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physics
thermodynamics

Materials Science and Engineering An Introduction 8th edition William D. Callister Jr., David G. Rethwisch - Solutions

For each of the metals listed in the table, compute the Pilling-Bedworth ratio. Also, on the basis of this value, specify whether or not you would expect the oxide scale that forms on the surface to be protective, and then justify your decision. Density data for both the metal and its oxide are
According to Table 17.3, the oxide coating that forms on silver should be non protective, and yet Ag does not oxidize appreciably at room temperature and in air. How do you explain this apparent discrepancy?
Demonstrate that(a) The value of „± in Equation 17.19 is 96,500 C/mol.(b) At 25°C (298 K),
In the table, weight gain-time data for the oxidation of copper at an elevated temperature are tabulated. W (mg/cm2) Time (min) 0.316........................... 15 0.524........................... 50 0.725........................... 100 (a) Determine whether the oxidation kinetics obey a
In the table, weight gain-time data for the oxidation of some metal at an elevated temperature are tabulated. W (mg/cm2) Time (min) 4.66...................... 20 11.7...................... 50 41.1...................... 135 (a) Determine whether the oxidation kinetics obey a linear, parabolic,
In the table, weight gain-time data for the oxidation of some metal at an elevated temperature are tabulated. W (mg/cm2) Time (min) 1.90........................ 25 3.76........................ 75 6.40........................ 250 (a) Determine whether the oxidation kinetics obey a linear,
(a) Compute the voltage at 25°C of an electrochemical cell consisting of pure cadmium immersed in a 2 × 10-3 M solution of Cd2+ ions, and pure iron in a 0.4 M solution of Fe2+ ions. (b) Write the spontaneous electrochemical reaction. Solution
A Zn/Zn2+ concentration cell is constructed in which both electrodes are pure zinc. The Zn2+ concentration for one cell half is 1.0 M, for the other, 10-2 M. Is a voltage generated between the two cell halves? If so, what is its magnitude and which electrode will be oxidized? If no voltage is
An electrochemical cell is composed of pure copper and pure lead electrodes immersed in solutions of their respective divalent ions. For a 0.6 M concentration of Cu2+, the lead electrode is oxidized yielding a cell potential of 0.507 V. Calculate the concentration of Pb2+ ions if the temperature is
An electrochemical cell is constructed such that on one side a pure nickel electrode is in contact with a solution containing Ni2+ ions at a concentration of 3 × 10-3 M. The other cell half consists of a pure Fe electrode that is immersed in a solution of Fe2+ ions having a concentration of 0.1 M.
For the following pairs of alloys that are coupled in seawater, predict the possibility of corrosion; if corrosion is probable, note which metal/alloy will corrode. (a) Aluminum and magnesium (b) Zinc and a low-carbon steel (c) Brass (60Cu-40Zn) and Monel (70Ni-30Cu) (d) Titanium and 304 stainless
(a) From the galvanic series (Table 17.2), cite three metals or alloys that may be used to galvanically protect 304 stainless steel in the active state.
A brine solution is used as a cooling medium in a steel heat exchanger. The brine is circulated within the heat exchanger and contains some dissolved oxygen. Suggest three methods, other than cathodic protection, for reducing corrosion of the steel by the brine. Explain the rationale for each
Suggest an appropriate material for each of the following applications, and, if necessary, recommend corrosion prevention measures that should be taken. Justify your suggestions.
A 95 wt% Pt-5 wt% Ni alloy is known to have an electrical resistivity of 2.35 × 10-7 Ω-m at room temperature (25°C). Calculate the composition of a platinum-nickel alloy that gives a room-temperature resistivity of 1.75 × 10-7 Ω-m. The room-temperature resistivity of pure platinum may be
Using information contained in Figures 18.8 and 18.38, determine the electrical conductivity of an 80 wt% Cu-20 wt% Zn alloy at -150°C (-240°F).
Is it possible to alloy copper with nickel to achieve a minimum tensile strength of 375 MPa (54,400 psi) and yet maintain an electrical conductivity of 2.5 × 106 (Ω-m)-1? If not, why? If so, what concentration of nickel is required?
Specify an acceptor impurity type and concentration (in weight percent) that will produce a p-type silicon material having a room temperature electrical conductivity of 50 (Ω-m)-1.
One integrated circuit design calls for diffusing boron into very high purity silicon at an elevated temperature. It is necessary that at a distance 0.2 Î¼m from the surface of the silicon wafer, the room-temperature electrical conductivity be 1.2 Ã— 103 (Î©-m)-1. The concentration of B at
Problem 18.47 noted that FeO (wustite) may behave as a semiconductor by virtue of the transformation of Fe2+ to Fe3+ and the creation of Fe2+ vacancies; the maintenance of electroneutrality requires that for every two Fe3+ ions, one vacancy is formed. The existence of these vacancies is reflected
One of the procedures in the production of integrated circuits is the formation of a thin insulating layer of SiO2 on the surface of chips (see Figure 18.26). This is accomplished by oxidizing the surface of the silicon by subjecting it to an oxidizing atmosphere (i.e., gaseous oxygen or water
The base semiconducting material used in virtually all of our modern integrated circuits is silicon. However, silicon has some limitations and restrictions. Write an essay comparing the properties and applications (and/or potential applications) of silicon and gallium arsenide.
(a) Compute the electrical conductivity of a 5.1-mm (0.2-in.) diameter cylindrical silicon specimen 51 mm (2 in.) long in which a current of 0.1 A passes in an axial direction. A voltage of 12.5 V is measured across two probes that are separated by 38 mm (1.5 in.). (b) Compute the resistance over
(a) Calculate the drift velocity of electrons in germanium at room temperature and when the magnitude of the electric field is 1000 V/m. (b) Under these circumstances, how long does it take an electron to traverse a 25-mm (1-in.) length of crystal?
At room temperature the electrical conductivity and the electron mobility for copper are 6.0 × 107 (Ω-m)-1 and 0.0030 m2/V-s, respectively. (a) Compute the number of free electrons per cubic meter for copper at room temperature. (b) What is the number of free electrons per copper atom? Assume a
(a) Calculate the number of free electrons per cubic meter for gold assuming that there are 1.5 free electrons per gold atom. The electrical conductivity and density for Au are 4.3 × 107 (Ω-m)-1 and 19.32 g/cm3, respectively.
Estimate the value of A in Equation 18.11 for zinc as an impurity in copper-zinc alloys.
(a) Using the data in Figure 18.8, determine the values of ρ0 and a from Equation 18.10 for pure copper. Take the temperature T to be in degrees Celsius.(b) Determine the value of A in Equation 18.11 for nickel as an impurity in copper, using the data in Figure 18.8.
Determine the electrical conductivity of a Cu-Ni alloy that has a yield strength of 125 MPa (18,000 psi). You will find Figure 7.16 helpful.
Tin bronze has a composition of 92 wt% Cu and 8 wt% Sn, and consists of two phases at room temperature: an α phase, which is copper containing a very small amount of tin in solid solution, and an ε phase, which consists of approximately 37 wt% Sn. Compute the room temperature conductivity of this
A cylindrical metal wire 2 mm (0.08 in.) in diameter is required to carry a current of 10 A with a minimum of 0.03 V drop per foot (300 mm) of wire. Which of the metals and alloys listed in Table 18.1 are possible candidates?
(a) Using the data presented in Figure 18.16, determine the number of free electrons per atom for intrinsic germanium and silicon at room temperature (298 K). The densities for Ge and Si are 5.32 and 2.33 g/cm3, respectively.(b) Now explain the difference in these free-electron-per-atom values.
For intrinsic semiconductors, the intrinsic carrier concentration ni depends on temperature as follows:or taking natural logarithms,Thus, a plot of ln ni versus 1/T (K)-1 should be linear and yield a slope of -Eg/2k. Using this information and the data presented in Figure 18.16, determine the band
A copper wire 100 m long must experience a voltage drop of less than 1.5 V when a current of 2.5 A passes through it. For Information: Using the data in Table 18.1, compute the minimum diameter of the wire.
Briefly explain the presence of the factor 2 in the denominator of Equation 18.35a.
At room temperature the electrical conductivity of PbTe is 500 (Ω-m)-1, whereas the electron and hole mobilities are 0.16 and 0.075 m2/V-s, respectively. Compute the intrinsic carrier concentration for PbTe at room temperature.
Is it possible for compound semiconductors to exhibit intrinsic behavior? Explain your answer.
For each of the following pairs of semiconductors, decide which will have the smaller band gap energy, Eg, and then cite the reason for your choice.(a) ZnS and CdSe.(b) Si and C (diamond).(c) Al2O3 and ZnTe.(d) InSb and ZnSe.(e) GaAs and AlP.
Define the following terms as they pertain to semiconducting materials: intrinsic, extrinsic, compound, elemental. Now provide an example of each.
An n-type semiconductor is known to have an electron concentration of 3 × 1018 m-3. If the electron drift velocity is 100 m/s in an electric field of 500 V/m, calculate the conductivity of this material.
(a) Explain why no hole is generated by the electron excitation involving a donor impurity atom. (b) Explain why no free electron is generated by the electron excitation involving an acceptor impurity atom.
Will each of the following elements act as a donor or an acceptor when added to the indicated semiconducting material? Assume that the impurity elements are substitutional. Impurity Semiconductor P............................ Ge S............................
(a) The room-temperature electrical conductivity of a silicon specimen is 5.93 × 10-3 (Ω-m)-1. The hole concentration is known to be 7.0 × 1017 m-3. Using the electron and hole mobilities for silicon in Table 18.3, compute the electron concentration. (b) On the basis of the result in part (a),
An aluminum wire 4 mm in diameter is to offer a resistance of no more than 2.5 Ω. For Information: Using the data in Table 18.1, compute the maximum wire length.
Germanium to which 5 × 1022 m-3 Sb atoms have been added is an extrinsic semiconductor at room temperature, and virtually all the Sb atoms may be thought of as being ionized (i.e., one charge carrier exists for each Sb atom). (a) Is this material n-type or p-type? (b) Calculate the electrical
The following electrical characteristics have been determined for both intrinsic and p-type extrinsic indium phosphide (InP) at room temperature:Calculate electron and hole mobilities.
Calculate the conductivity of intrinsic silicon at 100°C.
At temperatures near room temperature, the temperature dependence of the conductivity for intrinsic germanium is found to equalwhere C is a temperature-independent constant and T is in Kelvins. Using Equation 18.36, calculate the intrinsic electrical conductivity of germanium at 150°C.
Using Equation 18.36 and the results of Problem 18.33, determine the temperature at which the electrical conductivity of intrinsic germanium is 22.8 (Ω-m)-1.
Estimate the temperature at which GaAs has an electrical conductivity of 3.7 3 1023 (V-m)21 assuming the temperature dependence for σ of Equation 18.36. The data shown in Table 18.3 might prove helpful.
Compare the temperature dependence of the conductivity for metals and intrinsic semiconductors. Briefly explain the difference in behavior.
Calculate the room-temperature electrical conductivity of silicon that has been doped with 5 × 1022 m-3 of boron atoms.
Calculate the room-temperature electrical conductivity of silicon that has been doped with 2 × 1023 m-3 of arsenic atoms.
Estimate the electrical conductivity, at 125°C, of silicon that has been doped with 1023 m-3 of aluminum atoms.
Demonstrate that the two Ohm's law expressions, Equations 18.1 and 18.5, are equivalent.
Estimate the electrical conductivity, at 85°C, of silicon that has been doped with 1020 m-3 of phosphorus atoms.
Some hypothetical metal is known to have an electrical resistivity of 4 × 10-8 (Ω-m). Through a specimen of this metal that is 25 mm thick is passed a current of 30 A; when a magnetic field of 0.75 tesla is simultaneously imposed in a direction perpendicular to that of the current, a Hall voltage
Some metal alloy is known to have electrical conductivity and electron mobility values of 1.5 × 107 (Ω-m)-1 and 0.0020 m2/V-s, respectively. Through a specimen of this alloy that is 35 mm thick is passed a current of 45 A. What magnetic field would need to be imposed to yield a Hall voltage of
We noted in Section 12.5 (Figure 12.22) that in FeO (wüstite), the iron ions can exist in both Fe2+ and Fe3+ states. The number of each of these ion types depends on temperature and the ambient oxygen pressure. Furthermore, we also noted that in order to retain electroneutrality, one Fe2+ vacancy
At temperatures between 775°C (1048 K) and 1100°C (1373 K), the activation energy and preexponential for the diffusion coefficient of Fe2+ in FeO are 102,000 J/mol and 7.3 × 10-8 m2/s, respectively. Compute the mobility for an Fe2+ ion at 1000°C (1273 K).
A parallel-plate capacitor using a dielectric material having an εr of 2.5 has a plate spacing of 1 mm (0.04 in.). If another material having a dielectric constant of 4.0 is used and the capacitance is to be unchanged, what must be the new spacing between the plates?
(a) Using the data in Table 18.1, compute the resistance of a copper wire 3 mm (0.12 in.) in diameter and 2 m (78.7 in.) long.(b) What would be the current flow if the potential drop across the ends of the wire is 0.05 V?(c) What is the current density?(d) What is the magnitude of the electric
A parallel-plate capacitor with dimensions of 100 mm by 25 mm and a plate separation of 3 mm must have a minimum capacitance of 38 pF (3.8 × 10-11 F) when an ac potential of 500 V is applied at a frequency of 1 MHz. Which of those materials listed in Table 18.5 are possible candidates? Why?
Consider a parallel-plate capacitor having an area of 2500 mm2 and a plate separation of 2 mm, and with a material of dielectric constant 4.0 positioned between the plates. (a) What is the capacitance of this capacitor? (b) Compute the electric field that must be applied for 8.0 × 10-9 C to be
For NaCl, the ionic radii for Na+ and Cl ions are 0.102 and 0.181 nm, respectively. If an externally applied electric field produces a 5% expansion of the lattice, compute the dipole moment for each Na+-Cl- pair. Assume that this material is completely unpolarized in the absence of an electric
The polarization P of a dielectric material positioned within a parallel-plate capacitor is to be 1.0 × 10-6 C/m2. (a) What must be the dielectric constant if an electric field of 5 × 104 V/m is applied? (b) What will be the dielectric displacement D?
A charge of 3.5 × 10-11 C is to be stored on each plate of a parallel-plate capacitor having an area of 160 mm2 (0.25 in.2) and a plate separation of 3.5 mm (0.14 in.).(a) What voltage is required if a material having a dielectric constant of 5.0 is positioned within the plates?(b) What voltage
(a) For each of the three types of polarization, briefly describe the mechanism by which dipoles are induced and/or oriented by the action of an applied electric field. (b) For solid lead titanate (PbTiO3), gaseous neon, diamond, solid KCl, and liquid NH3 what kind(s) of polarization is (are)
(a) Compute the magnitude of the dipole moment associated with each unit cell of BaTiO3, as illustrated in Figure 18.35. (b) Compute the maximum polarization that is possible for this material.
The dielectric constant for a soda-lime glass measured at very high frequencies (on the order of 1015 Hz) is approximately 2.3. What fraction of the dielectric constant at relatively low frequencies (1 MHz) is attributed to ionic polarization? Neglect any orientation polarization contributions.
Briefly explain why the ferroelectric behavior of BaTiO3 ceases above its ferroelectric Curie temperature.
How does the electron structure of an isolated atom differ from that of a solid material?
In terms of electron energy band structure, discuss reasons for the difference in electrical conductivity between metals, semiconductors, and insulators.
Briefly tell what is meant by the drift velocity and mobility of a free electron.
Estimate the energy required to raise the temperature of 2 kg (4.42 lbm) of the following materials from 20 to 100°C (68 to 212°F): aluminum, steel, soda-lime glass, and high-density polyethylene.
Compute the density for nickel at 500°C, given that its room-temperature density is 8.902 g/cm3. Assume that the volume coefficient of thermal expansion, αv, is equal to 3αl.
When a metal is heated its density decreases. There are two sources that give rise to this diminishment of ρ: (1) the thermal expansion of the solid, and (2) the formation of vacancies (Section 4.2). Consider a specimen of copper at room temperature (20°C) that has a density of 8.940 g/cm3.(a)
The difference between the specific heats at constant pressure and volume is described by the expressionwhere Î±v is the volume coefficient of thermal expansion, v0 is the specific volume (i.e., volume per unit mass, or the reciprocal of density), Î² is the compressibility, and T is the
To what temperature must a cylindrical rod of tungsten 10.000 mm in diameter and a plate of 316 stainless steel having a circular hole 9.988 mm in diameter have to be heated for the rod to just fit into the hole? Assume that the initial temperature is 25°C.
(a) Calculate the heat flux through a sheet of steel 10 mm (0.39 in.) thick if the temperatures at the two faces are 300 and 100°C (572 and 212°F); assume steady-state heat flow. (b) What is the heat loss per hour if the area of the sheet is 0.25 m2 (2.7 ft2)? (c) What will be the heat loss per
(a) Would you expect Equation 19.7 to be valid for ceramic and polymeric materials? Why or why not?(b) Estimate the value for the Wiedemann-Franz constant L [in Ω-W/(K)2] at room temperature (293 K) for the following nonmetals: silicon (intrinsic), glass-ceramic (Pyroceram), fused silica,
Briefly explain why the thermal conductivities are higher for crystalline than non crystalline ceramics.
Briefly explain why metals are typically better thermal conductors than ceramic materials.
(a) Briefly explain why porosity decreases the thermal conductivity of ceramic and polymeric materials, rendering them more thermally insulative. (b) Briefly explain how the degree of crystallinity affects the thermal conductivity of polymeric materials and why.
For some ceramic materials, why does the thermal conductivity first decrease and then increase with rising temperature?
To what temperature would 25 lbm of a 1025 steel specimen at 25°C (77°F) be raised if 125 Btu of heat is supplied?
For each of the following pairs of materials, decide which has the larger thermal conductivity. Justify your choices. (a) Pure copper; aluminum bronze (95 wt%Cu-5 wt% Al). (b) Fused silica; quartz. (c) Linear polyethylene; branched polyethylene. (d) Random poly(styrene-butadiene) copolymer;
We might think of a porous material as being a composite wherein one of the phases is a pore phase. Estimate upper and lower limits for the room-temperature thermal conductivity of a magnesium oxide material having a volume fraction of 0.30 of pores that are filled with still air.
Non steady-state heat flow may be described by the following partial differential equation:where DT is the thermal diffusivity; this expression is the thermal equivalent of Fick's second law of diffusion (Equation 5.4b). The thermal diffusivity is defined according to In this expression, k,
Beginning with Equation 19.3, show that Equation 19.8 is valid.
(a) Briefly explain why thermal stresses may be introduced into a structure by rapid heating or cooling. (b) For cooling, what is the nature of the surface stresses? (c) For heating, what is the nature of the surface stresses?
(a) If a rod of 1025 steel 0.5 m (19.7 in.) long is heated from 20 to 80°C (68 to 176°F) while its ends are maintained rigid, determine the type and magnitude of stress that develops. Assume that at 20°C the rod is stress free. (b) What will be the stress magnitude if a rod 1 m (39.4 in.) long
A copper wire is stretched with a stress of 70 MPa (10,000 psi) at 20°C (68°F). If the length is held constant, to what temperature must the wire be heated to reduce the stress to 35 MPa (5000 psi)?
If a cylindrical rod of nickel 100.00 mm long and 8.000 mm in diameter is heated from 20°C to 200°C while its ends are maintained rigid, determine its change in diameter. You may want to consult Table 6.1.
The two ends of a cylindrical rod of 1025 steel 75.00 mm long and 10.000 mm in diameter are maintained rigid. If the rod is initially at 25°C, to what temperature must it be cooled to have a 0.008-mm reduction in diameter?
What measures may be taken to reduce the likelihood of thermal shock of a ceramic piece?
(a) Determine the room temperature heat capacities at constant pressure for the following materials: aluminum, silver, tungsten, and 70Cu-30Zn brass. (b) How do these values compare with one another? How do you explain this?
For aluminum, the heat capacity at constant volume Cv at 30 K is 0.81 J/mol-K, and the Debye temperature is 375 K. Estimate the specific heat (a) At 50 K (b) At 425 K.
The constant A in Equation 19.2 is 12π4R/5 θD3, where R is the gas constant and θD is the Debye temperature (K). Estimate θD for copper, given that the specific heat is 0.78 J/kg-K at 10 K.
(a) Briefly explain why Cv rises with increasing temperature at temperatures near 0 K. (b) Briefly explain why Cv becomes virtually independent of temperature at temperatures far removed from 0 K.

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