Homework 11. Problems: 20.37, 22.33, 22.41, 22.67


 Amice Lynn Reynolds
 2 years ago
 Views:
Transcription
1 Homework 11 roblems: 0.7,.,.41,.67
2 roblem kg block o alumnum s heated at atmospherc pressure such that ts temperature ncreases rom.0 to Fnd (a) the work done by the alumnum, (b) the energy added to t by heat, and (c) the change n ts nternal energy. a) he macroscopc work done by a system s dened by the change n the system's volume m 1 kg dw d. º; 40 º he stress (hydrostatc pressure) n the block s equal to the external pressure o 1atm. Snce, n ths process, the pressure s constant, t s easy to nd the work (ntegral) ΔW dw process Δ he thermal expanson o the block causes a change n volume. From the denton o the volumetrc coecent o expanson we can relate the change n volume to the change n temperature. ssumng that the change n volume s small when compared wth the ntal volume we can use the approxmate relaton Δ βδ αδ We can express the volume n terms o the mass o the block, usng the denton o densty. For a unorm object ntegraton o the densty leads to a smple relaton
3 m ρ Work done n the process s thereore m ΔW α ρ l Δ 1.01a K 1 1kg kg.7 10 m o o ( 40 ) 48mJ b) he process s sobarc and the specc heat n ths temperature nterval does not depend on temperature. he ntegraton o heat s thereore easy to perorm ΔQ process dq J 1kg 900 kg K mcd mcδ ( 40 ) K 16.kJ c) From the rst law o thermodynamcs, the change n the nternal energy o the block s ΔU ΔQ ΔW 16. kj 0. 48mJ 16. kj
4 roblem. In a cylnder o an automoble engne just ater combuston, the gas s conned to a volume o 0.0 cm and has an ntal pressure o 10 6 a. he pston moves outward to a nal volume o 00 cm, and the gas expands wthout energy loss by heat. (a) I 1.4 or the gas, what s the nal pressure? How much work s done by the gas n expandng? Wth good approxmaton, we can assume that the gas n the engne s deal whch satses the ollowng state equaton (relatng pressure, volume and the temperature o the gas) 1) nr where n s the amount o the gas expressed n moles and R s the gas constant. For an deal gas, the change n nternal energy s related to the change n temperature only ) du n v d where v s the molar heat capacty at constant volume. ccordng to the rst law o thermodynamcs, or an adabatc process (no heat delvered to the gas), the change n nternal energy s opposte to the work perormed by the gas ) du 0  d he rest s math. Snce the pressure and volume s gven n the problem we want to elmnate the temperature rom the consderaton. From equaton (1), we can express the temperature derental n terms o the volume and pressure derentals d + d nrd Usng () and () we can elmnate temperature rom last equaton d d + d nr n v ecause the derence between the molar heat capacty as the constant pressure and the constant volume or one mole o gas s equal to the gas constant
5 4) p  v R we can rearrange the last equaton and wrte p v 1+ d d v or smply t even urther by substtutng the rato o the molar heat capacty at constant pressure and the molar heat capacty at constant volume p ) v lso dvdng both sdes o the equaton by the product o volume and pressure we can separate the varables (group terms wth volume on one sde o the equaton and terms wth pressure on the other sde o the equaton d Integratng both sde over the consdered process (rom ntal volume and pressure to the nal volume and pressure) process d d process we get ( ln ln ) ( ln ln ) Usng the propertes o logarthmc uncton we can smply the last equaton hereore ln ln d
6 (We can present the last equaton n the tradtonally used orm ) Solvng or the only unknown (the nal pressure) we can nd the answer 10 6 a ( 0cm ) ( 00cm ) omment. In ths problem t s assumed that ntrogen undergoes the process. In the combuston, sgncant amounts o water (H O) and carbon doxde (O ) are produced. hereore, t would be more accurate to assume that 1.< <1.4. (See table 1.) a
7 roblem.41 L contaner has a center partton that dvdes t nto two equal parts, as shown n Fgure.41. he lethand sde contans H gas, and the rghthand sde contans O gas. oth gases are at room temperature and at atmospherc pressure. he partton s removed, and the gasses are allowed to mx. What s the entropy ncrease o the system?.044 mole H.044 mole O a) When the gases are mxed they ll the entre volume o the contaner. he ntal and the nal temperatures are equal, thereore we can choose an sothermal process n order to calculate the change n entropy. (he sobarc process s ncorrect, because although the pressure n the mxture s 1 atm as each gas expands and ts partal pressure decreases.) In the consdered condtons, both gases can be treated as deal gases. her partal pressure, volume and temperature are related by the equaton o the state o an deal gas. 1) nr In the sothermal process or an deal gas, the nternal energy o the gas does not change. From the rst law o thermodynamcs, the heat delvered to the deal gas must be equal to the work done by the gas n an sothermal process. nrd ) dqr dwr d Usng the denton o entropy, the change n entropy o the deal gas undergong an nntesmal expanson s thereore dq ds r nrd he entropy n the entre expanson process o an deal gas changes by
8 ΔSx x x nrd nr ln oth the hydrogen and the oxygen ncrease entropy. he change n the entropy o the system s thereore ΔS H + ΔS O n H R ln H H + n R ln J l J 0.44mol 8.1 ln mol 8.1 ln mol K 1l mol K,, O O O,, x x l 1l 0.07 J K
9 roblem.6 One mole o an deal monatomc gas s taken through the cycle shown n Fgure.67. he process s a reversble sothermal expanson. alculate (a) the net work done by the gas, (b) the (thermal) energy added to the gas, (c) the (thermal) energy expelled by the gas, and (d) the ecency o the cycle. (atm) a) In each process the work depends on the change n volume o the gas and the pressure o the gas durng the process. 1) dw d 1 In order to nd the value o the (lters) 10 0 work, we have to know the explct dependence o the pressure durng the process. In an sothermal process, the pressure o the gas s nversely proportonal to ts volume ) ( ) nr hereore the work done n the sothermal process s W d atm 1atm nr d a ln m 0l ln 10l 811.8J
10 In process, the pressure o the gas s constant. In ths sobarc process the ntegraton wll be much easer W d ( ) a ( m 0 10 m ) 40J In the thrd process, the volume s not changed, thereore the gas does not perorm work. he work done by the gas n the whole cycle s thereore Δ W W + W + W 81J 40J + 0J 4kJ b,c) We have to perorm smlar calculatons or the heat. In the sothermal expanson o an deal gas ts nternal energy does not change. ccordng to the rst law o thermodynamcs, the heat delvered to the gas s equal to the work done by the gas n ths process. ) Q ΔU + W W 8.1kJ In ths process the heat s delvered to the gas. In the sobarc process the temperature o the gas changes. We can express the heat Q delvered to the gas, wth the change n ts temperature and the molar heat capacty (at constant pressure) o a monatomc deal gas 1 p R 1 See chapter 1 or the molar heat capacty o an deal gas.
11 Q n p d n p nr nr ( ) nr ( ) ( a m a 0 10 m ) 10.1kJ In ths process the gas expels the heat. In the sochorc process the temperature o the gas also changes. We can express the heat Q delvered to the gas, n terms o the change n ts temperature and the molar heat capacty v R (at constant volume) o a monatomc deal gas Q n v d n atm 1atm v ( ) nr ( ) a nr m nr a m 6.1kJ Heat s delvered to the gas n ths process. In ths cycle heat was delvered to the gas rom the heat reservor n processes and. he heat delvered n the whole cycle s thereore Δ Qh Q + Q 8.1kJ + 6.1kJ 14.kJ In ths cycle, the gas only n process expels heat. he heat expelled n the whole cycle s thereore Δ Qc Q 10.1kJ (o very our calculatons we can check energy s conserved. In a cycle the nternal energy o the gas does not change thereore the energy delvered must be equal to the sum o the energy used and wasted n the heat snk 14.kJ 4.1kJ kJ.
12 In the soluton, we could use ths act to nd heat delvered to the gas n one o the three processes.) d) From the denton o ecency, we have to compare the energy used n the orm o work perormed by the gas to the energy delvered to the gas engne rom the reservor ΔW e ΔQ h 4.1kJ 14.kJ 8.9%
University Physics AI No. 11 Kinetic Theory
Unersty hyscs AI No. 11 Knetc heory Class Number Name I.Choose the Correct Answer 1. Whch type o deal gas wll hae the largest alue or C C? ( D (A Monatomc (B Datomc (C olyatomc (D he alue wll be the same
More informationPhysics 41 HW Set 11 Chapters 20 and 21
Physcs 41 HW Set 11 Chapters 0 and 1 Chapter 0 1 An deal gas ntally at P,, and T s taken through a cycle as shown Fnd the net work done on the gas per cycle What s the net energy added by heat to the system
More informationESCI 341 Atmospheric Thermodynamics Lesson 9 Entropy
ESCI 341 Atmosherc hermodynamcs Lesson 9 Entroy References: An Introducton to Atmosherc hermodynamcs, sons Physcal Chemstry (4 th edton), Levne hermodynamcs and an Introducton to hermostatstcs, Callen
More informationLecture 2 The First Law of Thermodynamics (Ch.1)
Lecture he Frst Law o hermodynamcs (Ch.) Outlne:. Internal Energy, Work, Heatng. Energy Conservaton the Frst Law 3. Quasstatc processes 4. Enthalpy 5. Heat Capacty Internal Energy he nternal energy o
More informationTHERMAL PROPERTIES OF MATTER 12
HERMAL PROPERIES OF MAER Q.. Reason: he mass o a mole o a substance n grams equals the atomc or molecular mass o the substance. Snce neon has an atomc mass o 0, a mole o neon has a mass o 0 g. Snce N has
More informationsubstances (among other variables as well). ( ) Thus the change in volume of a mixture can be written as
Mxtures and Solutons Partal Molar Quanttes Partal molar volume he total volume of a mxture of substances s a functon of the amounts of both V V n,n substances (among other varables as well). hus the change
More informationGibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments)
Gbbs Free Energy and Chemcal Equlbrum (or how to predct chemcal reactons wthout dong experments) OCN 623 Chemcal Oceanography Readng: Frst half of Chapter 3, Snoeynk and Jenkns (1980) Introducton We want
More informationCHAPTER 9 SECONDLAW ANALYSIS FOR A CONTROL VOLUME. blank
CHAPTER 9 SECONDLAW ANALYSIS FOR A CONTROL VOLUME blank SONNTAG/BORGNAKKE STUDY PROBLEM 91 9.1 An deal steam turbne A steam turbne receves 4 kg/s steam at 1 MPa 300 o C and there are two ext flows, 0.5
More informationMean Molecular Weight
Mean Molecular Weght The thermodynamc relatons between P, ρ, and T, as well as the calculaton of stellar opacty requres knowledge of the system s mean molecular weght defned as the mass per unt mole of
More informationA ThreePoint Combined Compact Difference Scheme
JOURNAL OF COMPUTATIONAL PHYSICS 140, 370 399 (1998) ARTICLE NO. CP985899 A ThreePont Combned Compact Derence Scheme Peter C. Chu and Chenwu Fan Department o Oceanography, Naval Postgraduate School, Monterey,
More informationFaraday's Law of Induction
Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationa) Use the following equation from the lecture notes: = ( 8.314 J K 1 mol 1) ( ) 10 L
hermodynamics: Examples for chapter 4. 1. One mole of nitrogen gas is allowed to expand from 0.5 to 10 L reversible and isothermal process at 300 K. Calculate the change in molar entropy using a the ideal
More information= T T V V T = V. By using the relation given in the problem, we can write this as: ( P + T ( P/ T)V ) = T
hermodynamics: Examples for chapter 3. 1. Show that C / = 0 for a an ideal gas, b a van der Waals gas and c a gas following P = nr. Assume that the following result nb holds: U = P P Hint: In b and c,
More informationJet Engine. Figure 1 Jet engine
Jet Engne Prof. Dr. Mustafa Cavcar Anadolu Unversty, School of Cvl Avaton Esksehr, urkey GROSS HRUS INAKE MOMENUM DRAG NE HRUS Fgure 1 Jet engne he thrust for a turboet engne can be derved from Newton
More informationn + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2)
MATH 16T Exam 1 : Part I (InClass) Solutons 1. (0 pts) A pggy bank contans 4 cons, all of whch are nckels (5 ), dmes (10 ) or quarters (5 ). The pggy bank also contans a con of each denomnaton. The total
More information6. EIGENVALUES AND EIGENVECTORS 3 = 3 2
EIGENVALUES AND EIGENVECTORS The Characterstc Polynomal If A s a square matrx and v s a nonzero vector such that Av v we say that v s an egenvector of A and s the correspondng egenvalue Av v Example :
More information8.4. Annuities: Future Value. INVESTIGATE the Math. 504 8.4 Annuities: Future Value
8. Annutes: Future Value YOU WILL NEED graphng calculator spreadsheet software GOAL Determne the future value of an annuty earnng compound nterest. INVESTIGATE the Math Chrstne decdes to nvest $000 at
More informationQuotes. Research Findings. The First Law of Thermodynamics. Introduction. Introduction. Thermodynamics Lecture Series
8//005 Quotes Thermodynamcs Lecture Seres Frst Law of Thermodynamcs & Control Mass, Open Appled Scences Educaton Research Group (ASERG) Faculty of Appled Scences Unverst Teknolog MARA emal: drjjlanta@hotmal.com
More informationRotation Kinematics, Moment of Inertia, and Torque
Rotaton Knematcs, Moment of Inerta, and Torque Mathematcally, rotaton of a rgd body about a fxed axs s analogous to a lnear moton n one dmenson. Although the physcal quanttes nvolved n rotaton are qute
More informationNONCONSTANT SUM REDANDBLACK GAMES WITH BETDEPENDENT WIN PROBABILITY FUNCTION LAURA PONTIGGIA, University of the Sciences in Philadelphia
To appear n Journal o Appled Probablty June 2007 OCOSTAT SUM REDADBLACK GAMES WITH BETDEPEDET WI PROBABILITY FUCTIO LAURA POTIGGIA, Unversty o the Scences n Phladelpha Abstract In ths paper we nvestgate
More informationReview C: Work and Kinetic Energy
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department o Physcs 8.2 Revew C: Work and Knetc Energy C. Energy... 2 C.. The Concept o Energy... 2 C..2 Knetc Energy... 3 C.2 Work and Power... 4 C.2. Work Done by
More informationgreatest common divisor
4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no
More informationSafety and Reliability of Distributed Embedded Systems
Saety and Relablty o Dstrbuted Embedded Systems Techncal Report ESL 0401 Smulaton o Vehcle Longtudnal Dynamcs Mchael Short Mchael J. Pont and Qang Huang Embedded Systems Laboratory Unversty o Lecester
More informationENERGY BALANCE. Heat liberated within the reactor due to reaction = 1414.575 kcal/kmol
ENERGY BALANCE Deulphurzer ere Sulphur n Naphtha made to react wth ydrogen n preence of catalyt to gve ydrogen Sulphde. h reacton take place at a temperature of 63 K + S ydrogen and Naphtha are aumed to
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationCHAPTER 8 Potential Energy and Conservation of Energy
CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and nonconservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated
More information05 Enthalpy of hydration of sodium acetate
05 Enthaly of hydraton of sodum acetate Theoretcal background Imortant concets The law of energy conservaton, extensve and ntensve quanttes, thermodynamc state functons, heat, work, nternal energy, enthaly,
More informationScalar and Vector Quantization
Scalar and Vector Quantzaton Máro A. T. Fgueredo, Departamento de Engenhara Electrotécnca e de Computadores, Insttuto Superor Técnco, Lsboa, Portugal maro.fgueredo@st.utl.pt November 2008 Quantzaton s
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More information5 Solving systems of nonlinear equations
umercal Methods n Chemcal Engneerng 5 Solvng systems o nonlnear equatons 5 Solvng systems o nonlnear equatons... 5. Overvew... 5. assng unctons... 5. D ewtons Method somethng you dd at school... 5. ewton's
More informationFORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER
FORCED CONVECION HEA RANSFER IN A DOUBLE PIPE HEA EXCHANGER Dr. J. Mchael Doster Department of Nuclear Engneerng Box 7909 North Carolna State Unversty Ralegh, NC 276957909 Introducton he convectve heat
More informationExperiment 8 Two Types of Pendulum
Experment 8 Two Types of Pendulum Preparaton For ths week's quz revew past experments and read about pendulums and harmonc moton Prncples Any object that swngs back and forth can be consdered a pendulum
More informationColligative Properties
Chapter 5 Collgatve Propertes 5.1 Introducton Propertes of solutons that depend on the number of molecules present and not on the knd of molecules are called collgatve propertes. These propertes nclude
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationBERNSTEIN POLYNOMIALS
OnLne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More information1 Approximation Algorithms
CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons
More informationPsych 5741 (Carey): 8/22/97 Parametric Statistics  1
Psych 5741 (Carey): 8//97 Parametrc Statstcs  1 1 Parametrc Statstcs: Tradtonal Approach 11 Denton o parametrc statstcs: Parametrc statstcs assume that the varable(s) o nterest n the populaton(s) o nterest
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationPhysics 2101 Section 3 April 26th: Chap. 18 : Chap Ann n ce n e t nnt : Exam #4, April Exam #4,
Physics 2101 Section 3 April 26 th : Chap. 181919 Announcements: n nt Exam #4, April 28 th (Ch. 13.618.8) 18.8) Final Exam: May 11 th (Tuesday), 7:30 AM Make up Final: May 15 th (Saturday) 7:30 AM Class
More informationClustering Gene Expression Data. (Slides thanks to Dr. Mark Craven)
Clusterng Gene Epresson Data Sldes thanks to Dr. Mark Craven Gene Epresson Proles we ll assume we have a D matr o gene epresson measurements rows represent genes columns represent derent eperments tme
More informationSection 2 Introduction to Statistical Mechanics
Secton 2 Introducton to Statstcal Mechancs 2.1 Introducng entropy 2.1.1 Boltzmann s formula A very mportant thermodynamc concept s that of entropy S. Entropy s a functon of state, lke the nternal energy.
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationTopical Workshop for PhD students Adsorption and Diffusion in MOFs Institut für Nichtklassische Chemie, Germany, www.unileipzig.
Gas Separaton and Purfcaton Measurement of Breakthrough Curves Topcal Workshop for PhD students Adsorpton and Dffuson n MOFs Adsorpton on Surfaces / Separaton effects Useful features Thermodynamc effect
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More information+ + +   This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationMOLECULAR PARTITION FUNCTIONS
MOLECULR PRTITIO FUCTIOS Introducton In the last chapter, we have been ntroduced to the three man ensembles used n statstcal mechancs and some examples of calculatons of partton functons were also gven.
More informationThe final numerical answer given is correct but the math shown does not give that answer.
Note added to Homework set 7: The solution to Problem 16 has an error in it. The specific heat of water is listed as c 1 J/g K but should be c 4.186 J/g K The final numerical answer given is correct but
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationChapter 22 Heat Engines, Entropy, and the Second Law of Thermodynamics
apter 22 Heat Engnes, Entropy, and te Seond Law o erodynas 1. e Zerot Law o erodynas: equlbru > te sae 2. e Frst Law o erodynas: de d + d > adabat, sobar, sovoluetr, soteral 22.1 Heat Engnes and te Seond
More informationNumerical Analysis of the Natural Gas Combustion Products
Energy and Power Engneerng, 2012, 4, 353357 http://dxdoorg/104236/epe201245046 Publshed Onlne September 2012 (http://wwwscrporg/journal/epe) Numercal Analyss of the Natural Gas Combuston Products Fernando
More informationIntroduction to Statistical Physics (2SP)
Introducton to Statstcal Physcs (2SP) Rchard Sear March 5, 20 Contents What s the entropy (aka the uncertanty)? 2. One macroscopc state s the result of many many mcroscopc states.......... 2.2 States wth
More informationz(t) = z 1 (t) + t(z 2 z 1 ) z(t) = 1 + i + t( 2 3i (1 + i)) z(t) = 1 + i + t( 3 4i); 0 t 1
(4.): ontours. Fnd an admssble parametrzaton. (a). the lne segment from z + to z 3. z(t) z (t) + t(z z ) z(t) + + t( 3 ( + )) z(t) + + t( 3 4); t (b). the crcle jz j 4 traversed once clockwse startng at
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationMolecular spectroscopy II: Electronic transitions. Characteristic frequencies and wavelengths. Hierarchy of energy levels. E el >> E rot >> E vib
Molecular spectroscopy II: Electronc transtons Characterstc requences and wavelengths Herarchy o energy levels E el >> E rot >> E vb Electronc transtons Vbratonal transtons Rotatonal transtons Energy Energy
More informationInterlude: Interphase Mass Transfer
Interlude: Interphase Mass Transfer The transport of mass wthn a sngle phase depends drectly on the concentraton gradent of the transportng speces n that phase. Mass may also transport from one phase to
More informationSolutions to the exam in SF2862, June 2009
Solutons to the exam n SF86, June 009 Exercse 1. Ths s a determnstc perodcrevew nventory model. Let n = the number of consdered wees,.e. n = 4 n ths exercse, and r = the demand at wee,.e. r 1 = r = r
More information(6)(2) (6)(4) (4)(6) + (2)(3) + (4)(3) + (2)(3) = 1224 + 24 + 6 + 12 6 = 0
Chapter 3 Homework Soluton P3., 4, 6, 0, 3, 7, P3.3, 4, 6, P3.4, 3, 6, 9, P3.5 P3.6, 4, 9, 4,, 3, 40  P 3. Determne the alues of, 4,, 3, and 6
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationThe Mathematical Derivation of Least Squares
Pscholog 885 Prof. Federco The Mathematcal Dervaton of Least Squares Back when the powers that e forced ou to learn matr algera and calculus, I et ou all asked ourself the ageold queston: When the hell
More informationViscosity of Solutions of Macromolecules
Vscosty of Solutons of Macromolecules When a lqud flows, whether through a tube or as the result of pourng from a vessel, layers of lqud slde over each other. The force f requred s drectly proportonal
More informationAPPLICATIONS OF VARIATIONAL PRINCIPLES TO DYNAMICS AND CONSERVATION LAWS IN PHYSICS
APPLICATIONS OF VAIATIONAL PINCIPLES TO DYNAMICS AND CONSEVATION LAWS IN PHYSICS DANIEL J OLDE Abstract. Much of physcs can be condensed and smplfed usng the prncple of least acton from the calculus of
More informationv a 1 b 1 i, a 2 b 2 i,..., a n b n i.
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are
More informationEntropy Changes & Processes
Entropy Changes & Processes Chapter 4 of Atkins: he Second Law: he Concepts Section 4.3, 7th edition; 3.3, 8th edition Entropy of Phase ransition at the ransition emperature Expansion of the Perfect Gas
More informationTexas Instruments 30Xa Calculator
Teas Instruments 30Xa Calculator Keystrokes for the TI30Xa are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the tet, check
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationAnswer, Key Homework 6 David McIntyre 1
Answer, Key Homework 6 David McIntyre 1 This printout should have 0 questions, check that it is complete. Multiplechoice questions may continue on the next column or page: find all choices before making
More informationA Binary Particle Swarm Optimization Algorithm for Lot Sizing Problem
Journal o Economc and Socal Research 5 (2), 2 A Bnary Partcle Swarm Optmzaton Algorthm or Lot Szng Problem M. Fath Taşgetren & YunCha Lang Abstract. Ths paper presents a bnary partcle swarm optmzaton
More informationChem 338 Homework Set #2 solutions September 12, 2001 From Atkins: 2.8, 2.15, 2.16, 2.17, 2.18, 2.21, 2.23, 2.26
Chem 8 Homework Set # solutions September 1, 001 From Atkins:.8,.15,.16,.17,.18,.1,.,.6.8) A sample of methane of mass 4.50 g occupies 1.7 L at 10 K. (a) Calculate the work done when the gas expands isothermally
More informationLevel Annuities with Payments Less Frequent than Each Interest Period
Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Symoblc approach
More informationOPTIMIZATION OF THE IRREVERSIBLE DIESEL CYCLE USING FINITE SPEED THERMODINAMICS AND THE DIRECT METHOD
Bulletn of the Translvana Unversty of Braşov Vol. (51)  9 Seres I: Engneerng Scences OPTIMIZATION OF THE IRREVERSIBLE DIESEL CYCLE USING FINITE SPEED THERMODINAMICS AND THE DIRECT METHOD S. PETRESCU 1
More informationExperiment 5 Elastic and Inelastic Collisions
PHY191 Experment 5: Elastc and Inelastc Collsons 8/1/014 Page 1 Experment 5 Elastc and Inelastc Collsons Readng: Bauer&Westall: Chapter 7 (and 8, or center o mass deas) as needed 1. Goals 1. Study momentum
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount in the account, the balance, is
Payout annutes: Start wth P dollars, e.g., P = 100, 000. Over a 30 year perod you receve equal payments of A dollars at the end of each month. The amount of money left n the account, the balance, earns
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationExpansion and Compression of a Gas
Physics 6B  Winter 2011 Homework 4 Solutions Expansion and Compression of a Gas In an adiabatic process, there is no heat transferred to or from the system i.e. dq = 0. The first law of thermodynamics
More informationOptimal maintenance of a productioninventory system with continuous repair times and idle periods
Proceedngs o the 3 Internatonal Conerence on Aled Mathematcs and Comutatonal Methods Otmal mantenance o a roductonnventory system wth contnuous rear tmes and dle erods T. D. Dmtrakos* Deartment o Mathematcs
More informationShielding Equations and Buildup Factors Explained
Sheldng Equatons and uldup Factors Explaned Gamma Exposure Fluence Rate Equatons For an explanaton of the fluence rate equatons used n the unshelded and shelded calculatons, vst ths US Health Physcs Socety
More informationChapter 2 Thermodynamics of Combustion
Chapter 2 Thermodynamcs of Combuston 2.1 Propertes of Mxtures The thermal propertes of a pure substance are descrbed by quanttes ncludng nternal energy, u, enthalpy, h, specfc heat, c p, etc. Combuston
More informationVolumetric Calculations
olumetrc Calculatons I. Calculatng Ol n Place by the olumetrc Method Ol n place by the volumetrc method s gven by: (t) ( 1  (t)) (p(t)) Bo(p(t)) w (1) Where: (t) ol n place at tme t, TB b 7758 A h bulk
More informationLiquidVapor Equilibria in Binary Systems 1
LqudVapor Equlbra n Bnary Systems 1 Purpose The purpose of ths experment s to study a bnary lqudvapor equlbrum of chloroform and acetone. Measurements of lqud and vapor compostons wll be made by refractometry.
More informationAnalysis of Reactivity Induced Accident for Control Rods Ejection with Loss of Cooling
Analyss of Reactvty Induced Accdent for Control Rods Ejecton wth Loss of Coolng Hend Mohammed El Sayed Saad 1, Hesham Mohammed Mohammed Mansour 2 Wahab 1 1. Nuclear and Radologcal Regulatory Authorty,
More informationAS1 MOLES. oxygen molecules have the formula O 2 the relative mass will be 2 x 16 = 32 so the molar mass will be 32g mol 1
Moles 1 MOLES The mole the standard unit of amount of a substance the number of particles in a mole is known as Avogadro s constant (L) Avogadro s constant has a value of 6.023 x 10 23 mol 1. Example
More informationQUANTUM MECHANICS, BRAS AND KETS
PH575 SPRING QUANTUM MECHANICS, BRAS AND KETS The followng summares the man relatons and defntons from quantum mechancs that we wll be usng. State of a phscal sstem: The state of a phscal sstem s represented
More informationProblem Set 3 Solutions
Chemistry 360 Dr Jean M Standard Problem Set 3 Solutions 1 (a) One mole of an ideal gas at 98 K is expanded reversibly and isothermally from 10 L to 10 L Determine the amount of work in Joules We start
More information4 Cosmological Perturbation Theory
4 Cosmologcal Perturbaton Theory So far, we have treated the unverse as perfectly homogeneous. To understand the formaton and evoluton of largescale structures, we have to ntroduce nhomogenetes. As long
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount owed is. P (1 + i) A
Amortzed loans: Suppose you borrow P dollars, e.g., P = 100, 000 for a house wth a 30 year mortgage wth an nterest rate of 8.25% (compounded monthly). In ths type of loan you make equal payments of A dollars
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More information21 Vectors: The Cross Product & Torque
21 Vectors: The Cross Product & Torque Do not use our left hand when applng ether the rghthand rule for the cross product of two vectors dscussed n ths chapter or the rghthand rule for somethng curl
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationModelling of Hot Water Flooding
Unversty of Readng Modellng of Hot Water Floodng as an Enhanced Ol Recovery Method by Zenab Zargar August 013 Department of Mathematcs Submtted to the Department of Mathematcs, Unversty of Readng, n Partal
More informationF321 MOLES. Example If 1 atom has a mass of 1.241 x 1023 g 1 mole of atoms will have a mass of 1.241 x 1023 g x 6.02 x 10 23 = 7.
Moles 1 MOLES The mole the standard unit of amount of a substance (mol) the number of particles in a mole is known as Avogadro s constant (N A ) Avogadro s constant has a value of 6.02 x 10 23 mol 1.
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More information8 Algorithm for Binary Searching in Trees
8 Algorthm for Bnary Searchng n Trees In ths secton we present our algorthm for bnary searchng n trees. A crucal observaton employed by the algorthm s that ths problem can be effcently solved when the
More informationSupplementary material: Assessing the relevance of node features for network structure
Supplementary materal: Assessng the relevance of node features for network structure Gnestra Bancon, 1 Paolo Pn,, 3 and Matteo Marsl 1 1 The Abdus Salam Internatonal Center for Theoretcal Physcs, Strada
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationPassive Filters. References: Barbow (pp 265275), Hayes & Horowitz (pp 3260), Rizzoni (Chap. 6)
Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called
More informationVENTILATION MEASUREMENTS COMBINED WITH POLLUTANT CONCENTRATION MEASUREMENTS DISCRIMINATES BETWEEN HIGH EMISSION RATES AND INSUFFICIENT VENTILATION
VENTILTION MESREMENTS OMINED WITH OLLTNT ONENTRTION MESREMENTS DISRIMINTES ETWEEN HIGH EMISSION RTES ND INSFFIIENT VENTILTION Mkael orlng 1, Hans Stymne 2, Magnus Mattsson 2, and laes lomqvst 2 1 Department
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More information