, claim that their device can cool a bottle of wine from $25^{\circ} \mathrm{C}$ to $4^{\circ} \mathrm{C}$ in six
A sugar cube $\left(L_{o}=1 \mathrm{~cm}\right)$ is dissolving in a cup of tea. The mass transfer coefficient, $k_{c}$, to the tea is $5.0 \times 10^{-5} \mathrm{~m} / \mathrm{s}$. You may
A steel cube, $2.0 \mathrm{~cm}$ on a side, is initially at a temperature of $300^{\circ} \mathrm{C}$. The cube is dropped into a cooling bath \(\left(T_{\infty}=25^{\circ} \mathrm{C}, h=100
The development of safe nuclear fuel pellets is critical to future reactor designs. One project the engineers have is to look into what happens when the reactor cooling system fails and the
You are attempting to model the growth of bacteria and decrease in nutrient over time in a well-stirred flask of volume, $V$. You want to chart the total number of cells per unit volume (cell
Carbon steel can be converted into martensite by heating the steel above its eutectic temperature and then rapidly quenching it. In a particular experiment, a steel pellet, $1 \mathrm{~cm}$ in
It is desired to harden a cylindrical steel rod by changing its structural form from austenite to martensite. In order to do this, the steel must be cooled rapidly by a process called quenching. The
Estimate the time required to heat a cubical piece of chicken to $120^{\circ} \mathrm{C}$. The temperature of the grill used for cooking is $250^{\circ} \mathrm{C}$. The temperature of the air
An electronic device that dissipates(generates) $30 \mathrm{~W}$ is used infrequently. Its maximum allowable operating temperature is limited to $75^{\circ} \mathrm{C}$; as soon as \(75^{\circ}
A cylindrical roll of cloth was soaked in a dye mixture to color it. After the dye binds to the cloth, the cloth is soaked in a well-mixed tank of solvent to remove the unbound dye. The concentration
We would like to consider mass transfer to a porous cylinder from a solution, similar to the process we analyzed previously. The only difference is that the tank, into which the particle is placed,
While making the perfect soft-boiled egg is hard, making a good hard-boiled egg is equally hard. The problem lies at the interface between the yolk and egg. If you boil too long, the yolk turns green
Convection ovens assist in the cooking of food by having a fan force hot air inside the oven to flow across the food at a relatively high velocity. As we will see in later chapters, this forced
In preparation to attend a concert on a hot summer day, you straighten your hair to give yourself a new 'do. Unfortunately, it is very humid outside. Water vapor will penetrate your hair eventually
As a master chef, chemical engineer, and employee of Pillsbury, you are devising a new devil's food cake mix. You would like to have some idea of how long to bake the thing and your only guideline is
The thermal oxidation of a silicon wafer to form a thin film of protective oxide on the surface can be modeled as follows:a. Oxygen from the atmosphere is transported to the surface of the wafer and
Consider the case of diffusion and reaction inside a slab. Initially the concentration of solute in the slab is $c_{a o}$. The slab is made of a material that when heated catalyzes the reaction of
Surgical implants are cylindrical pellets of powdered drug that are inserted into the body for controlled release of medication. These implants must be sterilized, and since they are water soluble,
Toothbrush manufacturer's have been impregnating their bristles with dye to use as wear indicators. Each bristle is $0.1 \mathrm{~mm}$ in diameter and $12 \mathrm{~mm}$ long. Assuming the dye is
A porous cylinder absorbent was used to soak up a toxic material. This material is now to be destroyed by immersing the cylinder in a neutralizing bath (Figure P6.29). The toxic liquid diffuses from
Polishing operations involve rubbing two plates past one another with an intervening fluid. The fluid holds abrasive for the polishing and keeps the surfaces cool. One theory asserts that the degree
A new method for polishing the inside of ferrules used in optical fiber connectors involves a wire that reciprocates through the ferrule opening. We would like to determine the velocity profile of
Pyrethrin is an insecticide derived from the pyrethrum plant. Polymeric supports are impregnated with pyrethrin and the insecticide slowly diffuses through the polymer and into a room (for example,
In Fahrenheit 451, Ray Bradbury writes about firemen whose job it is to burn books. The 451 refers to the temperature $\left(232.8^{\circ} \mathrm{C}\right)$ at which paper starts to burn. Assume
Revisit the example of diffusion and instantaneous reaction of Section 6.5.2. There we determined the flux of species $a$ through the original vapor-liquid interface at $y=0$. However, we would
As the infrastructure engineer for the City of Troy the coming cold wave has made you nervous about the water main on 4th street. The situation is shown Figure P6.35. Current temperature at the
Consider the transfer of substance $a$ between water (1) and isooctane (2). The two solvents are immiscible, and both can be assumed to extend out toward infinity. The concentrations of $a$ in
Although it's only October, you have purchased your copy of The Farmer's Almanac and are excited to learn that the average air temperature predicted for the first two weeks of January is
You plan to build a Koi pond in your backyard but worry about how long the fish can survive if the pond freezes over. Without access to new supplies of oxygen, what would happen? Suppose midwinter
There is no physiological difference between a burn caused by scalding (boiling water) and a burn caused by dry ice or liquid nitrogen. We are interested in the time required to cause irreparable
Anyone suffering from a sports injury knows that one must put ice on the area immediately. Moreover, the recommended icing time is 20 -minute intervals. Assuming the structure for a muscular region
Semiconductor devices are prepared by doping silicon to create the source, gate, and drain regions used in a typical transistor. This doping is done primarily by diffusion processes and occurs in two
The second diffusion step in semiconductor processing is drive-in, where we no longer expose the wafer to dopant but allow the dopant to redistribute itself within the substrate. To model this
Optical waveguides can be fabricated in glass or crystal substrates by dopant diffusion as shown in Figure P6.43. The process is similar to fabricating a transistor, but diffusion depths are deeper
As an engineer working for a large military firm, you are testing the effectiveness of a heat gun on various materials. The situation is shown in Figure P6.44. This gun shines a light on the surface
In 1951, Skellem suggested that the spread of a population was similar to the spread of a chemical component via diffusion [13]. Let's consider the spread of Native Americans across North America.
We are often interested in modeling the growth and spread of a population of bacteria. While we often have a good idea of bacterial reproduction rates, getting a handle on how fast they spread is
Experimentally, it has been observed that rust advances through a highly susceptible metal at a rate proportional to $t^{1 / 2}$. Explain why this should be so, assuming:a. Oxygen diffuses through
Two semi-infinite solids, initially at temperatures $T_{1}$ and $T_{2}$, are suddenly placed in contact. Find the resulting temperature profiles and the temperature at the interface. See Figure
Experiments like Kirkendalls's are performed at elevated temperature. One such experiment using a 70:30 mole $\%$ copper mixture on one side and pure zinc on the other, was conducted at
Meat left exposed to the air slowly turns brown due to reaction with atmospheric oxygen. You have purchased a steak and inadvertently left it out on the counter for $3 \mathrm{hrs}$. Upon cutting
A fluid has the following velocity profile in three dimensions:\[\begin{array}{ll}v_{r}=v_{o}\left(r^{2} \theta+\theta^{2} z-r^{2} z\right) & v_{\theta}=v_{o}\left(\theta^{2} z-\theta^{2}
In 1856, H. Darcy published a paper where he described experiments showing that the flow of fluid through a porous medium was linearly related to the pressure drop across the
and through all of them by:\[\dot{V}=\frac{\pi n d_{0}^{4}}{128 \mu} \frac{\Delta P}{L}\]a. Derive an expression for the permeability, $k$.b. What is the void fraction of the material and can you
We can look at flow between flat plates in the same way. Many layered materials can be modeled in this way and a particular experimental set-up for studying fluid dynamics, the Hele-Shaw cell, is
Many fluids are non-Newtonian. A classic non-Newtonian material is low-fat Mayonnaise [13]. The reason behind this is the modified starches and xanthan gum used to stabilize the water and oil
The Carreau-Yasuda model is a popular formulation for representing non-Newtonian fluid behavior. The model
Prove that all forms of Fick's Law agree with thermodynamics; that is, "At equilibrium, the concentration of all species throughout the system should be uniform."
Prove that in a binary mixture whose total concentration of species, $c_{t}$, remains constant, there is only one diffusion coefficient; $D_{a b}=D_{b a}$.
A solid containing species $a$ has been analyzed and the mole fraction profile has been found to obey the following function of $y$ alone:\[x_{a}=a_{o}\left(y-K y_{o}\right)^{\frac{1}{3}} \quad
A new lithium sulfate $\left(\mathrm{Li}_{2} \mathrm{SO}_{4}\right)$ electrolyte has been developed for battery applications. Assuming ideal solutions and a stationary coordinate system, what does
We defined a molar flux relative to the molar average velocity as:\[\overrightarrow{\mathbf{J}}_{i}=-c_{t} D_{i j} \vec{abla} x_{i}\]We could just as easily have defined the flux relative to the
The mass flux of a species can be written using the chemical potential as a driving force. Consider the simple case of binary diffusion in an ideal mixture of liquids. If the chemical potential is
In Section 2.4 we discussed the definition of a molar flux, in one dimension defined by\[J_{a x}=v_{a x} c_{a}=-D_{a b} \frac{d c_{a}}{d x}\]We can use this to define the velocity, $v_{a x}$. Given
Gasoline-contaminated ground water from a nearby gas station has diffused underneath a house. Sticking a probe 3 meters into the floor in the basement, you find that the concentration of the
Thermocouples attached to a truncated, conical roller bearing in Figure P2.15 show that the temperature profile and heat flow rate are:\[T(x)=450\left(2-3 x+x^{2}-x^{3}\right) \quad q=7500 W\]If the
The two-dimensional object shown in Figure P2.16 is insulated with the exception of two flat portions that are exposed to two different temperatures. The temperature gradient at surface 1 is measured
A spherical shell of inner radius, $r_{i}$, outer radius, $r_{o}$, and thermal conductivity, $k$, is being used to dissipate heat. At a particular time, the temperature profile within the shell is
The heat flux, $\overrightarrow{\mathbf{q}}^{\prime \prime}$, due to a volume source distribution (expressed in spherical coordinates) is given by:\[\overrightarrow{\mathbf{q}}_{r}^{\prime \prime}=C
The heat flow by conduction through a cylindrical object whose inner diameter, $d_{i}=20 \mathrm{~mm}$, outer diameter, $d_{o}=30 \mathrm{~mm}$, and length, $L=1$ meter, is given theoretically
The voltage $(\mathrm{V})-\operatorname{current}(\mathrm{I})$ behavior for a new material was measured. The material was fashioned into a wire $1 \mathrm{~mm}$ in diameter and $1 \mathrm{~m}$ long.
We showed that one of the most often used forms of Fick's Law for multi-component systems could be written as:\[\overrightarrow{\mathbf{J}}_{i}=-\underbrace{D_{i j o}\left(1+\frac{\partial \ln
Activities in solution can often be correlated by the Margules equations.\[\ln \gamma_{1}=x_{2}^{2}\left[A_{12}+2\left(A_{21}-A_{12}\right) x_{1}\right] \quad \ln
A student tries to dissolve a congealed mass of $\mathrm{NaOH}$ by adding water to the beaker. The concentration profile of $\mathrm{NaOH}$ in the water above it was measured and found to
A young engineer has the bright idea of trying to separate methanol and water by centrifugation as shown in Figure P2.24. The target system is an antifreeze consisting of $30 \mathrm{~mol} %$

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