Questions and Answers of Fundamentals Of Chemical Engineering Thermodynamics

Water flows at \(0.20 \mathrm{~kg} / \mathrm{s}\) through a thick-walled tube. The inside diameter of the tube is \(25 \mathrm{~mm}\) in diameter and the tube is \(5 \mathrm{~m}\) long. The outside
A spherical steel rivet \((r=5 \mathrm{~mm})\), initially at a temperature of \(250^{\circ} \mathrm{C}\), falls from a tall building \((100 \mathrm{~m})\) through ambient air \((300 \mathrm{~K})\).
Water at \(10^{\circ} \mathrm{C}\) is in crossflow over the tubes of a shell-and-tube heat exchanger. The mass flow rate is \(1 \mathrm{~kg} / \mathrm{s}\left(6 \mathrm{~m} / \mathrm{s}\right.\)
A tube of radius \(r_{0}=0.2 \mathrm{~m}\) is being dissolved by passing a reactive fluid through the interior. The reactant in the fluid is in great excess and so we can express the enhancement as a
Repeat the External and Internal Tube Flow example (example 14.7) using the Churchill/ Zajic expression for \(\overline{N u_{d}}\). How much does the outlet temperature change compared with the
Drag reduction is generally done by injecting the polymer into the center of the tube with the fluid. However, then one needs to wait for the polymer to move toward the wall. Injecting through the
Air flows over a vertical flat plate at a velocity of \(3 \mathrm{~m} / \mathrm{s}\). The plate temperature is constant at \(175^{\circ} \mathrm{C}\) and the free stream temperature of the air is
A spherical laundry detergent pod, \(2 \mathrm{~cm}\) in diameter, is placed in a washing machine. The cold wash cycle lasts 20 minutes at \(T=300 \mathrm{~K}\). To effectively clean one's clothes,
A thin cylinder, \(2 \mathrm{~mm}\) in diameter and \(0.3 \mathrm{~m}\) long, is to be coated via a variant of chemical vapor deposition. The wire is spun on its axis at 20 revolutions per second. A
Explain why the net heat exchange between two blackbodies at temperatures \(T_{1}\) and \(T_{2}\), \(q_{12}(B B)\), is greater than the net heat exchange between two graybodies, \(q_{12}(G B)\), at
To insure a radiation shield that has two different emissivities (like alumni foil, for example) is at a minimum temperature, which side should be pointed toward the highest temperature?
Wien's Law, \(\lambda_{\max } T=2.884 \times 10^{-3} \mathrm{mK}\), was derived from Planck's Law for blackbodies. Real objects at a given temperature also exhibit maximum emission at a particular
Natural convection and radiation are often linked because they can be of the same order of magnitude at temperatures around room temperature. In air, for example, assuming graybodies of emissivity
A recent mission to Venus used radar to penetrate the clouds and map the surface. A similar process has been used to penetrate the sands of the Sahara and see the long dead rivers that once used to
Spacecraft must be cooled via radiative mechanisms and one means of doing this is radiation fins. In many instances, these fins are heated rods that protrude from the spacecraft. Assume that the rod
Optical fibers are made by drawing the hot glass from a furnace as shown in Figure P15.7. Heat, generated in the furnace, is transferred by conduction along the drawn glass fiber, by convection to
A diffuse surface has the following spectral emissivity.\[\varepsilon(\lambda)=\left\{\begin{array}{cc}0.5 & \lambda
The emissivity of a body is generally a function of temperature and this makes calculation of the heat exchange difficult. Show that if the emissivity varies linearly with temperature, that we can
Two approximations to Planck's Law are useful in the extreme low and high limits of \(\lambda T\).a. Show that in the limit where \(\left(C_{1} / \lambda T\right) \gg 1\) that Planck's spectral
An opaque, diffuse surface has a spectral reflectivity that varies with wavelength as shown below. The surface is held at \(850 \mathrm{~K}\) and one side is exposed to thermal radiation while the
What fraction of the Sun's energy lies in the spectral range:a. \(0
Contractors in the Southwest generally coat roofs with light materials designed to keep the interior of homes cool. It has been suggested that the same practice be followed in the North. We would
People who apply facial makeup are often vexed by their difference in appearance under daylight, incandescent, and fluorescent lighting conditions. Assuming daylight acts like illumination from a
Planck's radiation law assumes a body radiating into a vacuum. If the body is radiating within another medium the wavelength of the emitted radiation changes because the speed of light in the medium
The spectral emissivity for a material is shown in Figure P15.16 and does not depend much on the temperature.a. What is the total hemispherical absorptivity for the material if it is exposed to
A new, dielectric material was developed as a protective coating for metal parts that must withstand high temperature. For designers to make use of the material, they must know what its emissivity
Find the view factors for the following enclosures.a. Long, hemispherical, duct of radius, \(r_{o}\).b. A paraboloid \(\left(z=1-x^{2}-y^{2}\right)\) bounded at the bottom by the plane \(z=0\).
Find the view factor \(F_{12}\) for the rectangles shown in Figure P15.19. FIGURE P15.19 3 m A 3 m 3 m A 1 m 1 m 3 m 1 m 1 m
A diffuse, gray radiation shield \(90 \mathrm{~mm}\) in diameter with emissivities of \(\varepsilon_{2, i}^{r}\) and \(\varepsilon_{2, o}^{r}\) on its inner and outer surfaces respectively, is
Pizzas in large restaurants are often made in belt furnaces. The pizza is placed on a translating belt that carries it through the oven for a specified length of time. Assume a semicylindrical oven,
As an engineer for a heating and cooling company you must design the refrigeration for a new ice-skating rink. As a first crack you assume a rink \(35 \mathrm{~m}\) in diameter covered by a dome \(45
Cryogenic gases are often stored in double-walled, spherical containers. The space between the two walls is evacuated so that all heat transfer between the walls occurs via radiation. Assume liquid
A toaster oven is fabricated from aluminum that has been oxidized over time (properties akin to anodized aluminum). The cylindrical heater element ( \(0.5 \mathrm{~cm}\) in diameter) is located \(5
A new radiant heating system is installed in the floor of a room \(4 \mathrm{~m}\) long by \(3 \mathrm{~m}\) wide. The floor is held at a temperature of \(35^{\circ} \mathrm{C}\) and the ceiling,
Consider the room problem above in problem 25 . Of the four walls in the room, two are external walls with surface temperatures of \(17^{\circ} \mathrm{C}\). The other two are internal walls whose
Derive an expression for the net radiation exchange between the two uniform concentric spheres shown in Figure P15.27. You may assume each sphere is a diffuse graybody with emissivity
The frustrum of a cone has its base heated as shown in Figure P15.28. The top of the cone is held at \(600 \mathrm{~K}\), the bottom at \(1500 \mathrm{~K}\), and its sides are insulated.a. What is
Two hollow rods of diameter \(0.04 \mathrm{~m}\) and length of \(1 \mathrm{~m}\) run parallel to one another separated by a distance of \(0.25 \mathrm{~m}\). The rods can be assumed to be diffuse
A copper ball bearing of radius \(r_{0}=0.01 \mathrm{~m}\) is exposed to a small heat source that operates at a temperature of \(2000 \mathrm{~K}\) and has an emissivity of 0.75 . The situation is
Most cooks know that you must tent a large bird during roasting to prevent the skin from burning. Assume we have a turkey in a \(475 \mathrm{~K}\) oven. The oven surface area is \(2
Repeat example 15.3, "Temperature on the Surface of Jupiter" for a more realistic scenario using the moon. The moon has an emissivity of about 0.94 and an albedo or reflectivity of 0.12 . Perform a
Hot coffee is contained in a cylindrical thermos bottle that is of length \(L=0.3 \mathrm{~m}\) and is laying its side as shown in Figure P15.34. The coffee container consists of a glass flask of
Solar panels are often used on spacecraft to provide power. Calculate the amount of power generated by the solar panels near Earth, Mars, and Saturn. Also calculate the temperature of the spacecraft
Calculate the average temperature of Earth. Assume that \(30 \%\) of incident light is reflected. The mean intensity of incident light at the Earth's surface is \(1350 \mathrm{~W} / \mathrm{m}^{2}
A new type of flow meter is shown in Figure P11.18. In it we read the two pressure gauges and the force on the pipe bend (using strain gauges). From those three readings we compute the fluid velocity
The Einstein formula in problem 6 only applies when the volume fraction of particles is very small. Often, we deal with very concentrated suspensions such as in a fermentation of yeast cells. An
The thermal conductivity of gases in confined spaces or at very low pressures is quite different from diffusion at atmospheric pressure. The motion of the gas is governed by collisions of the gas
Based on the results obtained in problem 35, how much total nicotine is stored directly beneath the patch in the skin and in the fat layers?Problem 35A nicotine patch is designed to deliver \(24
Reconsider the first example in the chapter regarding heterogeneous reaction on the boundary. In that example we used the simplest boundary condition for the reaction. In reality, the reaction occurs
For an unbounded fluid, the speed of sound is a thermodynamic property. What is its definition?
What is the change of the speed of sound with frequency called?
Is wavelike motion an example of conservative or diffusive motion?
For tidal waves in a channel, what is the mathematical relationship between the speed of the wave and the depth of the channel?
In the design of a horn tweeter, which parameter is most critical in specifying where the cutoff frequency for the loudspeaker would lie? Why?
Often a linearly sloped beach is not a good model. Waves coming from deep water up a gradually shelving beach are better approximated by assuming a parabolic shape like that shown in Figure P7.6
We can look at a slight variant of the problem above. Given the differential equation:\[\frac{\partial^{2} \delta}{\partial t^{2}}=\frac{\partial}{\partial x}\left(g h \frac{\partial \delta}{\partial
It is possible to consider the effect of small disturbing forces acting on water waves in canal of depth \(h\). Since the height of a wave is assumed to be very small, the only component of force
Consider a shallow lake on the equator and assume that the only tide-raising force is due to the Moon. In Figure P7.9, \(O\) represents the center of the Earth. \(M\) is the point on the equator
Consider a spherical wave formed from a disturbance at the center of a shallow pool. At time \(t=0\) a small, steady, stream of droplets begins hitting the pool. They cause a disturbance of
Consider an isolated wave traveling in a shallow canal. The wave strikes the end of the canal. We have shown that the wave is reflected with only a change in phase. Show that during the impact of the
We can transform the wave equation from a partial differential equation to an ordinary differential equation by considering sustained harmonic motion of the type \(\cos (n t+\phi)\). Using the
Many musical instruments operate by the formation of plane waves inside a cylindrical tube. To describe them we seek periodic solutions to the wave equation of the form\[\delta_{\lambda}=f(x) \cos (n
Sound waves can deeply influence our emotional state and certain combinations of waves sound particularly appealing. Chords in general are composed of three separate frequencies. A major chord is
Some feel that chords exist because they sound more pleasing than single tones.a. Compare the waveforms for the major and minor harmonic chords with something that does not generally sound so
A point source of sound gives rise to a wave whose amplitude can be described by:\[\delta=\left(\frac{B}{r}\right) \cos (\omega t-k r)\]If the energy density per unit radial position associated with
Consider an effectively infinite transmission line (telephone line). Initially the line is dead, with both potential, \(\Phi\), and current, \(d \Phi / d t\), being equal to zero. At \(t=0\) we
Alternating current flowing through a conductor prefers to flow close to the surface so the current density in the conductor increases with radial position. If we assume the current is of the form,
In heat transfer situations, the fin number represents the ratio of what two resistances?
For a fin that is effectively infinite in length, what would the tip temperature be?
In the Knudsen diffusion regime within a catalyst pore, what is the magnitude of the mean free path for a gas molecule?
The Thiele modulus represents the ratio of what two time scales?
The catalyst effectiveness is the analog of what derived property of a fin?
A copper rod, \(15 \mathrm{~mm}\) in diameter, is attached to a wall that is at a temperature of \(200^{\circ} \mathrm{C}\). The opposite end of the rod is insulated. The rod is \(100 \mathrm{~mm}\)
Consider the composite pin fin shown in Figure P8.7. Half of the fin is formed of a material with thermal conductivity \(k_{1}\), and the other half is formed of material with thermal conductivity
A flat fin of length, \(L\), width, \(w\), and thickness, \(d\), is exposed to a uniform heat flux of \(q_{o}^{\prime \prime}\) along its length (see Figure P8.8). The base of the fin is attached to
Let's consider the example of a composite fin shown in Figure P8.9. A carbon steel fin of circular cross-section is coated with a thin dielectric layer for corrosion protection. The dielectric layer
Springs are often annealed by passing a current through them. Care must be taken to ensure that the temperature along the spring does not exceed the desired annealing range. Consider a thin wire of
A rod of diameter \(25 \mathrm{~mm}\) and thermal conductivity \(k=40 \mathrm{~W} / \mathrm{m} \mathrm{K}\) is part of a handle that protrudes from a furnace wall. The wall temperature is
A microprocessor has an aluminum heat sink attached that consists of a series of parallel, rectangular fins. Each fin is \(2 \mathrm{~mm}\) thick, \(25 \mathrm{~mm}\) long, \(25 \mathrm{~mm}\) high,
A heat pipe is basically a hollow fin that is partially filled with fluid. The fluid evaporates at the hot end, travels the length of the fin and condenses at the cold end. Capillary forces return
Since heat pipes are sealed objects, whatever liquid gets evaporated must be condensed. Thus, if one were to integrate the internal heat transfer rate, \(h\left(T-T_{v}\right)\) over the entire
The other way to operate a heat pipe is to fix the tip temperature as we did before and to use the internal integral to define the "operating temperature" of the pipe \(\left(T_{v}\right)\).a. Solve
The stegosaurus had two long rows of armored plates running along its spine. Some paleontologists have suggested that this dinosaur used these plates to regulate body temperature (like present day
Triangular shaped fins offer high heat transfer capability and low weight when compared to other geometries. Consider the triangular fin whose base is held a constant temperature of \(T_{b}\). Since
A series of \(10 \mathrm{fins}\) is to be used to dissipate \(100 \mathrm{~W}\) from a piece of equipment whose surface temperature must be kept below \(80^{\circ} \mathrm{C}\). Air at \(300
Fins can be designed to operate via radiative, rather than convective exchange from their outer surfaces. In such instances, we must use the Stefan-Boltzmann radiation law instead of Newton's Law of
Consider a fin incorporating facilitated transport only at its base. The reaction occurring there is given by \(-r_{a}=k^{\prime \prime} c_{a}\) (moles/s). The fin is essentially infinitely long, has
The alveoli in your lungs can be modeled as conventional pin fins. Each fin is \(10 \mu \mathrm{m}\) in diameter and \(100 \mu \mathrm{m}\) long. The fin is designed to pick up oxygen from the air
One way to increase the flux of ionic materials through a mass transfer fin is to apply an electric field along its length as shown in Figure P8.23. The fin has a diameter, \(d\), and length, \(L\).
A villus of diameter, \(d\), and length, \(L\), is attached to a membrane. At the base of the villus, the membrane has enzymes immobilized on it that catalyze the transformation of the substrate
Consider a highly idealized model of the root of a leguminous plant shown in Figure P8.25. A root of diameter, \(d\), and length, \(L\), is composed of two sections. The section near the base is
The alveoli of the lungs can be modeled as pin fins with a diameter of \(20 \mu \mathrm{m}\) and a length of \(250 \mu \mathrm{m}\). The asthma drug isoproterenol is administered by inhalation. The
Consider the absorption of water through a plant root like that in Figure P8.27. The plant is a desert plant that has just experienced its first rain storm in over four months. The surface of the
A neuron is designed to provide a stimulus to a muscle at a frequency of \(2 \mathrm{~s}^{-1}\). The neuron's axon can be modeled as a cylinder with a permeable tip. For the stimulus to be effective,
We can rig up a mass transfer fin so that there is a reaction occurring within the volume of the fin.a. Derive the differential equation for the concentration in the fin assuming a zero-order
We are interested in using a large surface area, pin fin based adsorbent for removing toxic material from a water solution. The system operates in batch mode with a stirred tank of contaminated fluid
Biological organisms often couple extended surface transport with a facilitated mechanism to enhance mass transport. We have talked about facilitated transport and have shown how we can model it
What is effectiveness factor for a cylindrical catalyst pore like Figure 8.14, but where the reaction rate is zero order with a rate constant, \(k_{s 0}^{\prime \prime} \mathrm{mole} / \mathrm{m}^{3}
A cylindrical catalyst pore of radius, \(r_{0}\), and length, \(L\), catalyzes two competing first-order reactions.\[\begin{array}{ll}a \rightarrow b & r_{a}=-k_{a b}^{\prime \prime} c_{a} \\a
A cylindrical catalyst pellet of radius, \(r_{o}\), and length, \(L\), has a chemical reaction occurring in it. In the free stream of the fluid the concentration of reactant is \(c_{a \infty}\) and

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