Chemistry 456 (10:30AM Bagley 154) Homework 7A (due Wednesday 9PM 2/22/12)


 Raymond Dorsey
 1 years ago
 Views:
Transcription
1 Homework 7A (due Wednesday 9PM 2/22/12) Q1) Suppose 18 grams of water (one mole) at 298K falls on a large slab of ron (our heat reservor) that s mantaned at 423 K. Calculate the entropy change for the water, the ron and the unverse (whch s just the sum of the system and ts surroundngs, assumng they are adabatcally solated from the rest of creaton.) All of ths happens at 1 Atm. Assume the heat capactes are constant over the applcable ntervals. Cm, p ( ce) = 37 J Cm, p ( water ) = 75.3 J Cm, p ( steam) = 33 K mol K mol J K mol And for water H m, melt ( H 2 O) = 6.kJ Hm, vap ( H 2O) = 4.1kJ mol mol a) Outlne the transformaton that must take place to the water. b) Wrte the entropy term for each step. You may assume that the heat capacty of water and steam (although dfferent) are ndependent of temperature. And determne the total entropy change for the water to steam transformaton. c) Descrbe the physcal transformaton of the ron slab. d) Determne the entropy change for the ron slab. (All heat that went nto the water had to come from the ron slab). e) Determne the total entropy change and verfy that the change s consstent wth he Clausus Inequalty. Q2) Consder a system that s a mxture of 4 moles of N 2, n moles of H 2 and (8 n) moles of O 2. he gasses behave as deal gasses and do not react. a) Wrte a general expresson for the entropy of mxng as a functon of n. n S = n ln n ot b) Fnd the value of n whch maxmzes the mxng entropy c) Fnd the entropy at the maxmum value of n. Q3). he entropy has been defned as tme s arrow. Explan ths defnton usng thermodynamc reasonng. Utlze n your argument the statstcal nterpretaton of entropy. 1/9
2 Q4) Explan the Carnot engne s relevance to the effcency of heat engnes. Explan also the relatonshp between entropy and the effcency of a heat engne. Use a drawng of the engne f you thnk t helps to explan ts functon. Q5) he Helmholtz (A) energy and Gbbs energy (G) are sometmes called free energes. In the old lterature the Gbbs energy s called the free enthalpy. Why are the Gbbs and Helmholtz energes referred to as free? In your explanaton, you may want to recall the defntons of A and G n terms of U, H, and S. Explan also why the Gbbs energy G s so often dscussed n chemstry and bochemstry texts. Q6) Ammona s a common metabolc byproduct. It s also very toxc so terrestral anmals convert ammona to urea: NH 2 CONH 2. Consder the synthess of urea from ts consttuent elements: C gr N g O g H g NH CONH s he table below shows entropy values at for =298K and heat capacty values for each reacton component. Substance ( 1 S JK mol ) CP ( JK mol ) C(gr) N 2 (g) O 2 (g) H 2 (g) Urea(s) Calculate the entropy change for ths reacton at =31K. Assume all heat capactes are constant between 298K and 31K. 2/9
3 Q7) he shells of marne organsms contan calcum carbonate CaCO 3, largely n a crystallne form known as calcte. here s a second crystallne form of calcum carbonate known as aragonte. Physcal and thermodynamc propertes of calcte and aragonte are gven below. [hs compares wth the graphte to damond reacton n the text example 6.13] Propertes (=298K, P=1atm) Calcte Aragonte H f (kj/mole) G f (kj/mole) S f (J/mole K) C P (J/mole K) Densty (gm/ml) a) Based on the thermodynamc data gven, would you expect an solated sample of calcte at =298K and P=1 atm to convert to aragonte, gven suffcent tme. Explan. b) Suppose the pressure appled to an solated sample of calcte s ncreased. Can the pressure be ncreased to the pont that solated calcte wll be converted to aragonte? Explan. 3/9
4 c) What pressure must be acheved to nduce the converson of calcte to aragonte at =298K. Assume both calcte and aragonte are ncompressble at =298K. d) Can solated calcte be converted to aragonte at P=1 atm f the temperature s ncreased? Explan. [Assume the reacton enthalpy and entropy wll reman constant wth temperature.] Q8) One vessel contans 1 mole of gas A and 1 mole of gas B at pressure Pot = 2Bar, at ntal volume V A. A second vessel contans 1 mole of gas A only, at volume V, also at pressure P = 2Bar. A valve separatng the two vessels s B ot opened, mxng wll occur. Both A and B are deal gases, and the ntal pressure n both vessels s 2 bar. Use the pressure dependence of the chemcal potental of each gas. here s a pston on top that can allow the volumes of the two contaners to vary to mantan pressure at 2 Bar, and the temperature s held constant at 298K. a) Determne the composton of the gasses n the two vessels after the valve connectng them s open. b) What thermodynamc crteron dd you use to determne equlbrum composton? c) What s the pressure of the gasses n the two vessels? d) How has the total volume, V + V, changed? A B e) Determne the change n the free energy of each gas f) Determne the change n the total Free Energy. g) Determne the change n the total entropy. h) Determne the change n the total enthalpy. ) How much heat was transferred to the system (and n what drecton)? Q9) he pressure dependence of G s qute dfferent for gases and condensed phases. Calculate for the process (C, sold, graphte, 1 bar, K) to (C, Gm sold, graphte, 25 bar, K) and Gm for the process (He, g, 1 bar, K) to (He, g, 25 bars, K). By what factor s the change n m G greater for He than for graphte? he densty of graphte s about 2.2 g/cc. [For 4/9
5 smplcty assume He s an deal gas. Assume graphte s ncompressble over ths pressure range.] 2) One mole of an deal monatomc gas undergoes the followng transformaton from an ntal state P=1 bar and =3K. Calculate q, w, U, H, and S for each process. a) he gas s heated to =45K at a constant pressure of P=1. bar. b) he gas s heated to =45K at constant volume. c) he gas undergoes a reversble sothermal expanson at =3K untl ts pressure s P=.5 bar. 3) Calculate the entropy change f 2 moles of lqud ammona at P= 1atm and =233.2K are heated to = 473K. he normal bolng pont of ammona s 239.7K. he heat of vaporzaton of ammona s Hm, Vap = 23.2 kj he heat mol capacty of lqud ammona sc 74.8 J P = and s constant from 233K to molk 239.7K. he heat capacty of ammona gas between 239.7k and 473K s gven n able 2.4 of your text. You may use that heat capacty over the range of the gas (.e. from 233K up.) Q1) Fve moles of an deal monatomc gas contract adabatcally and rreversbly when subjected to a constant external pressure of 1 atm from an ntal volume V1=2L and ntal pressure P1=.5 atm. Assume the contracton ceases when the system reaches equlbrum. Calculate S. sys Q11) A sample consstng of 2.5 moles of an deal gas at 298K s expanded from an ntal volume of 1.L to a fnal volume of 5.L. Calculate G and A for: a) an sothermal reversble path; b) an sothermal expanson aganst a constant external pressure of.75 bar. c) Explan why G and A do not dffer. 5/9
6 Q12) hs s an openended queston, and wll requre you to make several assumptons about how much reacton s actually takng place, and how the energy s transferred. Background nformaton: A hot pack can be made by a soluton of sodum acetate (NaAc) n water. he solublty of NaAc at 1C (~bolng) s 18 g NaAc per 1 grams of water. At 2C the solublty s 2 grams NaAc per 1 grams of water. You can look up the solublty on the web at other temperatures. he reacton yelds kj/mole of NaAc. Let us assume: A hot pack weghs about 12 grams (a few ounces) and conssts of about 8 grams of NaAc and 4 grams of water. Assume that the hot pack has a heat capacty of that of water ( 4J/gram). he human hand s about 31C (core temperature s 37.C for humans). he hotpack s generated by placng t n bolng water where all the salt dssolves and remans supersaturated even at room temperature or below, untl t s dsturbed by bendng a metal dsk n the soluton at whch pont the NaAc ppt. out and soldfes releasng the heat. So the queston s: How much heat s released and how warm wll the hot pack get f used around C? Would ths devce be able to warm your hands? Be clear about the assumptons you need to make to determne the amount of heat avalable that wll flow nto you hands. Q13) A box as shown n fgure 6.2 of your text contans a volume VL on the left and the same volume VR on the rght. 1 mole of He s on the left and one mole of Ar s on the rght. A sempermeable membrane separates the two parts. Only the He may pass through the membrane. he temperature s kept constant What s the concentraton of He on the left after the system comes to equlbrum? What crteron dd you use to determne ths? How does the presence of the Ar on the rght mpact ths result? Explan. What s the pressure nsde the two parts (left and rght) of the contaner before and after equlbrum? In the prevous steps the volumes were fxed. Now suppose, pror to any He movng out of the left compartment, that the rght compartment has a pston and 6/9
7 a mass on t that gves the pressure needed to keep the volume the same as the orgnal volume, VR. And now the He s allowed to move across the membrane. What wll the new volume of the rght be relatve to the old volume? he volume of the left compartment, VL, does not change. he temperature s kept constant. [If you can t work t exactly, you can argue approxmately based on the constant volume results and get pretty close.] Be sure to show what ntal assumptons (and equatons) you have to solve ths problem. 7/9
8 Chemstry 456 (Bagley 154, 1:3 AM) Informaton that wll be avalable to you on the second exam. Law I U = q + w U = U (, V ) U U du = d + dv V V Law II: ds = q rev S = S(, V ) S S ds = d + dv V V Comb I,II: du = ds PdV hermodynamc Equaton of State H P S CP S V = ; = P P P V = V S P = V Dalton's Law V P = χ P; P = P ; G = n µ A A A A P Gmx = R n ln Po Calculus Identtes: P x f Z Z = dx x x y dx dz dy = 1 dy dx y dzx z 8/9
9 Chemstry 456 (Bagley 154, 1:3 AM) d( yz) d( y) d( z) = z + y dx dx dx dx dy dx x y x = ; = dz dz dy z z y a a a hermal expanson and compresson coeffcent 1 V 1 V β = κ = V V P P vdw Gas EoS: P R a = V b V 2 Reacton Info o o rxn f o o rxn f Int P, rxn P, m o o H = H rxndx H = ν H S = ν S dn = n n = ν dx m C = ν C Gas Constant: R = 8.3 J / mol K R =.82 L atm / mol K R 298K = 2.48 kj / mol 11J = 1 L atm Atm bar = Pa ( K ) = ( C) m 9/9
substances (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 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 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 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 information1 Battery Technology and Markets, Spring 2010 26 January 2010 Lecture 1: Introduction to Electrochemistry
1 Battery Technology and Markets, Sprng 2010 Lecture 1: Introducton to Electrochemstry 1. Defnton of battery 2. Energy storage devce: voltage and capacty 3. Descrpton of electrochemcal cell and standard
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 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 informationUniversity 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 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 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 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 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 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 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 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 informationRiskbased Fatigue Estimate of Deep Water Risers  Course Project for EM388F: Fracture Mechanics, Spring 2008
Rskbased Fatgue Estmate of Deep Water Rsers  Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
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 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 informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
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 information1 Example 1: Axisaligned rectangles
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton
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 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 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 informationThe Magnetic Field. Concepts and Principles. Moving Charges. Permanent Magnets
. The Magnetc Feld Concepts and Prncples Movng Charges All charged partcles create electrc felds, and these felds can be detected by other charged partcles resultng n electrc force. However, a completely
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 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 information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
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= 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 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 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 informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
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 information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationLoop Parallelization
  Loop Parallelzaton C52 Complaton steps: nested loops operatng on arrays, sequentell executon of teraton space DECLARE B[..,..+] FOR I :=.. FOR J :=.. I B[I,J] := B[I,J]+B[I,J] ED FOR ED FOR analyze
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationLaws of Electromagnetism
There are four laws of electromagnetsm: Laws of Electromagnetsm The law of BotSavart Ampere's law Force law Faraday's law magnetc feld generated by currents n wres the effect of a current on a loop of
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 informationErrorPropagation.nb 1. Error Propagation
ErrorPropagaton.nb Error Propagaton Suppose that we make observatons of a quantty x that s subject to random fluctuatons or measurement errors. Our best estmate of the true value for ths quantty s then
More informationGive all answers in MKS units: energy in Joules, pressure in Pascals, volume in m 3, etc. Only work the number of problems required. Chose wisely.
Chemistry 45/456 0 July, 007 Midterm Examination Professor G. Drobny Universal gas constant=r=8.3j/molek=0.08latm/molek Joule=J= Ntm=kgm /s 0J= Latm. Pa=J/m 3 =N/m. atm=.0x0 5 Pa=.0 bar L=03 m 3.
More informationTrade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity
Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton
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 informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationwhere the coordinates are related to those in the old frame as follows.
Chapter 2  Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of noncoplanar vectors Scalar product
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 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 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 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 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 informationWe are now ready to answer the question: What are the possible cardinalities for finite fields?
Chapter 3 Fnte felds We have seen, n the prevous chapters, some examples of fnte felds. For example, the resdue class rng Z/pZ (when p s a prme) forms a feld wth p elements whch may be dentfed wth the
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 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 informationHedging InterestRate Risk with Duration
FIXEDINCOME SECURITIES Chapter 5 Hedgng InterestRate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cashflows Interest rate rsk Hedgng prncples DuratonBased Hedgng Technques Defnton of duraton
More information14.74 Lecture 5: Health (2)
14.74 Lecture 5: Health (2) Esther Duflo February 17, 2004 1 Possble Interventons Last tme we dscussed possble nterventons. Let s take one: provdng ron supplements to people, for example. From the data,
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 informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationFault tolerance in cloud technologies presented as a service
Internatonal Scentfc Conference Computer Scence 2015 Pavel Dzhunev, PhD student Fault tolerance n cloud technologes presented as a servce INTRODUCTION Improvements n technques for vrtualzaton and performance
More informationCS 2750 Machine Learning. Lecture 3. Density estimation. CS 2750 Machine Learning. Announcements
Lecture 3 Densty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 5329 Sennott Square Next lecture: Matlab tutoral Announcements Rules for attendng the class: Regstered for credt Regstered for audt (only f there
More informationLecture 7 March 20, 2002
MIT 8.996: Topc n TCS: Internet Research Problems Sprng 2002 Lecture 7 March 20, 2002 Lecturer: Bran Dean Global Load Balancng Scrbe: John Kogel, Ben Leong In today s lecture, we dscuss global load balancng
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 informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationConversion between the vector and raster data structures using Fuzzy Geographical Entities
Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,
More informationASSESSMENT OF STEAM SUPPLY FOR THE EXPANSION OF GENERATION CAPACITY FROM 140 TO 200 MW, KAMOJANG GEOTHERMAL FIELD, WEST JAVA, INDONESIA
ASSESSMENT OF STEAM SUPPLY FOR THE EXPANSION OF GENERATION CAPACITY FROM 14 TO 2 MW, KAMOJANG GEOTHERMAL FIELD, WEST JAVA, INDONESIA Subr K. Sanyal 1, Ann RobertsonTat 1, Chrstopher W. Klen 1, Steven
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 informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationProductForm Stationary Distributions for Deficiency Zero Chemical Reaction Networks
Bulletn of Mathematcal Bology (21 DOI 1.17/s11538195174 ORIGINAL ARTICLE ProductForm Statonary Dstrbutons for Defcency Zero Chemcal Reacton Networks Davd F. Anderson, Gheorghe Cracun, Thomas G. Kurtz
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 informationDescription of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t
Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set
More information2.4 Bivariate distributions
page 28 2.4 Bvarate dstrbutons 2.4.1 Defntons Let X and Y be dscrete r.v.s defned on the same probablty space (S, F, P). Instead of treatng them separately, t s often necessary to thnk of them actng together
More informationSCALAR A physical quantity that is completely characterized by a real number (or by its numerical value) is called a scalar. In other words, a scalar
SCALAR A phscal quantt that s completel charactered b a real number (or b ts numercal value) s called a scalar. In other words, a scalar possesses onl a magntude. Mass, denst, volume, temperature, tme,
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
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 informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
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 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 information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
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 informationImplementation of Deutsch's Algorithm Using Mathcad
Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages  n "Machnes, Logc and Quantum Physcs"
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 informationAP Physics B 2009 FreeResponse Questions
AP Physcs B 009 FreeResponse Questons The College Board The College Board s a notforproft membershp assocaton whose msson s to connect students to college success and opportunty. Founded n 1900, the
More informationLecture 2 Sequence Alignment. Burr Settles IBS Summer Research Program 2008 bsettles@cs.wisc.edu www.cs.wisc.edu/~bsettles/ibs08/
Lecture 2 Sequence lgnment Burr Settles IBS Summer Research Program 2008 bsettles@cs.wsc.edu www.cs.wsc.edu/~bsettles/bs08/ Sequence lgnment: Task Defnton gven: a par of sequences DN or proten) a method
More informationA Secure PasswordAuthenticated Key Agreement Using Smart Cards
A Secure PasswordAuthentcated Key Agreement Usng Smart Cards Ka Chan 1, WenChung Kuo 2 and JnChou Cheng 3 1 Department of Computer and Informaton Scence, R.O.C. Mltary Academy, Kaohsung 83059, Tawan,
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationChapter 9. Linear Momentum and Collisions
Chapter 9 Lnear Momentum and Collsons CHAPTER OUTLINE 9.1 Lnear Momentum and Its Conservaton 9.2 Impulse and Momentum 9.3 Collsons n One Dmenson 9.4 TwoDmensonal Collsons 9.5 The Center of Mass 9.6 Moton
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
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 informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
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 informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
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 informationCompressible Flow Modeling in a Constant Area Duct
PDHonlne Course 98 ( PDH) Compressble Flow odelng n a Constant Area Duct Instructor: Nel Hcks, P.E. 0 PDH Onlne PDH Center 57 eadow Estates Drve Farfax, VA 0306658 Phone & Fax: 7039880088 www.pdhonlne.org
More informationNew bounds in BalogSzemerédiGowers theorem
New bounds n BalogSzemerédGowers theorem By Tomasz Schoen Abstract We prove, n partcular, that every fnte subset A of an abelan group wth the addtve energy κ A 3 contans a set A such that A κ A and A
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 information