Quantization of Energy

½ˇαíçβ Quantization of Energy Quantization of Energy Bởi: OpenStaxCollege Planck’s Contribution Energy is quantized in some systems, meaning that the system can have only certain energies and not a continuum of energies, unlike the classical case This would be like having only certain speeds at which a car can travel because its kinetic energy can have only certain values We also find that some forms of energy transfer take place with discrete lumps of energy While most of us are familiar with the quantization of matter into lumps called atoms, molecules, and the like, we are less aware that energy, too, can be quantized Some of the earliest clues about the necessity of quantum mechanics over classical physics came from the quantization of energy Graphs of blackbody radiation (from an ideal radiator) at three different radiator temperatures The intensity or rate of radiation emission increases dramatically with temperature, and the peak of the spectrum shifts toward the visible and ultraviolet parts of the spectrum The shape of the spectrum cannot be described with classical physics Where is the quantization of energy observed? Let us begin by considering the emission and absorption of electromagnetic (EM) radiation The EM spectrum radiated by a hot solid is linked directly to the solid’s temperature (See [link].) An ideal radiator is one that has an emissivity of at all wavelengths and, thus, is jet black Ideal radiators are therefore called blackbodies, and their EM radiation is called blackbody radiation It 1/6 Quantization of Energy was discussed that the total intensity of the radiation varies as T4, the fourth power of the absolute temperature of the body, and that the peak of the spectrum shifts to shorter wavelengths at higher temperatures All of this seems quite continuous, but it was the curve of the spectrum of intensity versus wavelength that gave a clue that the energies of the atoms in the solid are quantized In fact, providing a theoretical explanation for the experimentally measured shape of the spectrum was a mystery at the turn of the century When this “ultraviolet catastrophe” was eventually solved, the answers led to new technologies such as computers and the sophisticated imaging techniques described in earlier chapters Once again, physics as an enabling science changed the way we live The German physicist Max Planck (1858–1947) used the idea that atoms and molecules in a body act like oscillators to absorb and emit radiation The energies of the oscillating atoms and molecules had to be quantized to correctly describe the shape of the blackbody spectrum Planck deduced that the energy of an oscillator having a frequency f is given by ( E= n+ )hf Here n is any nonnegative integer (0, 1, 2, 3, …) The symbol h stands for Planck’s constant, given by h = 6.626 × 10–34 J⋅s ( ) The equation E = n + hf means that an oscillator having a frequency f (emitting and absorbing EM radiation of frequency f) can have its energy increase or decrease only in discrete steps of size ΔE = hf It might be helpful to mention some macroscopic analogies of this quantization of energy phenomena This is like a pendulum that has a characteristic oscillation frequency but can swing with only certain amplitudes Quantization of energy also resembles a standing wave on a string that allows only particular harmonics described by integers It is also similar to going up and down a hill using discrete stair steps rather than being able to move up and down a continuous slope Your potential energy takes on discrete values as you move from step to step Using the quantization of oscillators, Planck was able to correctly describe the experimentally known shape of the blackbody spectrum This was the first indication that energy is sometimes quantized on a small scale and earned him the Nobel Prize in Physics in 1918 Although Planck’s theory comes from observations of a macroscopic object, its analysis is based on atoms and molecules It was such a revolutionary 2/6 Quantization of Energy departure from classical physics that Planck himself was reluctant to accept his own idea that energy states are not continuous The general acceptance of Planck’s energy quantization was greatly enhanced by Einstein’s explanation of the photoelectric effect (discussed in the next section), which took energy quantization a step further Planck was fully involved in the development of both early quantum mechanics and relativity He quickly embraced Einstein’s special relativity, published in 1905, and in 1906 Planck was the first to suggest the correct formula for relativistic momentum, p = γmu The German physicist Max Planck had a major influence on the early development of quantum mechanics, being the first to recognize that energy is sometimes quantized Planck also made important contributions to special relativity and classical physics (credit: Library of Congress, Prints and Photographs Division via Wikimedia Commons) Note that Planck’s constant h is a ... 1 2 3 4 5 6 7 8 9 10 11 A B C D E F G H I K L M N O P Q R S T U V X W Z Y E N V I R O N M E N T NATUAL ENVIRONMENT ecology grass Nitrogen (N) Oxygen (O2) Carbon dioxide (CO2) Petroleum Vital definition Task 1.listen and complete the Task 1.listen and complete the sentence by circling the letter sentence by circling the letter A,B,C or D A,B,C or D 1. Ecology is the study of………………… human beings and animals the environment and solar energy natural and alternative resources human beings and their environment ? a b c d 2. The natural environment consists of…………. the oceans and the land the sun and the air all natural resources the air and the oceans ? a b c d 3. If the resource can be……………., it is call renewable. burnt quickly used easily divided properly replaced quickly ? a b c d 4. Grass for animals is a…… .…. resource. renewable nonrenewable limited clean ? a b c d 5. According to the passage, coal is nonrenewable because it takes ……………to make coal. billions of years millions of years three millions of years three billions of years ? a b c d [...]...Task 2.listen again to the last part of the talk and write in the missing words Solar energy, air, and water are renewable 1 resources because there is ……… .Supply However, this definition may change if people are not careful with these resources The amount of solar energy that reaches the earth depends on 2 the……………….If the atmosphere is polluted, the solar, the solar energy that reaches the earth 3 …………………... is going to continue, the air must contain the correct amount of nitrogen (N), oxygen (O), carbon dioxide (CO2), 4 and other ……………… if humans continue to 5 pollute the air, it will not contain the correct………… of these gases an unlimited ? may amounts atmosphere gases Sources of energy Coal Geothermal heat Petroleum Solar energy Oil Wind energy Gas Nonrenewable nonrewable  I NTERNATIONAL J OURNAL OF E NERGY AND E NVIRONMENT Volume 3, Issue 4, 2012 pp.521-530 Journal homepage: www.IJEE.IEEFoundation.org ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2012 International Energy & Environment Foundation. All rights reserved. Integration of energy and environmental systems in wastewater treatment plants Suzanna Long 1 , Elizabeth Cudney 2 1 Department of Engineering Management and Systems Engineering, 600 W, 14 th Street, 215 EMGT Building, Rolla, MO-65401, 573-341-7621, U.S.A. 2 Department of Engineering Management and Systems Engineering, 600 W, 14 th Street, 217 EMGT Building, Rolla, MO-65401, 573-341-7931, U.S.A. Abstract Most wastewater treatment facilities were built when energy costs were not a concern; however, increasing energy demand, changing climatic conditions, and constrained energy supplies have resulted in the need to apply more energy-conscious choices in the maintenance or upgrade of existing wastewater treatment facilities. This research develops an integrated energy and environmental management systems model that creates a holistic view of both approaches and maps linkages capable of meeting high-performing energy management while meeting environmental standards. The model has been validated through a case study on the Rolla, Missouri Southeast Wastewater Treatment Plant. Results from plant performance data provide guidance to improve operational techniques. The significant factors contributing to both energy and environmental systems are identified and balanced against considerations of cost. Copyright © 2012 International Energy and Environment Foundation - All rights reserved. Keywords: Energy conservation; Environmental management; Process integration; Strategic management; Wastewater treatment systems. 1. Introduction Green environmental practices are increasingly important in combating serious global energy and environmental issues. Water and wastewater facilities are among the largest and most energy-intensive systems owned and operated by local governments and account for approximately 30 to 50% of municipal energy use. Most wastewater treatment facilities were built when energy costs were not a concern; however, increasing energy demand, changing climatic conditions, and constrained energy supplies have resulted in the need to apply more energy-conscious choices in the maintenance or upgrade of existing wastewater treatment facilities. Energy represents the largest controllable cost of water and wastewater treatment since energy use directly affects the amount of greenhouse gas (GHG) emissions, and indirectly affects the biological oxygen demand (BOD), chemical oxygen demand (COD), and pollutions levels. By controlling the level of energy consumption, wastewater treatment facilities can reduce the operating costs, increase efficiency, and reduce pollution in an effort to provide cleaner environments. In addition, increased training on advanced equipment by well-trained employees can lead to improved effluent and surface water quality and more compliant facilities [1, 2]. A strategic process to control these various factors could provide significant benefits to local governments and the communities they serve. International Journal of Energy and Environment (IJEE), Volume 3, Issue 4, I NTERNATIONAL J OURNAL OF E NERGY AND E NVIRONMENT Volume 2, Issue 4, 2011 pp.627-640 Journal homepage: www.IJEE.IEEFoundation.org ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved. Performance characteristic of energy selective electron (ESE) heat engine with filter heat conduction Zemin Ding, Lingen Chen, Fengrui Sun College of Naval Architecture and Power, Naval University of Engineering, Wuhan 430033, P. R. China. Abstract The model of an energy selective electron (ESE) heat engine with filter heat conduction via phonons is presented in this paper. The general expressions for power output and efficiency of the ESE heat engine are derived for the maximum power operation regime and the intermediate operation regime, respectively. The optimum performance and the optimal operation regions in the two different operation regimes of the ESE heat engine are analyzed by detailed numerical calculations. The influences of filter heat conduction and the temperature of hot reservoir on the optimum performance of the ESE heat engine are analyzed in detail. Furthermore, the influence of resonance width on the performance of the ESE heat engine in intermediate operation regime is also discussed. The results obtained herein have theoretical significance for understanding and improving the performance of practical electron energy conversion systems. Copyright © 2011 International Energy and Environment Foundation - All rights reserved. Keywords: Energy selective electron (ESE) heat engine; Filter heat conduction; Power and efficiency characteristic. 1. Introduction Recently, the study of energy conversion systems in microscopic scale is attracting considerable interests. Typical examples of these systems include thermionic power generators and refrigerators [1- 11], Brownian motors [12-23], quantum ratchet [24-29], and so on. For the thermionic energy conversion systems, heat transfer is achieved by removing high energy electrons from one reservoir to the other, and all the devices use barriers or other energy selection mechanisms such as resonant tunneling to limit the current flowing in the device to electrons in particular energy ranges [1-3, 30]. While Brownian motors usually use the temperature differential [31, 32] as the source of non-equilibrium to power a ratchet, which combines asymmetry with nonequilibrium process to generate directed motion of Brownian particles. In a quantum ratchet, the classical Brownian particles in the rocked ratchet are replaced by quantum particles, which have the ability to tunnel through narrow barriers and to be wave-reflected from sharp barriers. Comparing the quantum ratchet with the classical ratchet, it can be found that not only the height of a potential barrier but also the shapes of the ratchet potential have been changed in the quantum ratchet system. Reimann et al. [24] theoretically predicted the existence of the temperature dependent net current reversal for quantum particles in a rocked ratchet, and it was observed in the experiment by Linke et al. [25] for electrons in ballistic transport regime. Yukawa et al. [26] proposed two models of quantum ratchet and studied the finite net flow produced in them. Khrapai et al. [27, 28] studied the quantum ratchet phenomenon of quantum point contacts. Hoffmann and Linke [29] found International Journal of Energy and Ramachandran, R.P. “Quantization of Discrete Time Signals” Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton: CRC Press LLC, 1999 c  1999byCRCPressLLC 6 Quantization of Discrete Time Signals Ravi P. Ramachandran Rowan University 6.1 Introduction 6.2 Basic Definitions and Concepts Quantizer and Encoder Definitions • Distortion Measure • Optimality Criteria 6.3 Design Algorithms Lloyd-Max Quantizers • Linde-Buzo-Gray Algorithm 6.4 Practical Issues 6.5 Specific Manifestations Multistage VQ • Split VQ 6.6 Applications Predictive Speech Coding • Speaker Identification 6.7 Summary References 6.1 Introduction Signals are usually classified into four categories. A continuous time signal x(t) has the field of real numbers R as its domain in that t can assume any real value. If the range of x(t)(values that x(t) can assume) is also R, then x(t)is said to be a continuous time, continuous amplitude signal. If the range of x(t) is the set of integers Z, then x(t) is said to be a continuous time, discrete amplitude signal. In contrast, a discrete time signal x(n) has Z as its domain. A discrete time, continuous amplitude signal has R as its range. A discrete time, discrete amplitude signal has Z as its range. Here, the focus is on discrete time signals. Quantization is the process of approximating any discrete time, continuous amplitude signal into one of a finite set of discrete time, continuous amplitude signals based on a particular distortion or distance measure. This approximation is merely signal compression in that an infinite set of possible signals is converted into a finite set. The next step of encoding maps the finite set of discrete time, continuous amplitude signals into a finite set of discrete time, discrete amplitude signals. A signal x(n) is quantized one block at a time in that p (almost always consecutive) samples are taken as a vector x and approximated by a vector y. The signal or data vectors x of dimension p (derived from x(n)) are in the vector space R p over the field of real numbers R. Vector quantization is achieved by mapping the infinite number of vectors in R p to a finite set of vectors in R p . There is an inherent compression of the data vectors. This finite set of vectors in R p is encoded into another finite set of vectorsin a vector space of dimension q over a finite field (a field consisting of a finite set of numbers). For communication applications, the finite field is the binary field (0, 1). Therefore, the c  1999 by CRC Press LLC original vector x is converted or compressed into a bit stream either for transmission over a channel or for storage purposes. This compression is necessary due to channel bandwidth or storage capacity constraints in a system. The purpose of this chapter is to describe the basic definition and properties of vectorquantization, introduce the practical aspects of design and implementation, and relate important issues. Note that two excellent review articles [1, 2] give much insight into the subject. The outline of the article is as follows. The basic concepts are elaborated on in Section 6.2. Design algorithms for scalar and vector quantizers are described in Section 6.3. A design example is also provided. The practical issues are discussed in Section 6.4. The multistage and split manifestations of vector quantizers are described in Section 6.5. In Section 6.6, two applications of vector quantization in speech processing are discussed. 6.2 Basic Definitions and Concepts In this section, we will elaborate on the definitions of a vector and scalar .. .Quantization of Energy was discussed that the total intensity of the radiation varies as T4, the fourth power of the absolute temperature of the body, and that the peak of the spectrum... radiation of frequency f) can have its energy increase or decrease only in discrete steps of size ΔE = hf It might be helpful to mention some macroscopic analogies of this quantization of energy. .. that the energy is quantized (a) What is the difference in energy in joules between allowed 5/6 Quantization of Energy oscillator states? (b) What is the value of n for a state where the energy