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Prove analytically that the entropy of a two-statesystem? is maximized when p + = p ? = 1/2. S = -kB (p+ In p+ +p_ In p_) = -kB (P+ In p4 + (1 P+) In(1 P+)) In isobaric heating (and expansion), heat is added reversibly to a gas kept at constant pressure. Find the change in volume and entropy when a sample of an ideal, monatomic gas, initially at... An SI engine, modeled as an ideal Otto cycle, runs at a compression ratio of 9.6:1 with a maximum cylinder volume (V 1 ) of 2 L and a corresponding displacement of 1.8 L. Combustion leads to a... An example of a thermal-neutron fission reaction isn th + 235 U 139 Ba + 94 Kr + 3n. Perform the analysis of Example 18.1 for this case. Show that an infinite, homogeneous reactor fueled with natural uranium (0.72% 235 U) and moderated by heavy water (D 2 O) can sustain a fission chain reaction. What is the optimal ratio of moderator... Thermal neutrons wandering through biological tissue are most likely to be absorbed by 1 H, 12 C, or 16 O. If absorption is accompanied by emission of a single -ray, what are the -ray energies... According to the text, roughly 1015% of lung cancer deaths in the US are due to radon exposure. Use the LNT model and average yearly effective dose from radon to estimate the cancer rate from this... Consider the circumstances described in Problem 21.8, but now suppose that 2 < 0. Use the transformation defined in Problem 21.7 to show that there is a reference frame traveling at a speed v < c in... Compute the power radiated in the visible range from the toaster oven coil radiating with a total power of 1500 W, as described in Example 22.1. Determine the maximum concentration C of a solar concentrator satisfying T 4 = CI 0 , where I 0 is the solar constant, directly from the second law of thermodynamics and the surface temperature of... The wind speed at any site can be written as the sum of its average v plus a fluctuating term that averages to zero, v(t) = v + v(t). Show that the effect of the fluctuations is always to make v 3 ... Compute the energy density and power density in a steady wind at 8 m/s and at 16 m/s. An entrepreneur claims to have devised a system for extracting thermal energy from the wind by cooling it. His device lowers the temperature of the air that passes through it by 1 C. He claims to... The isothermal compressibility of a fluid is the relative change of volume with pressure at constant temperature = (1/V)V/p| T . Qualitatively describe and sketch the compressibility of water as a... Estimate the power output possible for a hydroelectric dam with hydraulic head Z = 30 m, flow rate Q = 300 m 3 /s, and turbine efficiency 90%. Estimate the energy content of a coal seam measuring 1 km 2 by 1 m deep. Estimate the electrical power output of a coal plant burning this fuel over one year, and the area required for a solar... A 345 kV transmission line consisting of three conductors has a resistance per unit length of R =R/l = 0.0351/km, and an inductive reactance per unit length of L = L/l = 0.371 /km, as described in... A beaker containing 400 g of water has 1200 J of work done on it by stirring and 200 cal of heat added to it from a hot plate. a. What is the change in the internal energy of the water in joules? b.... A guitar string has an overall length of 1.25 m and a total mass of 40 g (0.04 kg) before it is strung on the guitar. Once on the guitar, however, there is a distance of 64 cm between its fixed end... A pipe that is open at both ends will form standing waves, if properly excited, with antinodes near both ends of the pipe. Suppose we have an open pipe 40 cm in length. a. Sketch the standing-wave... Radiation shields are commonly used in the design of superinsulations for use in space and cryogenics applications. Write an essay on superinsulations and how they are used in different applications. A baryon frequently encountered in particle physics experiments is known as the (Lambda). Its quark content is uds. Sometimes the decays by the process n, where n is a neutron (ddu) and is a... The radius of Mars orbit around the Sun averages roughly R Mars 2.28 10 8 km. Assuming that the surface temperature is roughly uniform over the planets surface and constant over a Martian day, that... The eccentricity of Mars elliptic orbit is roughly 0.0935. Estimate the range over which the solar constant and average surface temperature (in the uniform temperature blackbody approximation) vary... Why does the efficiency of a silicon PV drop as it heats up? eq. (25.25). E- kBT In dE Egap Voc < SE dE gap E2 eE/kgT e The absorption coefficient of silicon has a strong dependence on photon energy, as shown in Figure 25.16 For simplicity, consider an idealized material, material S, similar to crystalline silicon,... What is the energy of sunlight (in units of W/m 2 at normal incidence)? Discuss how energy is destroyed when sunlight is converted to electricity by photo voltaic cells, by solar thermal electric... A microsecond is one-____ of a second. What is the meaning of cross-sectional area? Fill in each blank (round to three significant digits when necessary): 75 ms = ____ s A very thin silicon chip is bonded to a 6-mm thick aluminum substrate by a 0.02-mm thick epoxy glue. Both surfaces of this chip-aluminum system are cooled by air at 25C, where the convective heat... The electric power generator for an orbiting satellite is composed of a long, cylindrical uranium heat source that is housed within an enclosure of square cross section. The only way for heat that is... The temperature of a flowing gas is to be measured with a thermocouple junction and wire stretched between two legs of a sting, a wind tunnel test fixture. The junction is formed by butt-welding two... A new type of porous material serves as food packaging film, as shown in the figure below. The film rests on a nonporous metal plate. The packaging film is 0.20 cm thick (2.0 mm). The food contains... It is desired to diffuse a blue dye molecule (solute A) into a solid material (species B) near the surface of the material, as shown in the figure below. Initially, there is no dye in the solid (c Ao... Consider the concentric tubular mass transfer device shown in the figure below. This device is designed to gradually introduce hydrogen (H 2 ) gas (species A) into a pure oxygen gas (O 2 ) inlet... Tetraethoxysilane, also called TEOS or Si(OC 2 H 5 ) 4 , is a liquid chemical used in the semiconductor industry to produce thin films of silicon dioxide by chemical vapor deposition (CVD). In order... Pipes often contain solid residue that adheres to the inner wall of the pipe. If these pipes are not properly cleaned before use, then the flow of water through the pipe will slowly dissolve the... The Teachers' Retirement System of a midwestern state is selling a bond investment from its portfolio to generate cash to make payments to retirees for the coming year It plans to sell $100 million... Use the 2-dimensional spacetime diagrams of Fig. 3.4 to show that are frame independent [Eqs. (3.7a) and (3.7b)]. Fig 3.4 EdVx and dVp/E Monroe Outpatient Surgery Center (MOSC) is developing an operating budget for the month ending June 30, 2024. MOSC expects to perform 80 surgical procedures during the month. MOSCs average charge... How many significant figures does each of the following numbers have? (a) 0.73 (b) 7.30 (c) 73 (d) 0.073 How many significant figures does each of the following numbers have? (a) 290 (b) 2.90 10 4 (c) 0.0029 (d) 2.90 Draw a pictorial representation for the following problem. Do not solve the problem. What acceleration does a rocket need to reach a speed of 200 m/s at a height of 1.0 km? Youre driving down the highway late one night at 20 m/s when a deer steps onto the road 35 m in front of you. Your reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration... A 1000 kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 16 s, then the motor stops. The rocket altitude 20 s after launch is 5100 m. You can ignore any... A projectiles horizontal range over level ground is v 0 2 sin 2/g. At what launch angle or angles will the projectile land at half of its maximum possible range? A stunt man drives a car at a speed of 20 m/s off a 30-m-high cliff. The road leading to the cliff is inclined upward at an angle of 20. a. How far from the base of the cliff does the car land? b.... On Planet X, you drop a 25-kg stone from rest and measure its speed at various times. Then you use the data you obtained to construct a graph of its speed as a function of time t (Fig. P2.78). From... A test car travels in a straight line along the x-axis. The graph in Fig. E2.11 shows the cars position x as a function of time. Find its instantaneous velocity at points A through G. Figure E2.11: x... Recall the stirred-tank heating process with variable holdup as described in Section 2.4.2. Recalculate the degrees of freedom for this example under the following separate circumstances (be sure to... A thermometer with first-order time constant = 0.1 min and gain = 1.0 is placed in a temperature bath (25 C). After the thermometer comes to equilibrium with the bath, the temperature of the bath is... For a stirred-tank heater, assume the transfer function between the heater input change u(t) (cal/sec) and the tank temperature change y(t)( C) can be modeled as G(s) = 5 / 3s + 1 (a) Using the... A process has the transfer function (a) For a step change in the input U(s) = 2/s, sketch the response y(t) (you do not need to solve the differential equation). Show as much detail as possible,... Example 5.1 derives the gain and time constant for a first-order model of a stirred tank heating process. (a) Simulate the response of the tank temperature to a step change in heat input from 310 7... The level in a tank responds as a first-order system to changes in its inlet flow. The data shown below were gathered after the inlet flow was increased quickly from 1.5 to 4.8 gal/min. (a) Determine... Consider the liquid storage system in Fig. E8.13. Suppose that q 1 must be kept constant, and, consequently, h 2 is to be controlled by adjusting q 2 . Suppose that the q 2 control valve is... A steam-heated evaporator used to concentrate a feed stream by evaporating water is shown in Fig. E8.14. The mass fraction of solute in the exit stream x is measured and controlled by adjusting the... A plasma etching batch process has a process gain of E A/min (but no dynamics). The manipulated variable is the etch time, so the controlled variable is the film thickness. There are no time... A cylindrical storage tank is 2 m tall and 1 m in diameter. A low-level alarm is activated when the liquid level decreases to 0.25 m. Suppose that the tank is initially half full when a slow leak... The cascade reactor control configuration shown in Fig. 16.3 utilizes a measurement of the cooling water temperature. It has been suggested that the temperature of the reactor wall be measured to... Calculate the zero-bias junction capacitance for the example in Problem 1.1, and also calculate the value at 5 V reverse bias and 0.3 V forward bias. Assume a junction area of 2 10 5 cm 2 . Data... Repeat Problem 1.8 for I C = 1 mA, V CB = 1 V, and V CS = 2 V. Data from Prob. 1.8: Derive and sketch the complete small-signal equivalent circuit for a bipolar transistor at I C = 0.2 mA, V CB = 3V,... The 20.0 cm x 35.0 cm rectangular circuit shown in Fig. E27.45 is hinged along side ab. It carries a clockwise 5.00-A current and is located in a uni-form 1.20-T magnetic field oriented perpendicular... A charge of 1 nC is located at the origin in free space. What charge must be located at (2, 0, 0) to cause E x to be zero at (3, 1, 1)? (a) Obtain the time-average auto correlation function of x(t) = 3 + 6 cos (20t) + 3 sin (20t). (Combine the cosine and sine terms into a single cosine with a phase angle.) (b) Obtain the power... Classify each of the following signals as an energy signal or as a power signal by calculating E, the energy, or P, the power (A, B, , , and are positive constants). (a) x 1 (t) = A| sin (t + )| (b)... Given a binary communication channel where A = input and B = output, let P(A) = 0.45, P(B | A) = 0.95, and P(B | A) = 0.65. Find P(A | B) and P(A | B). A power spectral density given by S Y (f) = f 2 / f 4 + 100 is desired. A white-noise source of two-sided power spectral density 1 W/Hz is available. What is the frequency response function of the... Using x r (t) = m(t) cos(2Ïf c t) and e 0 (t) = 2 cos (2Ïf c t + θ) for the assumed Costas PLL input and VCO output, respectively, verify that all signals shown at the various... Consider a random binary pulse waveform as an alyzed in Example 7.6, but with half-cosine pulses given by p(t) = cos(2t / 2T)II(t / T). Obtain and sketch the auto correlation function for the two... Find H in a material where (a) r = 4.2, there are 2.7 10 29 atoms/m 3 , and each atom has a dipole moment of 2.6 10 30 a y Am 2 ; (b) M = 270a z A/m and = 2 H/m; (c) m = 0.7 and B = 2a z T. (d)... The physics of circular motion sets an upper limit to the speed of human walking. (If you need to go faster, your gait changes from a walk to a run.) If you take a few steps and watch whats... A solid conductor of circular cross section with a radius of 5 mm has a conductivity that varies with radius. The conductor is 20 m long, and there is a potential difference of 0.1 V dc between its... Calculate the output resistance r c o of the common-emitter Darlington transistor of Fig. 3.75 as a function of I BIAS . Do not neglect either r o1 or r o2 in this calculation, but you may neglect r... Find the short-circuit transconductance of the super-source follower shown in Fig. 3.43. Assume I 1 = 200 A, I 2 = 100 A, W 1 = 30 m, and W 2 = 10 m. Also, assume that both transistors operate in the... Determine the output current and output resistance of the bipolar current mirror shown in Fig. 4.55. Find the output current if V out = 1 V, 5 V, and 30 V. Ignore the effects of nonzero base... Repeat problem 4.1 including the effects of nonzero base currents? Repeat problem 4.1: Determine the output current and output resistance of the bipolar current mirror shown in Fig. 4.55. Find the... Design a MOS Widlar current source using the circuit shown in Fig. 4.31b to meet the following constraints with V DD = 3 V: (a) The input current should be 100 µA, and the output current should... For the bias circuit shown in Fig. 4.66, determine the bias current. Assume that X d = L d = 0. Neglect base currents and the body effect. Comment on the temperature dependence of the bias current.... A circuit as shown in Fig. 5.1 has V CC = 15V, R 1 = R 2 = 0, R 3 = 5k¦, R L = 2k¦, V CE(sat) = 0.2 V, and V BE(on) = 0.7 V. All device areas are equal. (a). Sketch the transfer... (a) For the circuit of Problem 5.1, sketch load lines in the I c - V ce plane for R L = 2 k¦ and R L = 10 k¦. (b) Calculate the maximum average sinusoidal output power that can be... A two-stage bipolar amplifier is shown in Fig. 7.47. Calculate the low-frequency, small-signal voltage gain Ï o /Ï i and use the zero-value time constant method to estimate the3-dB... A small model car with mass m travels at constant speed on the inside of a track that is a vertical circle with radius 5.00 m (Fig. E5.45). If the normal force exerted by the track on the car when it... You are pushing a large crate from the back of a freight elevator to the front as the elevator is moving to the next floor. In which situation is the force you must apply to move the crate the least,... Objects A, B, and C are moving as shown in Fig. E8.3. Find the x- and y components of the net momentum of the particles if we define the system to consist of (a) A and C, (b) B and C, (c) all three... Two springs with the same unstretched length but different force constants k 1 and k 2 are attached to a block with mass m on a level, frictionless surface. Calculate the effective force constant k... In-compressible steady flow in the inlet between parallel plates is uniform, V 0 = 8 cm/s, while downstream, the flow develops into the parabolic profile v x = az(z 0 - z), where a is a constant.... A 75 g bungee cord has an equilibrium length of 1.20 m. The cord is stretched to a length of 1.80 m, then vibrated at 20 Hz. This produces a standing wave with two antinodes. What is the spring... FIGURE EX17.7 shows a standing wave on a string that is oscillating at 100 Hz. a. How many antinodes will there be if the frequency is increased to 200 Hz? b. If the tension is increased by a factor... If you peel two strips of transparent tape off the same roll and immediately let them hang near each other, they will repel each other. If you then stick the sticky side of one to the shiny side of... An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is given by (r) = /r, where a is a positive constant. (a) In terms of a and... A thin spherical shell with radius R 1 = 3.00 cm is concentric with a larger thin spherical shell with radius R 2 = 5.00 cm. Both shells are made of insulating material. The smaller shell has charge... The battery in the circuit shown in Fig. Q26.14 has no internal resistance. After you close the switch S, will the brightness of bulb B 1 increase, decrease, or stay the same? Figure Q26.14 B1 B2 The large magnetic fields used in MRI can produce forces on electric currents within the human body. This effect has been proposed as a possible method for imaging biocurrents flowing in the body,... A liquid of density r flows through a sluice gate as shown. The upstream and downstream flows are uniform and parallel, so that the pressure variations at stations 1 and 2 may be considered hydro... The horizontal Y-fitting (see figure on the next page) splits 80°F water into two equal parts. The first part goes through Exit 1 and the second part goes through Exit 2 (as shown in the figure).... A water jet at 60°F with a flow rate of 250 ft 3 /s and a velocity of 75 ft/s hits a stationary V-shaped splitter such that half of the fluid is directed upward and the other half is directed... Assume that the level of water in the tank remains the same and that there is no friction loss in the pipe, entrance, or nozzle. Determine a. The volumetric discharge rate from the nozzle b. The... Air of density 1.21 kg/m 3 is flowing as shown. If v = 15m/s, determine the readings on manometers (a) and (b) in the figures below. a. b. Air . U- 24 m/s Oil S.G. = 0.86
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