Principles of Humidity Dalton s law
|
|
- Louise Richard
- 5 years ago
- Views:
Transcription
1 Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid CO 2 0,03 0,04 Rst: H 2, N, H, Kr 0,02 0,01 On normal physical conditions ths gass bhav idal which mans that th gas molculs act indpndnt from ach othr which lads to Dalton s law : Th total prssur of a gas is th sum of th prssurs of ach componnt Th prssur of a singl componnt is calld partial prssur, so th total prssur of air is th sum of th partial prssurs of its componnts i.. p = p N2 + p O2 + p Ar +... dimnsion of p: [mbar] or [hpa] Watr in its gasous phas (vapour) is an additional idal gas componnt of air which appars in Dalton s law : p = p N2 + p O2 + p Ar = p da + p da partial prssur of (watr) vapour [mbar] partial prssur of dry air
2 Principls of Humidity - Vapour prssur Vapour prssur abov watr Vapour prssur cannot tak on any valu in air. Thr is a maximum partial prssur of vapour which dpnds only on air tmpratur. At high tmpraturs air can hold mor vapour than at low tmpraturs. This bhaviour can b xplaind in th following way : Th molculs, boundd in a liquid lik watr, ar moving with diffrnt vlocitis and th avrag kintic nrgy is proportional to th tmpratur of th liquid. Th nrgy distribution of th molculs is statistical as shown in Fig.1. numbr of molculs tmpratur 1 tmpratur 2 > tmpratur 1 Enrgy Fig. 1: Statistical nrgy distribution of molculs in a liquid at diffrnt tmpraturs. Th ovrall avrag kintic nrgy of th molculs is dpnding on tmpratur whras th nrgy of a singl molcul can b lowr or highr with a statistical probability. Molculs with nrgis blow th binding nrgy of th liquid cannot lav th watr surfac, but som hav nough nrgy to xcd th binding forc. Ths molculs can lav th liquid, thy vaporat from th watr surfac and incras th vapour concntration in th room abov th watr surfac. Th molculs in th vapour bhav similar but for thm th cas to hav lss nrgy than th binding nrgy of watr is xcptional: thy ar absorbd from th watr surfac by condnsation and dcras th vapour concntration. A closd box partly filld with watr at tmpratur t (Fig.2) will stabiliz in quilibrium btwn vaporation and condnsation. If thr is a lack of watr molculs in th moist rgion, mor vaporation will occur and th vapour concntration will incras. In th opposit cas mor molculs will condns than vaporat and th vapour concntration will dcras.
3 Vapour partial prssur w vaporation condnsation Watr Fig. 2 : Box partly filld with watr at constant tmpratur Th balanc btwn vaporation and condnsation lads to a vapour prssur, which dpnds only on tmpratur. Incrasing th tmpratur mor molculs hav highr nrgis (s Fig.1), will lav th watr surfac and shift th quilibrium to highr vapour concntrations. On normal nvironmntal conditions vapour is an idal gas with no intraction with othr prsnt idal gass. So th vapour concntration is practically indpndnt from othr xisting gass in th rgion abov th watr surfac. In th box at tmpratur t th balancd vapour prssur is a maximum at this tmpratur and is calld saturation vapour prssur abov watr w at tmpratur t. Th saturation prssur abov watr w dpnds approximatly xponntial on tmpratur t. Valus for w for diffrnt tmpraturs ar givn in Tab.1 [1].
4 t [dgc] w [mbar] t [dgc] w [mbar] E E E E-05 Tab. 1: Saturation vapour prssur valus w abov watr Vapour prssur abov ic Blow t=0.01 dgc (tripl point of watr) watr can xist in th liquid phas as wll as in th solid phas (ic) but th liquid phas is usually not stabl. Th physical intrprtation of vaporation abov ic is qual to watr. t [dgc] i [mbar] E E E E-05 Tab. 2 : Saturation vapour prssur valus i abov ic
5 According to th xistnc of a solid and liquid phas thr ar two saturation curvs blow t=0.01 dgc as shown in Fig.3 on a logarithmic scal. Mind that btwn -100 dgc and 100 dgc th saturation vapour prssur is changing ovr 8 ordrs of magnitud! 1.E+04 saturation vapour prssur [mbar] 1.E+03 1.E+02 1.E+01 1.E E-01 1.E-02 1.E-03 1.E-04 watr ic 1.E-05 tmpratur [dgc] Fig. 3 : Vapour saturation curvs abov ic and watr. Blow th tripl point (t=0.01 dgc) th curv splits into two graphs. Ral gas corrction As so far watr vapour was tratd as an idal gas i.. watr molculs act indpndnt from th surrounding air. In rality thr is an intraction btwn watr molculs and th air which lads to a small incras of saturation vapour prssur undr prsnc of air. This fact is takn into account by th nhancmnt factor f(p,t). Th saturation vapour prssur undr prsnc of air w is givn by w = w (t) f(p,t) At normal prssur (p<1100 mbar) th nhancmnt factor is clos to on and can usually b nglctd. This mans that watr vapour mostly bhavs lik an idal gas. If you wish highr accuracis you should corrct th saturation watr prssur using th nhancmnt factor f, which dpnds on air prssur p and tmpratur t (for valus s Tab.3 [2] ).
6 t [dgc] p [bar] Tab. 3 : Enhancmnt factor f(p,t)
7 Principls of Humidity - Magnus formula Th saturation vapour prssur abov ic and watr can b calculatd with good accuracy with th Magnus formula [1] : w, i = m t A xp Tn + t Th paramtrs A, m, T n ar diffrnt for ic and watr and ar givn in Tab. 4. Tmpratur rang t [dgc] A m T n abov ic : -80 to abov watr : -45 to Tab. 4 : Magnus formula paramtr [1]
8 Principls of Humidity Rlativ humidity Rlativ humidity U w [%] Tabl 1 and 2 (in sction Vapour prssur ) giv valus for th saturation watr vapour prssur as a function of tmpratur. Ths valus ar maximum valus, in practic partial vapour prssurs ar usually lowr. Rlativ humidity U w is dfind as th ratio btwn th actual partial vapour prssur and th saturation vapour prssur abov watr w U w = w 100 [%] Sinc th partial vapour prssur cannot xcd th saturation vapour prssur, th maximum valu of rlativ humidity is U w =100%. Rlativ humidity blow th tripl point Th dfinition of rlativ humidity blow th tripl point of watr t< 0.01 dgc rfrs again to th saturation prssur abov watr. In this xcptional tmpratur rgim you can ithr hav watr with saturation vapour prssur w or ic with a smallr valu i < w. In most applications howvr you will find ic sinc this is th stabl stat for tmpraturs t < 0.01 dgc. So th cas = i givs you an uppr limit for th rlativ humidity: t < 0.01 C: U max i w, = w 100 [%] t [dgc] i [mbar] w [mbar] U max [%] 100% 95% 91% 87% 83% 79% 76% 73% 70% Tab. 5 : Maximum rlativ humidity valus abov ic
9 Principls of Humidity - Dw Point, Frost Point Whn you cool down air containing vapour blow th saturation concntration th actual partial prssur initially stays constant whil th rlativ humidity is incrasing du to th dcras of th saturation vapour prssur with tmpratur t. U w = w 100 [%] t dcrasing w (t) dcrasing U w incrasing At th dw point tmpratur t d th saturation vapour prssur quals th actual vapour prssur i.. w (t d )= and th rlativ humidity rachs its maximum valu of U w =100%. Th dw point tmpratur t d is thrfor th tmpratur to which you hav to cool down moist air at constant prssur for bginning condnsation. It can b calculatd from th tmpratur and rlativ humidity using th Magnus formula : t [ C] saturation vapour prssur w w [mbar], U w [%] w U w = 100 t d = T n ln A m ln A Th Magnus paramtrs A, m, T n ar givn in Tabl 4 in th sction Magnus Formula. Dcrasing th tmpratur blow th dw point tmpratur th partial vapour prssur xcds th saturation valu, so condnsation occurs until th balanc is rachd again. Blow th tripl point of watr t < 0.01 C you will usually find ic ( i ) in your application instad of watr ( w ). Th tmpratur at which th partial vapour prssur rachs th saturation vapour prssur i and frosting starts is calld frost point t f > t d.
10 Principls of Humidity Absolut Humidity Absolut humidity d v [g/m³] Givs th mass of watr in 1 m³ moist air and can b calculatd from th tmpratur t [dgc] and th partial vapour prssur [mbar] : t [dgc] saturation vapour prssur w = w U w d v = t [ g / m 3 ]
11 Principls of Humidity Mixing ratio Mixing ratio r [g/kg] Givs th mass of watr you hav to vaporat and mix with 1 kg dry air to prform a crtain rlativ humidity U w or partial vapour prssur t [dgc] saturation vapour prssur w = w U w 622 r = ( p ) [ g / kg] p air prssur [mbar]
12 Principls of Humidity Spcific Enthalpy Spcific nthalpy h [kj/kg] Th spcific nthalpi of air with tmpratur t, rlativ humidity U w and corrsponding mixing ratio r is th sum of th nrgis you nd to crat this stat in th following way : a) warming up 1 kg dry air from 0 dgc to t b) vaporating th vapour insid th moist air c) warming up th vapour from 0 dgc to t fi Spcific Enthalpi pr 1 kg dry air: h = [c pa t + (l w + c pv t) r] [kj/kg] c pa = kj/kg spcific hat capacity of dry air at constant prssur c pv = kj/kg spcific hat capacity of vapour at constant prssur l w = kj/kg latnt hat of watr Th spcific nthalpy is a rlativ quantity i.. only diffrncs ar significant. Mor gnrally nthalpy givs you th amount of nrgy which you nd to bring moist air from a thrmal stat 1 into a stat 2. Exampl 1 : To warm up air from 20 to 25 dgc and humidify th air from 40 to 60 % rlativ humidity you will nd h=20.2 kj/kg. Exampl 2 : Warming up air from 20 to 25 dgc and kping th rlativ humidity constant dissipats only h=10.3 kj/kg. Exampl 3 : Whn warming up air from 20 to 25 dgc and kping th partial vapour prssur constant (r = constant, t d = constant) th rlativ humidity dcrass down to U w =29.5 % which wasts only h=5.1 kj/kg. Ths xampls ar summarizd in Tabl 6 and ar drawn as procss 1, 2, 3 in Fig. 4 in th sction Mollir diagram.
13 Exampl 1 t [dgc] U w [%] h [kj/kg] stat stat Exampl 2 t [dgc] diffrnc 5.1 U w [%] h [kj/kg] stat stat Exampl 3 t [dgc] diffrnc 10.3 U w [%] h [kj/kg] stat stat diffrnc 20.2 Tab. 6: Enthalpy diffrncs with diffrnt changs of stat
14 Principls of Humidity - Mollir diagram Tabl 7 summarizs humidity function valus at diffrnt tmpraturs. A Mollir diagram srvs for solving problms in air conditioning tchnology graphically. It summarizs diffrnt humidity functions in on chart. Using th mixing ratio r thr is a rlation btwn r and tmpratur t with rlativ humidity U w as fr paramtr : 622 p r w ( t) U w r = = = p r 100 Using th Magnus formula you can draw a band of curvs of constant rlativ humidity U w as functions t(r) which is calld Mollir diagram. It is convnint to add curvs of constant nthalpy to th Mollir diagram (as in Fig. 4) : h = [c pa t + (l w + c pv t) r] t = (h - l w r) / (c pa + c pv r) In this way you can dscrib graphically thrmodynamical procsss such as xampls 1, 2, 3 in th sction Spcific Enthalpy. In a profssional Mollir diagram usually furthr humidity functions ar includd. tmpratur t [dgc] %rh 2%rh 5%rh 10%rh 20%rh h = 0 kj/kg procss 1 procss 2 procss 3 h = 100 kj/kg 40%rh 60%rh 80%rh 100%rh fog rgion mixing ratio r [g/kg] h = 50 kj/kg Fig. 4 : Mollir diagram : curvs of constant rlativ humidity and nthalpy. Exampls 1, 2, 3 from th sction Spcific Enthalpy ar drawn as procsss 1, 2, 3.
15 Tab. 7: Humidity function valus at diffrnt tmpraturs (p = mbar, ral gas corrctions ar takn into account) : -20 dgc U w [%] t d [dgc] [mbar] d v [g/m³] r [g/kg] h [kj/kg] dgc Uw [%] t d [dgc] [mbar] d v [g/m³] r [g/kg] h [kj/kg]
16 20 dgc U w [%] t d [dgc] [mbar] d v [g/m³] r [g/kg] h [kj/kg] dgc U w [%] t d [dgc] [mbar] d v [g/m³] r [g/kg] h [kj/kg]
17 60 dgc U w [%] t d [dgc] [mbar] d v [g/m³] r [g/kg] h [kj/kg]
18 Principls of Humidity - Litratur [1] Sonntag D.: Important Nw Valus of Physical Constants of 1986, Vapour Prssur Formulations basd on th ITS-90 and Psychromtr Formula; Z.Mtorol.70 (1990) 5, [2] Hyland R.W.: A Corrlation for th scond Intraction Virial Cofficints and Enhancmnt Factors for Moist air; J.Rsarch NBS, A.Physics and Chmistry 79A (1975)
Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...
Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg
More informationUniversity of Illinois at Chicago Department of Physics. Thermodynamics & Statistical Mechanics Qualifying Examination
Univrsity of Illinois at Chicago Dpartmnt of hysics hrmodynamics & tatistical Mchanics Qualifying Eamination January 9, 009 9.00 am 1:00 pm Full crdit can b achivd from compltly corrct answrs to 4 qustions.
More informationBrief Introduction to Statistical Mechanics
Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationMCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)
MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl
More informationCoupled Pendulums. Two normal modes.
Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron
More informationElements of Statistical Thermodynamics
24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,
More informationph People Grade Level: basic Duration: minutes Setting: classroom or field site
ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:
More informationChapter 8: Electron Configurations and Periodicity
Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how
More informationWhere k is either given or determined from the data and c is an arbitrary constant.
Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is
More informationIntroduction to Condensed Matter Physics
Introduction to Condnsd Mattr Physics pcific hat M.P. Vaughan Ovrviw Ovrviw of spcific hat Hat capacity Dulong-Ptit Law Einstin modl Dby modl h Hat Capacity Hat capacity h hat capacity of a systm hld at
More informationThe pn junction: 2 Current vs Voltage (IV) characteristics
Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n
More information2. Laser physics - basics
. Lasr physics - basics Spontanous and stimulatd procsss Einstin A and B cofficints Rat quation analysis Gain saturation What is a lasr? LASER: Light Amplification by Stimulatd Emission of Radiation "light"
More informationATMO 551a Homework 6 solutions Fall 08
. A rising air parcl in th cor of a thundrstorm achivs a vrtical vlocity of 8 m/s similar to th midtrm whn it rachs a nutral buoyancy altitud at approximatly 2 km and 2 mb. Assum th background atmosphr
More informationExam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.
Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r
More information5.80 Small-Molecule Spectroscopy and Dynamics
MIT OpnCoursWar http://ocw.mit.du 5.80 Small-Molcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts
More informationTitle: Vibrational structure of electronic transition
Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum
More informationContemporary, atomic, nuclear, and particle physics
Contmporary, atomic, nuclar, and particl physics 1 Blackbody radiation as a thrmal quilibrium condition (in vacuum this is th only hat loss) Exampl-1 black plan surfac at a constant high tmpratur T h is
More information1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by:
Elctromagntic Induction. Lorntz forc on moving charg Point charg moving at vlocity v, F qv B () For a sction of lctric currnt I in a thin wir dl is Idl, th forc is df Idl B () Elctromotiv forc f s any
More informationECE507 - Plasma Physics and Applications
ECE507 - Plasma Physics and Applications Lctur 7 Prof. Jorg Rocca and Dr. Frnando Tomasl Dpartmnt of Elctrical and Computr Enginring Collisional and radiativ procsss All particls in a plasma intract with
More informationThe influence of electron trap on photoelectron decay behavior in silver halide
Th influnc of lctron trap on photolctron dcay bhavior in silvr halid Rongjuan Liu, Xiaowi Li 1, Xiaodong Tian, Shaopng Yang and Guangshng Fu Collg of Physics Scinc and Tchnology, Hbi Univrsity, Baoding,
More informationfiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics THERMODYNAMICS AND STATISTICAL PHYSICS
Institut for E/RF, GAE, II AM, M.Sc. Entranc, ES, IFR and GRE in Physics HERMODYAMICS AD SAISICAL PHYSICS E/RF (UE-) Q. Considr th transition of liquid watr to stam as watr boils at a tmpratur of C undr
More informationExam 2 Thursday (7:30-9pm) It will cover material through HW 7, but no material that was on the 1 st exam.
Exam 2 Thursday (7:30-9pm) It will covr matrial through HW 7, but no matrial that was on th 1 st xam. What happns if w bash atoms with lctrons? In atomic discharg lamps, lots of lctrons ar givn kintic
More informationRelate p and T at equilibrium between two phases. An open system where a new phase may form or a new component can be added
4.3, 4.4 Phas Equlbrum Dtrmn th slops of th f lns Rlat p and at qulbrum btwn two phass ts consdr th Gbbs functon dg η + V Appls to a homognous systm An opn systm whr a nw phas may form or a nw componnt
More informationorbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the
Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly
More informationA central nucleus. Protons have a positive charge Electrons have a negative charge
Atomic Structur Lss than ninty yars ago scintists blivd that atoms wr tiny solid sphrs lik minut snookr balls. Sinc thn it has bn discovrd that atoms ar not compltly solid but hav innr and outr parts.
More informationA General Thermal Equilibrium Discharge Flow Model
Journal of Enrgy and Powr Enginring 1 (216) 392-399 doi: 1.17265/1934-8975/216.7.2 D DAVID PUBLISHING A Gnral Thrmal Equilibrium Discharg Flow Modl Minfu Zhao, Dongxu Zhang and Yufng Lv Dpartmnt of Ractor
More informationWhy is a E&M nature of light not sufficient to explain experiments?
1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt
More informationQuasi-Classical States of the Simple Harmonic Oscillator
Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats
More informationCOMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.
C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH
More informationPRINCIPLES OF PLASMA PROCESSING Course Notes: Prof. J. P. Chang Part B3: ATOMIC COLLISIONS AND SPECTRA
Atomic Collisions and Spctra 125 PRINCIPLES OF PLASMA PROCESSING Cours Nots: Prof. J. P. Chang Part B3: ATOMIC COLLISIONS AND SPECTRA I. ATOMIC ENERGY LEVELS Atoms and molculs mit lctromagntic radiation
More informationIn this lecture... Subsonic and supersonic nozzles Working of these nozzles Performance parameters for nozzles
Lct-30 Lct-30 In this lctur... Subsonic and suprsonic nozzls Working of ths nozzls rformanc paramtrs for nozzls rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay Lct-30 Variation of fluid
More informationStatistical Thermodynamics: Sublimation of Solid Iodine
c:374-7-ivap-statmch.docx mar7 Statistical Thrmodynamics: Sublimation of Solid Iodin Chm 374 For March 3, 7 Prof. Patrik Callis Purpos:. To rviw basic fundamntals idas of Statistical Mchanics as applid
More informationPhysics 111. Lecture 38 (Walker: ) Phase Change Latent Heat. May 6, The Three Basic Phases of Matter. Solid Liquid Gas
Physics 111 Lctu 38 (Walk: 17.4-5) Phas Chang May 6, 2009 Lctu 38 1/26 Th Th Basic Phass of Matt Solid Liquid Gas Squnc of incasing molcul motion (and ngy) Lctu 38 2/26 If a liquid is put into a sald contain
More informationA Propagating Wave Packet Group Velocity Dispersion
Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to
More informationPair (and Triplet) Production Effect:
Pair (and riplt Production Effct: In both Pair and riplt production, a positron (anti-lctron and an lctron (or ngatron ar producd spontanously as a photon intracts with a strong lctric fild from ithr a
More informationNusselt number correlations for simultaneously developing laminar duct flows of liquids with temperature dependent properties
Journal of Physics: Confrnc Sris OPEN ACCESS Nusslt numbr corrlations for simultanously dvloping laminar duct flows of liquids with tmpratur dpndnt proprtis To cit this articl: Stfano Dl Giudic t al 2014
More informationHigher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
More informationDetermination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot
5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg
More informationFirst derivative analysis
Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points
More informationAddition of angular momentum
Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th
More informationElectrochemical Energy Systems Spring 2014 MIT, M. Z. Bazant. Midterm Exam
10.66 Elctrochmical Enrgy Systms Spring 014 MIT, M. Z. Bazant Midtrm Exam Instructions. This is a tak-hom, opn-book xam du in Lctur. Lat xams will not b accptd. You may consult any books, handouts, or
More information5.62 Physical Chemistry II Spring 2008
MIT OpnCoursWar http://ocw.mit.du 5.62 Physical Chmistry II Spring 2008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. 5.62 Lctur #7: Translational Part of
More informationLecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields
Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration
More informationA nonequilibrium molecular dynamics simulation of evaporation
Intrnational Confrnc Passiv and Low Enrgy Cooling 543 A nonquilibrium molcular dynamics simulation of vaporation Z.-J. Wang, M. Chn and Z.-Y. Guo Dpartmnt of Enginring Mchanics, Tsinghua Univrsity, Bijing
More informationPHA 5127 Answers Homework 2 Fall 2001
PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring
More information5. Equation of state for high densities
5 1 5. Equation of stat for high dnsitis Equation of stat for high dnsitis 5 Vlocity distribution of lctrons Classical thrmodynamics: 6 dimnsional phas spac: (x,y,z,px,py,pz) momntum: p = p x+p y +p z
More informationPipe flow friction, small vs. big pipes
Friction actor (t/0 t o pip) Friction small vs larg pips J. Chaurtt May 016 It is an intrsting act that riction is highr in small pips than largr pips or th sam vlocity o low and th sam lngth. Friction
More informationElectrochemistry L E O
Rmmbr from CHM151 A rdox raction in on in which lctrons ar transfrrd lctrochmistry L O Rduction os lctrons xidation G R ain lctrons duction W can dtrmin which lmnt is oxidizd or rducd by assigning oxidation
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!
More informationMath 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
More informationMath-3. Lesson 5-6 Euler s Number e Logarithmic and Exponential Modeling (Newton s Law of Cooling)
Math-3 Lsson 5-6 Eulr s Numbr Logarithmic and Eponntial Modling (Nwton s Law of Cooling) f ( ) What is th numbr? is th horizontal asymptot of th function: 1 1 ~ 2.718... On my 3rd submarin (USS Springfild,
More informationThermodynamical insight on the role of additives in shifting the equilibrium between white and grey tin
hrmodynamical insight on th rol of additivs in shifting th quilibrium btwn whit and gry tin Nikolay Dmntv Dpartmnt of Chmistry, mpl Univrsity, Philadlphia, PA 19122 Abstract In this study mthods of statistical
More informationde/dx Effectively all charged particles except electrons
de/dx Lt s nxt turn our attntion to how chargd particls los nrgy in mattr To start with w ll considr only havy chargd particls lik muons, pions, protons, alphas, havy ions, Effctivly all chargd particls
More information1. In the given figure PQRS is a parallelogram. Find the coordinates of R.
Tst Assss Achiv Class : 9 CLASS : 9 Mathmatics 1. In th givn figur PQRS is a paralllogram. Find th coordinats of R. Y S(2, 3) R O P(1, 0) Q(5, 0) X (5, 2) (5, 3) (6, 2) (6, 3) 2. Th prpndicular distanc
More informationRadiation Physics Laboratory - Complementary Exercise Set MeBiom 2016/2017
Th following qustions ar to b answrd individually. Usful information such as tabls with dtctor charactristics and graphs with th proprtis of matrials ar availabl in th cours wb sit: http://www.lip.pt/~patricia/fisicadaradiacao.
More informationAnswer Homework 5 PHA5127 Fall 1999 Jeff Stark
Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw
More information26-Sep-16. Nuclear energy production. Nuclear energy production. Nuclear energy production. Nuclear energy production
Aim: valuat nrgy-gnration rat pr unit mass. Sun: (chck L /M, human ) nrgy-gnration rat producd from fusion of two nucli a + A: nrgy rlasd pr raction raction rat pr unit volum (includs cross sction and
More informationHydrogen Atom and One Electron Ions
Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!
More informationAddition of angular momentum
Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat
More informationElectromagnetism Physics 15b
lctromagntism Physics 15b Lctur #8 lctric Currnts Purcll 4.1 4.3 Today s Goals Dfin lctric currnt I Rat of lctric charg flow Also dfin lctric currnt dnsity J Charg consrvation in a formula Ohm s Law vryon
More information1 Minimum Cut Problem
CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms
More informationHigh Energy Physics. Lecture 5 The Passage of Particles through Matter
High Enrgy Physics Lctur 5 Th Passag of Particls through Mattr 1 Introduction In prvious lcturs w hav sn xampls of tracks lft by chargd particls in passing through mattr. Such tracks provid som of th most
More informationComputing properties in simulations
Computing proprtis in simulations ChE210D Today's lctur: how to comput thrmodynamic proprtis lik th tmpratur and prssur, and kintic proprtis lik th diffusivity and viscosity, from molcular dynamics and
More informationSearch sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
More information15. Stress-Strain behavior of soils
15. Strss-Strain bhavior of soils Sand bhavior Usually shard undr draind conditions (rlativly high prmability mans xcss por prssurs ar not gnratd). Paramtrs govrning sand bhaviour is: Rlativ dnsity Effctiv
More informationAtomic energy levels. Announcements:
Atomic nrgy lvls Announcmnts: Exam solutions ar postd. Problm solving sssions ar M3-5 and Tusday 1-3 in G-140. Will nd arly and hand back your Midtrm Exam at nd of class. http://www.colorado.du/physics/phys2170/
More informationCOHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.
MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function
More informationcycle that does not cross any edges (including its own), then it has at least
W prov th following thorm: Thorm If a K n is drawn in th plan in such a way that it has a hamiltonian cycl that dos not cross any dgs (including its own, thn it has at last n ( 4 48 π + O(n crossings Th
More informationGive the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds.
1 Th diagram shows th lctronic configurations of six diffrnt atoms. A B C D E F (a) You may us th Priodic Tabl on pag 2 to hlp you answr this qustion. Answr ach part by writing on of th lttrs A, B, C,
More informationis an appropriate single phase forced convection heat transfer coefficient (e.g. Weisman), and h
For t BWR oprating paramtrs givn blow, comput and plot: a) T clad surfac tmpratur assuming t Jns-Lotts Corrlation b) T clad surfac tmpratur assuming t Tom Corrlation c) T clad surfac tmpratur assuming
More informationChapter 10. The singular integral Introducing S(n) and J(n)
Chaptr Th singular intgral Our aim in this chaptr is to rplac th functions S (n) and J (n) by mor convnint xprssions; ths will b calld th singular sris S(n) and th singular intgral J(n). This will b don
More informationCHAPTER 16 HW: CONJUGATED SYSTEMS
APTER 6 W: JUGATED SYSTEMS NAMING PLYENES. Giv th IUPA nam for ach compound, including cis/trans or E/Z dsignations whr ndd. ompound no E/Z trans or E 2 3 4 3 Nam trans-2-mthyl-2,4-hxadin 2-mthoxy-,3-cyclohptadin
More informationLecture 28 Title: Diatomic Molecule : Vibrational and Rotational spectra
Lctur 8 Titl: Diatomic Molcul : Vibrational and otational spctra Pag- In this lctur w will undrstand th molcular vibrational and rotational spctra of diatomic molcul W will start with th Hamiltonian for
More informationEXST Regression Techniques Page 1
EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy
More informationComplex Powers and Logs (5A) Young Won Lim 10/17/13
Complx Powrs and Logs (5A) Copyright (c) 202, 203 Young W. Lim. Prmission is grantd to copy, distribut and/or modify this documnt undr th trms of th GNU Fr Documntation Licns, Vrsion.2 or any latr vrsion
More informationThe van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012
Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor
More informationBrief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008
Brif ots on th Frmi-Dirac and Bos-Einstin Distributions, Bos-Einstin Condnsats and Dgnrat Frmi Gass Last Updat: 8 th Dcmbr 8 (A)Basics of Statistical Thrmodynamics Th Gibbs Factor A systm is assumd to
More informationBifurcation Theory. , a stationary point, depends on the value of α. At certain values
Dnamic Macroconomic Thor Prof. Thomas Lux Bifurcation Thor Bifurcation: qualitativ chang in th natur of th solution occurs if a paramtr passs through a critical point bifurcation or branch valu. Local
More informationThe graph of y = x (or y = ) consists of two branches, As x 0, y + ; as x 0, y +. x = 0 is the
Copyright itutcom 005 Fr download & print from wwwitutcom Do not rproduc by othr mans Functions and graphs Powr functions Th graph of n y, for n Q (st of rational numbrs) y is a straight lin through th
More informationCosmology and particle physics
Cosmology and particl physics Lctur nots Timm Wras Lctur 8 Th thrmal univrs - part IV In this lctur w discuss th Boltzmann quation that allows on to dscrib th volution of procsss in our univrs that ar
More informationPart 7: Capacitance And Capacitors
Part 7: apacitanc And apacitors 7. Elctric harg And Elctric Filds onsidr a pair of flat, conducting plats, arrangd paralll to ach othr (as in figur 7.) and sparatd by an insulator, which may simply b air.
More informationWhat are those βs anyway? Understanding Design Matrix & Odds ratios
Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.
More informationEinstein Equations for Tetrad Fields
Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for
More informationP3-4 (a) Note: This problem can have many solutions as data fitting can be done in many ways. Using Arrhenius Equation For Fire flies: T(in K)
# Hnc "r k " K ( $ is th rquird rat law. P- Solution is in th dcoding algorithm availabl sparatly from th author. P-4 (a Not: This problm can hav many solutions as data fitting can b don in many ways.
More informationCE 530 Molecular Simulation
CE 53 Molcular Simulation Lctur 8 Fr-nrgy calculations David A. Kofk Dpartmnt of Chmical Enginring SUNY Buffalo kofk@ng.buffalo.du 2 Fr-Enrgy Calculations Uss of fr nrgy Phas quilibria Raction quilibria
More informationSupplementary Materials
6 Supplmntary Matrials APPENDIX A PHYSICAL INTERPRETATION OF FUEL-RATE-SPEED FUNCTION A truck running on a road with grad/slop θ positiv if moving up and ngativ if moving down facs thr rsistancs: arodynamic
More informationare given in the table below. t (hours)
CALCULUS WORKSHEET ON INTEGRATION WITH DATA Work th following on notbook papr. Giv dcimal answrs corrct to thr dcimal placs.. A tank contains gallons of oil at tim t = hours. Oil is bing pumpd into th
More informationREGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds
How dos light intract with mattr? And what dos (this say about) mattr? REGISTER!!! If Schrödingr s Cat walks into a forst, and no on is around to obsrv it, is h rally in th forst? sourc unknown Phys 1010
More informationThe following information relates to Questions 1 to 4:
Th following information rlats to Qustions 1 to 4: QUESTIN 1 Th lctrolyt usd in this ful cll is D watr carbonat ions hydrogn ions hydroxid ions QUESTIN 2 Th product formd in th ful cll is D hydrogn gas
More informationClassical Magnetic Dipole
Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg
More informationHow can I control light? (and rule the world?)
How can I control light? (and rul th world?) "You know, I hav on simpl rqust. And that is to hav sharks with frickin' lasr bams attachd to thir hads! - Dr. Evil Phys 230, Day 35 Qustions? Spctra (colors
More informationA Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction
Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.
More informationCS 361 Meeting 12 10/3/18
CS 36 Mting 2 /3/8 Announcmnts. Homwork 4 is du Friday. If Friday is Mountain Day, homwork should b turnd in at my offic or th dpartmnt offic bfor 4. 2. Homwork 5 will b availabl ovr th wknd. 3. Our midtrm
More informationHomework #3. 1 x. dx. It therefore follows that a sum of the
Danil Cannon CS 62 / Luan March 5, 2009 Homwork # 1. Th natural logarithm is dfind by ln n = n 1 dx. It thrfor follows that a sum of th 1 x sam addnd ovr th sam intrval should b both asymptotically uppr-
More informationVII. Quantum Entanglement
VII. Quantum Entanglmnt Quantum ntanglmnt is a uniqu stat of quantum suprposition. It has bn studid mainly from a scintific intrst as an vidnc of quantum mchanics. Rcntly, it is also bing studid as a basic
More informationDesign Guidelines for Quartz Crystal Oscillators. R 1 Motional Resistance L 1 Motional Inductance C 1 Motional Capacitance C 0 Shunt Capacitance
TECHNICAL NTE 30 Dsign Guidlins for Quartz Crystal scillators Introduction A CMS Pirc oscillator circuit is wll known and is widly usd for its xcllnt frquncy stability and th wid rang of frquncis ovr which
More informationECE602 Exam 1 April 5, You must show ALL of your work for full credit.
ECE62 Exam April 5, 27 Nam: Solution Scor: / This xam is closd-book. You must show ALL of your work for full crdit. Plas rad th qustions carfully. Plas chck your answrs carfully. Calculators may NOT b
More information