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Consider the oven of Problem 1.54. The walls of the oven consist of L = 30-mm-thick layers of insulation characterized by k ins = 0.03 W/m K that are sandwiched between two thin layers of sheet... A batt of glass fiber insulation is of density = 28 kg/m 3 . Determine the maximum and minimum possible values of the effective thermal conductivity of the insulation at T = 300 K, and compare with... A dormitory at a large university, built 50 years ago, has exterior walls constructed of L s = 25-mm-thick sheathing with a thermal conductivity of k s = 0.1 W/m K. To reduce heat losses in the... A new building to be located in a cold climate is being designed with a basement that has an L = 200-mm-thick wall. Inner and outer basement wall temperatures are T i = 20C and T o = 0C,... Consider a one-dimensional plane wall of thickness 2L. The surface at x=L is subjected to convective conditions characterized by T ,1 , h 1 , while the surface at x = + L is subjected to conditions... Consider the wind turbine of Example 1.3. To reduce the nacelle temperature to T s = 30C, the nacelle is vented and a fan is installed to force ambient air into and out of the nacelle enclosure. What... Heat is transferred by radiation and convection between the inner surface of the nacelle of the wind turbine of Example 1.3 and the outer surfaces of the gearbox and generator. The convection heat... Consider the nanofluid of Example 2.2. Example 2.2 (a) Calculate the Prandtl numbers of the base fluid and nanofluid, using information provided in the example problem. (b) For a geometry of fixed... Experiments have shown that the transition from laminar to turbulent conditions for flow normal to the axis of a long cylinder occurs at a critical Reynolds number of Re D,c 2 X 10 5 , where D is... The temperature distribution within a laminar thermal boundary layer associated with flow over an isothermal flat plate is shown in the sketch. The temperature distribution shown is located at x = x... Steel-reinforced concrete pillars are used in the construction of large buildings. Structural failure can occur at high temperatures due to a fire because of softening of the metal core. Consider a... A constant-property, one-dimensional plane wall of width 2L, at an initial uniform temperature T i , is heated convectively (both surfaces) with an ambient fluid at T = T ,1 , h = h 1 . At a later... Consider Problem 5.9 except now the combined volume of the oil bath and the sphere is V tot = 1m 3 . The oil bath is well mixed and well insulated. (a) Assuming the quenching liquids properties are... Consider the plane wall of thickness 2L, the infinite cylinder of radius r o , and the sphere of radius r o . Each configuration is subjected to a constant surface heat flux q" s . Using the... A flaked cereal is of thickness 2L = 1.2 mm. The density, specific heat, and thermal conductivity of the flake are 700 kg/m 3 , c p = 2400 J/kg K, and k = 0.34 W/m K, respectively. The product is... The porosity of a packed bed can be decreased by vibrating the containment vessel as the vessel is filled with the particles. The vibration promotes particle settling. (a) Consider the air chilling... When a beam of monochromatic x rays is incident on a particular NaCl crystal, Bragg reflection in the first order (i.e., with m = 1) occurs at = 20. The value of d = 0.28 nm. What is the minimum... Consider a coupled shell-in-tube heat exchange device consisting of two identical heat exchangers A and B. Air flows on the shell side of heat exchanger A, entering at T h,i,A = 520 K and m h,A =... To maintain pump power requirements per unit flow rate below an acceptable level, operation of the oil pipeline of Problem 8.63 is subject to the constraint that the oil exit temperature T m,o exceed... Consider Problem 4.51. (a) The students are each given a flat, first-surface silver mirror with which they collectively irradiate the wooden ship at location B. The reflection from the mirror is... The NaCl molecule has a bond energy of 4.26 eV; that is, this energy must be supplied in order to dissociate the molecule into neutral Na and Cl atoms. (a) What are the minimum frequency and maximum... A countercurrent gas absorption tower packed with 1.5 in ceramic Intalox saddles is used to process 360 kgmole/h of an inlet gas stream containing 10 mole% sulfur dioxide (SO 2 ) in nitrogen (N 2 )... A rotating disk shown in the figure (at right) is used to plate a thin film of copper onto a silicon wafer by an electroless plating process at 25 C. The disk is 8.0 cm in diameter and rotates at a... The soil venting shown in the figure (next page) is used to treat soil contaminated with volatile, toxic liquids. In the present situation, the porous soil particles are saturated with liquid TCE, a... An open pond containing 200 m 3 of wastewater is contaminated with a small concentration of trichloroethylene (TCE), a common industrial solvent. The pond is 2.0 meters deep and 10 meters on a side.... The Li 2+ ion is essentially identical to the H atom in Bohrs theory, aside from the effect of the different nuclear charges and masses. (a) What transitions in Li 2+ will yield emission lines whose... The development of contact lenses has transformed the solutions that are available today for vision impairments. However, wearing them also poses several problems that includes the condition of dry... Design a heating system for a small factory in Denver, Colorado. This is a multistep problem that is continued in subsequent chapters. In the first step, you are to determine the heating load on the... Electrical resistance heaters are usually made from coils of nichrome wire. The coiled wire can be supported between insulators and backed with a reflector, for example, as in a supplemental room... Design a pressure vessel that can hold 45 kg of saturated steam at 2.75 MPa (abs) for a chemical process. The shape of the vessel is to be a cylinder with hemispherical ends. The vessel is to have... Benzene flowing at 12.5 kg/s is to be cooled continuously from 82C to 54C by 10 kg/s of water available at 15.5C. Using Table 10.6, estimate the surface area required for (a) Cross-flow with six tube... A hydrogen atom at rest in the laboratory emits the Lyman a radiation. (a) Compute the recoil kinetic energy of the atom. (b) What fraction of the excitation energy of the n = 2 state is carried by... It is possible for a muon to be captured by a proton to form a muonic atom. A muon is identical to an electron except for its mass, which is 105.7 MeV/c 2 . (a) Calculate the radius of the first Bohr... There is worldwide concern that the availability of oil will diminish within 20 or 30 years. (See, for example, Frank Kreith et al., Ground Transportation for the 21st Century, ASME Press, 2000.) In... This problem is to derive the Wien displacement law, Equation 3-5. (a) Show that the energy density distribution function can be written u = C -5 (e a/ -1) -1 , where C is a constant and a = hc/kT.... An electron in the K shell of Fe is ejected by a high-energy electron in the target of an x-ray tube. The resulting hole in the n = 1 shell could be filled by an electron from the n = 2 shell, the L... The wavelength of the K a x-ray line for an element is measured to be 0.0794 nm. What is the element? (a) The scattering angle for 50 eV electrons from MgO is 55.6. What is the crystal spacing D? (b) What would be the scattering angle for 100 eV electrons? What is the Bragg scattering angle for electrons scattered from a nickel crystal if their energy is (a) 75 eV, (b) 100 eV? Compute the wavelength of a cosmic-ray proton whose kinetic energy is (a) 2 GeV (b) 200 GeV. Three isotopes of hydrogen occur in nature; ordinary hydrogen, deuterium, and tritium. Their nuclei consist of, respectively, 1 proton, 1 proton and 1 neutron (deuteron), and 1 proton and 2 neutrons... A particle of mass m moves in a one-dimensional box of length L. (Take the potential energy of the particle in the box to be zero so that its total energy is its kinetic energy p 2 /2m.) Its energy... An early method testing Maxwells theoretical prediction for the distribution of molecular speeds is shown in Figure 8-34. In 1925 Otto Stern used a beam of Bi 2 molecules emitted from an oven at 850... Show that an electron in the n = 2, = 1 state of hydrogen is most likely to be found at r = 4a 0 . The prominent yellow doublet lines in the spectrum of sodium result from transitions from the 3P 3/2 and 3P 1/2 states to the ground state. The wavelengths of these two lines are 589.0 nm and 589.6... The wave function for a free electron, that is, one on which no net force acts, is given by (x) = Asin(2.5 x 10 10 x), where x is in meters. Compute the electrons (a) Momentum, (b) Total energy, and... (a) Show that the wave function (x, t) = Asin(kx - t) does not satisfy the time-dependent Schrdinger equation. (b) Show that (x, t) = Acos(kx - t) + iA sin(kx - t) does satisfy this equation. Problems 35 through 40 show a free-body diagram. For each: a. Identify the direction of the acceleration vector au and show it as a vector next to your diagram. Or, if appropriate, write a = 0. b. If... Problems 35 through 40 show a free-body diagram. For each: a. Identify the direction of the acceleration vector au and show it as a vector next to your diagram. Or, if appropriate, write a = 0. b. If... Use the masses in the table in Appendix A to compute the total binding energy and the binding energy per nucleon of the following nuclides: (a) 9 Be, (b) 13 C, and (c) 57 Fe. Problems 35 through 40 show a free-body diagram. For each: a. Identify the direction of the acceleration vector au and show it as a vector next to your diagram. Or, if appropriate, write a = 0. b. If... Approximating the mass of a nucleus with mass number A as A x u and using Equation 11-3, compute the nuclear density in SI units. R = RA/ with Ro= 1.2 0.2 fm 11-3 Problems 35 through 40 show a free-body diagram. For each: a. Identify the direction of the acceleration vector au and show it as a vector next to your diagram. Or, if appropriate, write a = 0. b. If... Electrons emitted in b decay have energies of the order of 1 MeV or smaller. Use this fact and the uncertainty principle to show that electrons cannot exist inside the nucleus. Problems 35 through 40 show a free-body diagram. For each: a. Identify the direction of the acceleration vector au and show it as a vector next to your diagram. Or, if appropriate, write a = 0. b. If... At one point in the novel Slapstick by Kurt Vonnegut, the force of gravity on Earth suddenly increased tremendously. The result: . . . elevator cables were snapping, airplanes were crashing, ships... Write down the wave function for the hydrogen atom when the electrons quantum numbers are n = 3, = 4, and m = -1. Check to be sure that the wave function is normalized. Problems 35 through 40 show a free-body diagram. For each: a. Identify the direction of the acceleration vector au and show it as a vector next to your diagram. Or, if appropriate, write a = 0. b. If... In Minkowski spacetime, the set of all events separated from the origin by a time like interval a 2 is a 3-surface, the hyperboloid t 2 x 2 y 2 z 2 = a 2 , where {t , x, y, z} are Lorentz... Use spacetime diagrams to prove the following:(a) Two events that are simultaneous in one inertial frame are not necessarily simultaneous in another. More specifically, if frame F moves with velocity... (a) Consider two identical chambers, each with volume V, separated by an impermeable membrane. Into one chamber put energy E and N atoms of helium, and into the other, energy E and N atoms of xenon,... A truck is traveling at 30 m/s on a slippery road. The driver slams on the brakes and the truck starts to skid. If the coefficient of kinetic friction between the tires and the road is 0.20, how far... A covered cubic tank 5.00 m by 5.00 m by 5.00 m is completely filled with water through a threaded hole in its lid. A hollow vertical pipe 5.00 m tall is screwed into the hole. The pipe has a... Following the epoch of primordial element formation (Ex. 4.10), the universe continued to expand and cool. Eventually when the temperature of the photons was 3,000 K, the free electrons and protons... Canonical transformations are treated in advanced textbooks on mechanics, such as Goldstein, Poole, and Safko or, more concisely, Landau and Lifshitz (1976). This exercise gives a brief introduction.... (a) Cygnus X-1 is a source of X-rays that has been studied extensively by astronomers. The observations (X-ray, optical, and radio) show that it is a distance r 6,000 light-years from Earth. It... Consider a nonrelativistic fluid that, in the neighborhood of the origin, has fluid velocity with ij symmetric and trace-free. As we shall see in Sec. 13.7.1, this represents a purely shearing flow,... Consider a collection of identical test particles with rest mass m 0 that diffuse through a collection of thermalized scattering centers. (The test particles might be molecules of one species, and... The 4-acceleration of a particle or other object is defined by a(vector) du(vector)/d, where u(vector) is its 4-velocity and is proper time along its world line. Show that, if an observer carries... The magnitude M of an earthquake, on modern variants of the Richter scale, is a quantitative measure of the strength of the seismic waves it creates. The earthquakes seismic-wave energy release can... Show how to construct a paraboloidal mirror of radius R and focal length f by stress polishing. (a) Adopt a strategy of polishing the stressed mirror into a segment of a sphere with radius of... Consider a slender wire of rectangular cross section with horizontal thickness h and vertical thickness w that is resting on a horizontal surface, so gravity is unimportant. Let the wire be bent in... A microcantilever, fabricated from a single crystal of silicon, is being used to test the inverse square law of gravity on micron scales (Weld et al., 2008). It is clamped horizontally at one end,... Consider a wave propagating through a dielectric medium that is anisotropic, but not necessarilyfor the momentaxisymmetric. Let the wave be sufficiently weak that nonlinear effects are unimportant.... An example of a Michelson interferometer is the Far Infrared Absolute Spectrophotometer (FIRAS) carried by the Cosmic Background Explorer satellite (COBE). COBE studied the spectrum and anisotropies... The longest radio-telescope separation available in 2016 is that between telescopes on Earths surface and a 10-m diameter radio telescope in the Russian RadioAstron satellite, which was launched into... Consider two spherical mirrors, each with radius of curvature R, separated by distance d so as to form an optical cavity (Fig. 7.9). A laser beam bounces back and forth between the two mirrors. The... We developed the theory of real-valued random processes that vary randomly with time t (i.e., that are defined on a 1-dimensional space in which t is a coordinate). Here we generalize a few elements... Consider an electron that can transition between two levels by emitting or absorbing a photon; and recall that we have argued that the stimulated transitions should be microscopically reversible.... (a) Show that the prototypical scalar wave equation (7.17) follows from the variational principle where L is the lagrangian density (b) For any scalar-field lagrangian density L(, /t , , x, t), the... Consider an L-C-R circuit as shown in Fig. 6.15. This circuit is governed by the differential equation (6.72), where F is the fluctuating voltage produced by the resistors microscopic degrees of... Consider a classical simple harmonic oscillator (e.g., the nanomechanical oscillator, LIGO mass on an optical spring, L-C-R circuit, or optical resonator briefly discussed in Ex. 6.17). Let the... (a) Write down the explicit form of the Langevin equation for the x component of velocity v(t) of a dust particle interacting with thermalized air molecules. (b) Suppose that the dust particle has... Consider an optically thick hydrogen gas in statistical equilibrium at temperature T. (Optically thick means that photons can travel only a small distance compared to the size of the system before... Consider a gigantic container of gas made of identical particles that might or might not interact. Regard this gas as a bath, with temperature T b and pressure P b . Pick out at random a sample of... Another interesting 1-dimensional map is provided by the recursion relation (a) Consider the asymptotic behavior of the variable x n for different values of the parameter a, with both x n and a being... To measure a very weak sinusoidal force, let the force act on a simple harmonic oscillator with eigenfrequency at or near the forces frequency, and measure the oscillators response. Examples range in... (a) When the early universe was 200 s old, its principal constituents were photons, protons, neutrons, electrons, positrons, and (thermodynamically isolated) neutrinos and gravitons. The photon... The north Atlantic Ocean exhibits the pattern of winds and ocean currents shown in Fig. 14.18. Westerly winds blow from west to east at 40 latitude. Trade winds blow from east to west at 20 latitude.... In Sec. 5.4.1, we explained the experimental meaning of the free energy F for a system in contact with a heat bath so its temperature is held constant, and in Ex. 5.5h we did the same for contact... Suppose that a spherical bubble has just been created in the water above the hydrofoil in the previous exercise. Here we analyze its collapsethe decrease of the bubbles radius R(t) from its value R o... Fluid flows down a long cylindrical pipe of length b much larger than radius a, from a reservoir maintained at pressure P 0 (which connects to the pipe at x = 0) to a free end at large x, where the... (a) Consider H 2 O in contact with a heat and volume bath with temperature T and pressure P. For certain values of T and P the H 2 O will be liquid water; for others, ice; for others, water vaporand... One does not have to be a biologist to appreciate the strong evolutionary advantage that natural selection confers on animals that can reduce their drag coefficients. It should be no surprise that... Earth has normal modes of oscillation, many of which are in the milli-Hertz frequency range. Large earthquakes occasionally excite these modes strongly, but the quakes are usually widely spaced in... Consider a point P in the curved interface between two fluids. Introduce Cartesian coordinates at P with x and y parallel to the interface and z orthogonal [as in diagram (b) in Box 16.4], and orient... Polarization observations of the CMB provide an extremely important probe of fluctuations in the early universe. (a) By invoking the electromagnetic features of Thomson scattering by free electrons,... (a) Derive the equation i = B ij j for the precession angular velocity of a gyroscope at the tip of as measured in an inertial frame at its tail. Here B ij is the frame-drag field introduced in... (a) Enthalpy H is a macroscopic thermodynamic variable defined by Show that this definition can be regarded as a Legendre transformation that converts from the energy representation of thermodynamics... (a) Place a local Lorentz frame at the center of Earth, and let jk be the tidal field there, produced by the Newtonian gravitational fields of the Sun and the Moon. For simplicity, treat Earth as...
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