Consider the PCM Furnace module of Appendix E, which is used to preheat a high-molecular-weight hydro-carbon feed (C 16 C 26 ) to a cracking unit at a petroleum refinery. Do the following sequence...
Consider the PCM distillation column module of Appendix E, in which a 50%50% mixture of methanol (MeOH) and ethanol is separated. Do the following sequence of simulations: (a) Change the Vapor Flow...
Show that when K = 1, the ramp response of the third-order system G(s)= K / (s+1) 3 lags behind the input signal (u = at) by three time constants, once the output is changing linearly in time.
An operator tests the dynamic behavior of a furnace in order to identify the transfer function relating the furnace temperature (output) to the heat input. The operator performs a series of step...
Assume that step response data obtained from an FOPTD system with K = = 1 are available. Determine the accuracy of the FOPTD approximate model derived from these data using the Sundaresan and...
Consider a standard feedback control system where each component is functioning properly. Briefly indicate whether you agree or disagree with the following statements: (a) For proportional-only...
The transfer function relating the blood pressure of a patient to the infusion rate of a blood pressure drug is given by where θ 1 = 30 s, θ 2 = 45 s, and Ï 1 = 40 s....
composition analyzer is used to measure the concentration of a pollutant in a wastewater stream. The relationship between the measured composition Cm and the actual composition C is given by the...
Consider a third-order process with G m = G v = 2 and G p = G d = 2 / (s + 2) 3 . (a) Find the roots of the characteristic equation for a proportional controller G c = K c for K c = 1, 8, and 27....
Suppose a control system is modeled by G v G p = 0.25 / (s + 1) 3 , G m = 4, and G c = K c . Find the maximum value of K c for a proportional controller for which the system is stable, using direct...
Repeat Exercise 10.7 for the case where the flow meters are triply redundant; that is, there are three identical flow meters with two in the backup mode. How much would the overall system reliability...
The system equations for two liquid surge tanks in series are Using state-space notation, determine the matrices A, B, C, and E, assuming that the level deviations is h² 1 and h² 2 are the...
A two-input / two-output process involving simultaneous heating and liquid-level changes is illustrated in Fig. E6.20. Find the transfer function models and expressions for the gains and the time...
Consider the following cascade connection of isothermal reactors. A first-order reaction A B occurs in both reactors, with reaction rate constant k. The volumes of liquid in the reactors,V, are...
The probability of a particular type of sensor functioning properly is 0.95. Consequently, a triply redundant sensor system has been proposed for a critical measurement. Thus, three independent...
Consider the PCM furnace module of Appendix E. Assume that hydrocarbon temperature T HC is the output variable and that air flow rate F A is the input variable. (a) Develop an FOPTD model from...
In the introduction to Section 16.4, it is stated that based on a steady-state degrees-of-freedom analysis of a control system, it is not possible to eliminate offset in the controlled variables for...
The analog exponential flter in Eq. 17-4 is used to flter the output signal from a transfer function G = 1/(2s + 1). The input signal is d(t) = 1 + 0.2 sin t. Compare the responses for no fltering (...
Section 18.1 states that ordinarily, pressure, volume, and temperature cannot change individually without one affecting the others. Yet when a liquid evaporates, its volume changes, even though its...
In the ideal-gas equation, could an equivalent Celsius temperature be used instead of the Kelvin one if an appropriate numerical value of the constant R is used? Why or why not?
On a chilly morning you can see your breath. Can you really? What are you actually seeing? Does this phenomenon depend on the temperature of the air, the humidity, or both? Explain.
When a car is driven some distance, the air pressure in the tires increases. Why? Should you let out some air to reduce the pressure? Why or why not?
The coolant in an automobile radiator is kept at a pressure higher than atmospheric pressure. Why is this desirable? The radiator cap will release coolant when the gauge pressure of the coolant...
Unwrapped food placed in a freezer experiences dehydration, known as freezer burn. Why?
If the collector doping density in a transistor is 6 10 15 atoms/cm 3 , and is much less than the base doping, find BV CEO for F = 200 and n = 4. Use crit = 3 10 5 V/cm.
A person who has skin of surface area and temperature 30.0C is resting in an insulated room where the ambient air temperature is 20.0C. In this state, a person gets rid of excess heat by radiation....
A 20.0-L tank contains 4.86 10 4 of helium at 18.0 o C. The molar mass of helium is 4.00 g/mol. (a) How many moles of helium are in the tank? (b) What is the pressure in the tank, in pascals and in...
A process is described by the transfer function Find the range of controller settings that yield stable closed-loop systems for: (a) A proportional-only controller. (b) A proportional-integral...
A PI controller is to be used in a temperature control system for a bioreactor. For nominal conditions, it has been determined that the closed-loop system is stable when I = 10 min and 10 < K c < 0....
Helium gas with a volume of 2.60 L, under a pressure of 0.180 atm and at a temperature of 41.0 o C, is warmed until both pressure and volume are doubled. a. What is the final temperature? b. How many...
A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m 3 of air at a pressure of 0.355 atm. The piston is slowly pulled...
A large cylindrical tank contains 0.750 m 3 of nitrogen gas at 27 o C and 7.50 10 3 (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the...
Using the failure rate data in Table 10.1, evaluate the reliability and mean time between failures for the high-pressure interlock in Fig. 10.4. Assume that the failure rate for the solenoid switch...
A certain heat engine operating on a Carnot cycle absorbs 150 J of heat per cycle at its hot reservoir at 135C and has a thermal efficiency of 22.0%. (a) How much work does this engine do per cycle?...
A 10.0-L gas tank containing 3.20 moles of ideal He gas at 20.0C is placed inside a completely evacuated, insulated bell jar of volume 35.0 L. A small hole in the tank allows the He to leak out into...
Air samples from a process area are continuously drawn through a 14 -in diameter tube to an analytical instrument that is located 60m away. The tubing has an outside diameter of 6.35 mm and a wall...
It has been suggested that the liquid flow rate in a large diameter pipeline could be better regulated by using two control valves instead of one. Suppose that one control valve has a large C v...
A 4.50-kg block of ice at 0.00C falls into the ocean and melts. The average temperature of the ocean is 3.50C, including all the deep water. By how much does the melting of this ice change the...
A refrigerator has a coefficient of performance of 2.25, runs on an input of 95 W of electrical power, and keeps its inside compartment at 5C. If you put a dozen 1.0-L plastic bottles of water at 31C...
The coefficient of performance K = H/P is a dimension-less quantity. Its value is independent of the units used for H and P, as long as the same units, such as watts, are used for both quantities....
(a) Calculate the mass of nitrogen present in a volume of 3000 cm 3 if the temperature of the gas is 22.0C and the absolute pressure of 2.00 10 13 atm is a partial vacuum easily obtained in...
Suppose that the temperature in an exothermic continuous stirred-tank reactor is controlled by manipulating the coolant flow rate using a control valve. A PID controller is used and is well tuned....
A container with volume 1.48 L is initially evacuated. Then it is filled with 0.226 g of N 2 . Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree...
A physics lecture room has a volume of 216 m 3 . (a) For a pressure of 1.00 atm and a temperature of 27.0 o C, use the ideal-gas law to estimate the number of air molecules in the room. Assume all...
A hot-air balloon stays aloft because hot air at atmospheric pressure is less dense than cooler air at the same pres-sure. If the volume of the balloon 500.0 m 3 is and the surrounding air is at...
Consider the PCM furnace module of Appendix E. Assume that hydrocarbon temperature T HC is the CV, that fuel gas flow rate F FG is the MV, and that they are related by the following transfer function...
Consider the PCM distillation column module of Appendix E. Assume that distillate MeOH composition x D is the CV, that reflux ratio R is the MV, and that they are related by the following transfer...
A stirred-tank heating system is shown in Fig. E13.9. Briefly critique these two control strategies. (a) It is proposed that h and T be controlled by manipulating w h and w c using two PI...
The speed of propagation of a sound wave in air at 27 o C is about 350 m/s. Calculate, for comparison, (a) v rms for nitrogen molecules (b) The rms value of v x at this temperature. The molar mass of...
One mole of ideal gas is slowly compressed to one-third of its original volume. In this compression, the work done on the gas has magnitude 600 J. For the gas, C P = 7R/2. (a) If the process is...
A very small object with mass 8.20 10 -9 kg and positive charge 6.50 10 -9 C is projected directly toward a very large insulating sheet of positive charge that has uniform surface charge density...
At time t = 0 a proton is a distance of 0.360 m from a very large insulating sheet of charge and is moving parallel to the sheet with speed 9.70 10 2 m/s. The sheet has uniform surface charge...
An insulating sphere of radius R = 0.160 m has uniform charge density p = +7.20 x 10 -9 C/m 3 . A small object that can be treated as a point charge is released from rest just outside the surface of...
Some critics of biological evolution claim that it violates the second law of thermodynamics, since evolution involves simple life forms developing into more complex and more highly ordered...
Consider the PCM furnace module of Appendix E. Assume that oxygen exit concentration c O2 is the CV, air ï¬ow rate AF is the MV, and fuel gas purity FG is the DV. (a) Using the transfer...
Suppose you had two small boxes, each containing 1.0 g of protons. (a) If one were placed on the moon by an astronaut and the other were left on the earth, and if they were connected by a very light...
A point charge is on the x-axis at x = 1.20 m. A second point charge Q is on the x-axis at -0.600. What must be the sign and magnitude of Q for the resultant electric field at the origin to be (a)...
At t = 0 a very small object with mass 0.400 mg and charge +9.00 C is traveling at 125 m/s in the -x direction. The charge is moving in a uniform electric field that is in the +y -direction and that...
Diabetes mellitus is characterized by insufficiency of the pancreas to produce enough insulin to regulate the blood sugar level. In type I diabetes, the pancreas produces no insulin, and the patient...
Consider a model of a hydrogen atom in which an electron is in a circular orbit of radius r = 5.29 10 -11 m around a stationary proton. What is the speed of the electron in its orbit?
In deriving the ideal-gas equation from the kinetic-molecular model, we ignored potential energy due to the earths gravity. Is this omission justified? Why or why not?
An electric motor has its shaft coupled to that of an electric generator. The motor drives the generator, and some current from the generator is used to run the motor. The excess current is used to...
Design a time-delay compensator (Smith predictor) for where G v = G m = 1 and θ = 1. Show closed-loop responses for unit step set-point and disturbance changes (G d = G p ). Use an IMC...
The dynamic behavior of a temperature sensor and transmitter can be described by the FOPTD transfer function where the time constant and time delay are in seconds and: T = actual temperature...
Freeze-drying food involves the same process as freezer burn, referred to in Discussion Question 18.6. For freeze-drying, the food is usually frozen first, and then placed in a vacuum chamber and...
You decide to use your body as a Carnot heat engine. The operating gas is in a tube with one end in your mouth (where the temperature is 37.0C) and the other end at the surface of your skin, at...
If no real engine can be as efficient as a Carnot engine operating between the same two temperatures, what is the point of developing and using Eq. (20.14)? Eq. (20.14) Tc TH Tc TH (efficiency of a...
The proportions of various gases in the earths atmosphere change somewhat with altitude. Would you expect the proportion of oxygen at high altitude to be greater or less than at sea level compared to...
A diver observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). The temperature at the bottom is and the...
(a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 K, with a CO 2 atmosphere), Venus (with an average temperature of...
Three moles of an ideal gas are in a rigid cubical box with sides of length 0.200 m. (a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 20.0C?...
An MOS transistor biased in the active region displays a drain current of 100 A at a VGS of 1.5 V and a drain current of 10 A at a V GS of 0.8 V. Determine the threshold voltage and n C ox (W/L)....
a. Calculate the change in air pressure you will experience if you climb a 1000-m mountain, assuming that the temperature and air density do not change over this distance and that they were 22C and...
If deep-sea divers rise to the surface too quickly, nitrogen bubbles in their blood can expand and prove fatal. This phenomenon is known as the bends. If a scuba diver rises quickly from a depth of...
The graph in Fig. E19.4 shows a pV-diagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat...
The graph in Fig. P19.48 shows a pV-diagram for 3.25 moles of ideal helium (He) gas. Part ca of this process is isothermal. (a) Find the pressure of the He at point a. (b) Find the temperature of the...
For carbon dioxide gas the constants in the van der Waals equation are = 0.364 J m 3 /mol 2 and (a) If 1.00 mol of gas at 350 K is confined to a volume of find the pressure of the gas using the...
A metal tank with volume 3.10 L will burst if the absolute pressure of the gas it contains exceeds 100 atm. (a) If 11.0 mol of an ideal gas is put into the tank at a temperature of to what...
A base-emitter voltage of 480 mV is measured on a super- test transistor with a 100 m 100 m emitter area at a collector current of 10 A. Calculate the Q B and the sheet resistance of the base...
An n-channel implanted transistor from the process described in Table 2.1 displays a measured output resistance of 5 MΩ at a drain current of 10 μA, biased in the active...
Show that two MOS transistors connected in parallel with channel widths of W 1 and W 2 and identical channel lengths of L can be modeled as one equivalent MOS transistor whose width is W 1 + W 2 and...
Show that two MOS transistors connected in series with channel lengths of L 1 and L 2 and identical channel widths of W can be modeled as one equivalent MOS transistor whose width is W and whose...
You are working late in your electronics shop and find that you need various resistors for a project. But alas, all you have is a big box of 10.0- resistors. Show how you can make each of the...
A resistor with R 1 = 25.0 is connected to a battery that has negligible internal resistance and electrical energy is dissipated R 1 by at a rate of 36.0 W. If a second resistor with R 2 = 15.0 is...
In the Bohr model of the hydrogen atom, the electron makes 6.0 10 15 rev/s around the nucleus. What is the average current at a point on the orbit of the electron?
A resistor with resistance R is connected to a battery that has emf 12.0 V and internal resistance r = 0.40. For what two values of R will the power dissipated in the resistor be 80.0 W?
A Nichrome heating element that has resistance 28.0 is connected to a battery that has emf 96.0 V and internal resistance . An aluminum 1.2 cup with mass 0.130 kg contains 0.200 kg of water. The...
Electric eels generate electric pulses along their skin that can be used to stun an enemy when they come into contact with it. Tests have shown that these pulses can be up to 500 V and produce...
Will a light bulb glow more brightly when it is connected to a battery as shown in Fig. Q25.16a, in which an ideal ammeter A is placed in the circuit, or when it is connected as shown in Fig. 25.16b,...
A parallel-plate vacuum capacitor has 8.38 J of energy stored in it. The separation between the plates is 2.30 mm. If the separation is decreased to 1.15 mm, what is the energy stored (a) If the...
If a + at rest decays into a proton and a 0 , what is the total kinetic energy of the decay products?
What is the mass (in kg) of the Z 0 ? What is the ratio of the mass of the Z 0 to the mass of the proton?
A 1.00-km cable having a cross-sectional area of 0.500 cm 2 is to be constructed out of equal lengths of copper and aluminum. This could be accomplished either by making a 0.50-km cable of each one...
Lightning strikes can involve currents as high as 25,000 A that last for about 40 s. If a person is struck by a bolt of lightning with these properties, the current will pass through his body. We...
How much energy is released when a - muon at rest decays into an electron and two neutrinos? Neglect the small masses of the neutrinos.
(a) A high-energy beam of alpha particles collides with a stationary helium gas target. What must the total energy of a beam particle be if the available energy in the collision is 16.0 GeV? (b) If...
An electron with a total energy of 20.0 GeV collides with a stationary positron. (a) What is the available energy? (b) If the electron and positron are accelerated in a collider, what total energy...
The starship Enterprise, of television and movie fame, is powered by combining matter and antimatter. If the entire 400 kg antimatter fuel supply of the Enterprise combines with matter, how much...
For the nuclear reaction given in Eq. (44.2) assume that the initial kinetic energy and momentum of the reacting particles are negligible. Calculate the speed of the particle immediately after it...
A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon (a) If the p and p are initially at rest. (b) If the p and p collide head-on,...