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# Principles of Physics I PHYS 1408

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This 28 page Class Notes was uploaded by Harry Jerde on Thursday October 22, 2015. The Class Notes belongs to PHYS 1408 at Texas Tech University taught by Sungwon Lee in Fall. Since its upload, it has received 17 views. For similar materials see /class/226439/phys-1408-texas-tech-university in Physics 2 at Texas Tech University.

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Date Created: 10/22/15

Physics 1408002 Principles of Physics Lecture 29 Chapter 14 amp 15 November 7 2008 SungWon Lee SungwonLeettuedu Football wih Ph sics Football is a source of good physics lessons Projectile motion footballs 6r players Speed and velocity Forces and Memento Inelastic collisions Levers foriues and mechanioal v 9 a Announcement Lecture notes 144 Ill 39 I 2V1th H11 nJ slee1408 SI Session Mitchell Lowery Tue 530 700 pm Thu 430 600 pm Holden Hall 226 HW Assignment 7 Ch13 is due by 1159 PM on Tuesday 1111 HW Assignment 8 Ch14 15 is now placed on MateringPHYSICS and is due by 1159 PM on Tuesday 1118 Announcement II Chapter 14 Exam 3 Osc111atlons 4 Oscillations of a Spring Simple Harmonic Motion 11 Energy in the Simple Harmonic Oscillator 0 Simple Harmonic Motion Related to Uniform Circular Motion The Simple Pendulum The Physical Pendulum and the Torsion Pendulum Damped Harmonic Motion Forced Oscillations Resonance Summary 1 3quot GENERAL pRmchEs Solution xt Acos wt 0 with w Ikm IMPORTANT CONCEPTS Dynarmts Energy wimpedcdfm mm mdci x umberW5 asyslemwan equil xium poa39lim diss cmim Lima and mm 2 Name 1 c nml ormwcnhrmouon V k WHERE A 39 T s ml v 0 is 12 phase W39M39a39mm lm mmme mm alkali Anznhmwmc o m mus 23 4a 1 T mesmuhenbnnm 57 39 mm mmmlemgy 4 o A m 23 139 j xu lemsd quot g E x t ismned t I Positionxmrgmnsmeog vs ammuam S mgfn gimmmum g I mpm 7 hit TlEphaseiun zm g 5sz7 r 75 r 6 rklemims einixizlciu hius39 y x 1F 39 mg venuemm tmsmmx gmmmxxmnspeea x AMQ VB mme k m m12 VEHM 39 ve 1 23 3 Accelrra ona uamp mm lb I d2 g 3 V lhc mm meih lcll d2 dtz L Agy Murmqu 1X 1 W A cos wt 0 39 Fwy Potenllul energy 17 Kmqu were M 2 w Acoswt 0 2 w xt l l l 1 Damped Oscillations In many real systems nonconservative forces are present 7 This is no longer an ideal system the type we have dealt with so far 7 Friction is a common non conservative force In this case the mechanical energy of the system diminishes in time the motion is said to be dumped A graph for a damped oscillation The amplitude decreases With time The orange solid curve represents a cosine times a decreasing exponential The blue dashed lines represent the envelope of the motion Damped Oscillations iliPInllmlumphlurle EneIE k cmch nu dimming p A aquot nu mm an m mi m mmmm y I m nms mmmm Fn d2 b d k 5 Mechanical x x 7 i i i X 0 gt x t A e 2m cos wt energy diminishes dl 2 m dt m o in ti ethe at X Fspx DX le va max Damping Sinusoidal k b2 2 1 Ampquot factor Variation motion is said to w 2 0 2 be dumped m 4m 41 HOE Et kxiax gkmam 2 mz eitT EoeitT The oscillator s mechanical energy decays exponentially With time constant 1 e 271828 e 103678368 3 e 2 01353 135 e73 004978 498 Energy u The oscillator starts with energy E The energy ha decreased to 37 of its initial value at t T The energy has decreased to IS VZI of its initial value 03750 551 1 Characteristics amp Types of Wave Motion Energy Transported by Waves Mathematical Representation of a Traveling Wave The Principle of Superposition Re ection and Transmission Interference amp Standing Waves Thc dmlul h39lnce is me rippling of lhc Willi s an 1 if The w am is Ill lllcdium We Will begin by distinguishing three types ofwaves he W ve Model We Will begin by distinguishing three types of Waves 1 Mechanical waves can travel only within a medium such as air or waiaquot PHYS 1408 Examples sound waves water waves 39 s are self 39 39 39 39 that require no medium and can travel through a vacuum Examples radio waves microwaves light xerays yerays etc 3 Matter waves also can travel in vacuum and are the basis for quantum physics ie quantum mechanics beyond this course Examples quantum wave iunctions ior electrons photons atoms etc 15 1 Characteristics of Wave Motion All types of traveling Waves transport energy Study of a single Wave pulse shows that it is begun Wi in vibration and is transmitted e hrough internal forces in the edi Continuous Waves start with vibrations too If the vibration is SHM then the Wave Will be sinusoidal 15 1 Characteristics of Wave Motion Wave characteristics Amplitude A 39 Wavelength J Frequencyfand period T Wave velocity U f Pushpull Mmlw oi we m swim gt A traveling wave or pulse that causes the elements ofmedium to move erpendicular to th direction ofpropagatjon is called a transverse wave The particle motion is shown by e arrow The direction ofpropagation is 39 shown by the red arrow 39 A traveling wave or pulse that causes the elements of the disturbed medium to move parallel to the direction of propagation is ca led a longitudinal wave 39 The displacement of the coils is parallel to the propagation 152 Types of Waves Longitudinal Sound waves are longitudinal waves mm C l memhmne Umrlcwun Expansion Surface Water Waves Earthquake Waves Earthquakes produce both longitudinal and transverse waves Both types can travel through solid material but only longitudinal waves can propagate through a uid in the transverse direction a uid has no restoring force O 0 P waves 7 P stands for primary or P for Pressure Water waves are a comhinution of transverse and longitudinal 7 Fastest at 7 7 8 kmS motion because each particle ofwater participating in the wave 7 Longitudinal motion travels in a circular path as the wave propagates The particles stay in the same average position as the waves 39 S Waves move to the right S stands for secondary or S for shear A 7 Slower at 4 7 5 kms vwam 4 speed depends on wavelength l 7 Transverse yr Traveling Waves 17 Slows down 1Dimensi0nal Waves eg Waves on a String Considering a string of total length L and total mass m String linear density p mL mass per unit length eg the linear density of a 2m M W 00020 kgm long string with a mass of 4 g L Z39Oml T The velocity of a transverse wave on m H 51 a cord is given by Vstring T wave speed of a stretched stnng M The wave speed on a string depends on both the string s linear density and tension force in the string Waves on a Strin Waves on a string are produced by lransvarse motion of each particle of the string participating in thewave motion by moving in a vertical path as the wave propagates Note that although the wave moves to the right the individual particles of thestring return to their original positions v wave speed of a stretched string string S n eed ofa Wave Pulse A Lm long m ingwi l a mass of m4gil lied to lell It one mil stretched horizontally by a pulley 15 In may tli lied to aphysic s hook f 774 f hanging from thushing I Experhnt nd that nwuve pulse trnvdr It v40 ml 15 m Whnhtlunnull ol thebook EietyTsWTsMg0 V2 Mg mv2 0004 kg40 rns2 M M mL 39 gL 980 ms220 m 0327 kg Mb M mL L 0327 kg 0001 kg 0326 kg Lonitudinal Waves Longitudinal waves eg sound are produced ina compressible medium by longitudinal motion of each particle of the medium participating in the wave motion by moving in a horizontal path as the wave propagates I vsound VKRT wave speed of sound K 1402 for air I Here R is the ideal as constant and T is the temperature in K When a iarnily oiiour with a total mass oi a 200 kg step into their 12007kg car the car s springs compress 30 cm aWhat is the spring constant orthe car s springs 300 kg rather than 200 SDLUI ION ll39l39w added low 71 12W kgn kr m lling IIYV 139 quotVH x m 1m i F 0 J u v bH0w iar will the car lower if loaded with vi kg 39 a 9mm CHLsL the hrrclurv m n l lh spring rrmdqu n A 7 7 5 x llJWnl 39 i lw H1 m 139 ll the cm is lll c l 3mm HCokLS MW givm y 300m Nm l inhir 451H m k m s lbwm smicit Determine the period and ireqaency oi a car mass 1400 kg 39 r 104 Nnl after hitting a blunpAssume the shock absorbers are poor so the car really oscillates up and down APPROACH w mu m MUM hm A n to Em I477 soummq me rq mm c INNm llollll39wmmplu M ii I lw yi 2739 001x y n m Nm nrshghll 1m lan lurcnd Th litlur llcy lT lmllr Physics 1408002 Principles of Physics Lecture 30 Chapter 15 l Imemiber ML SungWon Lee SungwonLeettuedu Football wih Ph sics Projectile motion footballs amp players Speed and velocity Forces and Momenfu I I i v Inelastic collisions Dr Lee N Announcement Lecture notes 144 Ill 39 I 234th H11 nI39 slee1408 SI Session Mitchell Lowery Tue 530 700 pm Thu 430 600 pm Holden Hall 226 HWAssignment 7 Ch13 is due by 1159 PM on Tuesday 1111 HW Assignment 8 Ch14 15 is now placed on MateringPHYSICS and is due by 1159 PM on Tuesday 11 18 Announcement 11 Exam 3 11 14 Friday 1100 am 1150 am Chapters 12 13 14 15 Chapter 12 Static Equilibrium Chapter 13 Fluids Chapter 14 Oscillations Chapter 15 Wave Motion College Football mu m 2003 NCAA Football Rankings Week 11 Nov 9 szsnnmzlmjlmlmilmlmlmm nlll lllslzl ll gm ll 2 Allstate Hopefully Exam Average 00 OIO ll20 23O 3 40 4l50 5l60 6l70 7l80 8l90 900 he Model We Will begin by distinguishing three types of waves 1 Mechanical waves can travel only within a medium such as air or water PHYS 1408 Examples sound waves water waves 2 Electromagnetic waves are selfsustaining oscillations that I Charadensucs amp Types wave Mono quire no medium and can travel through a Vacuum Energy Transport by waves Examples radio waves microwaves light xirays yirays etc 39 Mathematical Representation of a Traveling Wave 3 Matter waves also can travel in Vacuum and are the basis for quantum physics ie quantum mechanics beyond this course Interference amp Standing Waves Etxamples quantum wave functions for electrons photons a oms e c The Principle of Superposition Re ection and Transmission 15 1 Characteristics of Wave Motion Wave characteristics Amplitude A Wavelength l Frequency f and period T Wave velocity 1 t f rawmmmwmmm liougtl V T Suing j wave speed of a stretched stnng I vsound VKRT wave speed of sound K 1402 for air I Here R is the ideal as constant and T is the temperature in K Surface Water Waves Water waves are a combination of transverse and longitudinal motion because each particle ofwater participating in the wave motion travels in a circular path as the wave propagates The particles stay in the same average position as the waves move to the right vwam 4 speed depends on wavelength Earthquake Waves Earthquakes produce both longitudinal and transverse waves Both types can travel through solid material but only longitudinal waves can propagate through a uid7in the transverse direction a uid has no restoring force 0 P waves 7 P stands for primary or P for Pressure 7 Fastest at 7 7 8 kms 7 Longitudinal S waves 7 S stands for secondary or S for shear 7 Slower at 4 7 5 kms 7 Transverse 1Dimensional Waves eg Waves on a String 00020 kgm 00040 kg L 20m The velocity of a transverse wave on m H 51 a cord is given by Z vstdng E wave speed of a stretched stnng v m lm Sinusoidal Waves 0 The wave represented by the curve is a sinusoidal wave Simplest example of a periodic continuous wave The wave moves toward the right 7 The orange wave represents the initial po 7 As the wave moves toward the right it will eventually be at the position of the blue curve 0 Each element moves up and down in simple harmonic motion Amplitude amp Wavelength amp Period 0 The crest ofthe wave is the location of the maximum displacement ofthe element from its normal position 7 This distance is called the amplitudeA The wavelength A is the distance from one crest to the next 0 Period T is the time interval required for 2 identical points of adjacent wave to pass by a point m a m quotwlm ms Cale The wavelength A is 400 cm 0 The amplitude A is 150 cm 0 The wave function can be written in the form y A coskx wt 154 Mathematical Representation of a Traveling Wave Suppose the shape of a wave is given by Dx Asin x w I 277f V wave at t wave at time I v H 154 Mathematical Representation of a Traveling Wave After a time t the wave crest has traveled a distance vt so we write the wave function Dxt Asin2r x 7 v0 7 This is for a wave moving to the right 7 For a wave moving to the left replace x vt with x vt Or Dx r A sin kx ml with w27rf k Wave Equations 27r We can also de ne the angular wave number k or just wave number k 27239 The angular frequency can also be defined a 7 The wave function can be expressed as Dx I A sinkx cot The speed of the wave becomes v If If x 0 at t 0 the wave function can be generalized to Dxt A sin kx wt 5 where 96 is called the phase constant The Mathematics of Sinusoidal Waves D Snapshot graph at I W A on ij VxAx2x Dxt0Asin 27r 0j x vt DxtAsin2rr 0Asin Zn O The Angular Frequency 1 e Number k E 2quot 7 wave number radm vAjjmk or wvk Asm Imam Note that D00 Asxm A10m v200ms100Hz Av20m T100105 w 27 20aquot rads 628rads DaomoAAsmk1omm n n n k10 7 7 W m n 2 i39 5 2 7 2 Ba 10 msmJK radmxr 200 radst 42 If two pitching machines simultaneoust throw base Is they will collide and bounce 0 Two particles cannot occupy the same space point at the same time Alan 1 391 he mm mm and haunt Mum Txmpdrmlmmnnuznew 4 hummc pmm m pace m mm mm mm lhc mm pass Ihrtvugh cum Ulhcr thmugh each other wo collision Two waves can occupy the same space point at the same time 156 The Principle of Superposition I If two or more traveling waves mm are moving through a medium the resultant wave function is the algebraic sum of the wave D U 1 functions of the individual waves WV 03mm on v U xriDt1 133 i Sum of all lines Superposition Example I Two pulses are traveling in opposite directionsa The pulses have the same speed but different shapes ih Ml I When the waves start to overlap b I W the resultant wave function is y y2 I When crest meets crest c the resultant wave has a larger amplitude than either of the original waves 1 The two pulses separateThey continue moving in their original directionsThe ll gt shapes of the pulses remain unchanged Superposition and Interference I Two traveling waves can pass through each other without being destroyed I A consequence of the superposition principle I The combination of separate waves in the same region of space to produce a resultant wave is called interference 157 Re ection and Transmission When the pulse reaches the support the pulse moves back along the string in the opposite direction This is the re ection of the pulse The pulse is inverted lumlmi mm lnndr m a xii m With a free end the string is free to move vertically The pulse is re ected The pulse is not inverted Rtnmid 39 uiw 157 Re ection and Transmission Assume a light string is attached to a heavier string see Fig Light s HealY SCCUOH SCCUOH c mmmmmzm Pulse travels through the light string and reaches the boundary Transmitted pulse The part of the pulse is inverted 9 Re ected The re ected pulse has a smaller pulse amplitude Awave encountering a denser medium will be partly re ected and partly transmitted if the wave speed is less in the denser medium the wavelength will be shorter 158 Interference The superposition principle says that when two waves pass through the same point the displacement is the sum of the individual displacements In the figure below a exhibits destructive interference and b exhibits constructive interference gt gt 4 gelW Jb m 1 Time precisely for an instant gt lt gt Pulses far apart receding h Pulses far apart approaching Pulses overlap 158 Interference These graphs show the sum of two waves In a they add constructively in b they add destructively and in c they add partially destructively E E E W 39VV Constructive interference occurs when the displacements caused by the two pulses are in the same direction I Destructive interference occurs when the displacements caused by the two pulses are in opposite directions Destructive Interference yes I Two pulses traveling In W kmz uw opposite directions J x A Their displacements W and EQEMW are inverted with respect to each other M inf477x811 7 I When they overlap W Pg their displacements ii partially cancel each other m 0 XLWWIL lt azom39rmnaonlarwks eon Superposition of Sinusoidal Waves Assume two waves are traveling in the same direction with the same frequency wavelength and amplitude The waves differ in phase y1 A sinkx cut I y2 A sinkx wt 39 VV1V2 ii cosliZi sinkx wt 2 A Useful Trigonometric Identity sinasin b 2cos a b2 sina b2 yl Asinkx wt y2 Asinkx wt p akX at bkX atp Sinusoidal Waves with Constructive Interference y 2A c0 s 2 sinkx wt 452 I When 0 then cos 2 l u The amplitude of the resultant wave 2A the resulting wave has an amplitude that is twice the amplitude of the individual waves The waves interfere constructively h and 2 are identical Total Constructive Interference w W n W YI 2 Sinusoidal Waves with Destructive Interference y cos 2 sinkx at 2 When Jrthen cos 2 0 u The amplitude of the resultant wave 0 l the resulting wave has zero amplitude the two waves completely cancel The waves interfere destructiver total destructive interference w W n W YY2 Sinusoidal Waves General Interference y cos 2 sinkx at 2 H l When q is other than 0 or an even multiple of It the amplitude of the resultant is between 0 and 2A fall f ii i u i jl i wig l n i39 39 totally constructive totally destructive partially constructive Sinusoidal Waves Summary of Interference Constructive interference occurs when 439 O Amplitude of the resultant 2A Destructive interference occurs when rm where n is an even integer Amplitude 0 I General interference occurs when 0 lt lt rm Amplitude 0 lt A lt 2A resultant Physics 1408002 Principles of Physics Lecture 35 2 more amp donell Chapter 18 November 24 2008 SungWon Lee SungwonLeettuedu Announcements Lecture notes L 39 39 39 gnphVS ffquot 39 slee1408 SI Session Mitchell Lowery No SI session this week Final 81 122 Tue 430 730 pm Holden Hall 075 HW Assignment 9 Ch16 17 is now placed on MateringPHYSICS and is due by 1159 PM on Tuesday 121 Last Homeworkll Thanks for your hard work Exam Average 632 00 Hoang 93 Hoover 9 Xie 90 Keim 84 LeeAltowanou 82 Fuhrmann Crenshaw Crow 8 Pin 80 Britain Sartain 79 Schurr Schwartz 78 Azuaje Ong 77 RuchLe 76 HendersonWang Siri 010 IZO 2130 3I40 4I50 5l60 670 7I80 890 9lIOO Announcements 11 Final Exam All Chapters 125 Friday Sci 7 130 pm 400 pm 25 hours Exams Overview 1 quot ex 11 grade not the nal will be dropped since 9 u The exams are closed book You may bring there are no makeup exams one handwritten 3 X 5 index card With Homework 1000 each exam 1500 in class quiz 1500 Lab 2000 and the nal will count 25 ot w formulae etc Telephones iPod and other gizmos are not allowed Small calculators are allowed I The final exam is comprehensive 35 min Exam problems and is a common exam for all sections Tota12025 problems ie 12 chapter YES it s a multiple choice examll quot Homework amp Quiz 39 Please brlng a 503mm Sheet 0139 ange for the The grading scale is A100 90 B89 80 o C79 65 and exam D64 50 o F49 to 0 Chapter 18 Contents Kmetlc ThCOI39y 0f Gases 1 The Ideal Gas Law and the Molecular wIn this winter scene in 7 7 Interpretation of Temperature Quarter for water as a liquid as a solid m steam lhisChaPtrW91lmHethe 2 Distribution of Molecular Speeds call kinetic theoryWe will see thatthe te pe 3 Real Gases and Changes of Phase 4 Vapor Pressure and Humidity 5 of j R eam Free E 3h 4 i msion 181 The Ideal Gas Law and the Molecular Interpretation of Temperature Assumptions of kinetic theory 1 large number of molecules moving in random directions with a variety of speeds 2 molecules are far apart on average 3 molecules obey laws of classical mechanics and interact only when colliding J3 collisions are perfectly elastic 181 The Ideal Gas Law and the Molecular Interpretation of Temperature The force exerted on the wall by the collision of one molecule is F A rrm ZmL X 11171 Ar ZEvx l Amv rim Fmvx 2mm Then the force due to all molecules colliding with that wall is V m g 1 7 N157 a Molecules of a gas moving about in a rectangular container bArrows indicate the momentum of one molecule as it rebounds from the end wall 181 The Ideal Gas Law and the Molecular Interpretation of Temperature The averages of the squares of the speeds in all three directions are equal v2 vxz vyz v12 FanNE F N 12 LuleNl So the pressure P FA is i Nmz2 3 V 181 The Ideal Gas Law and the Molecular Interpretation of Temperature leP 3 V Rewriting PV Nmv SO The average translational kinetic energyK of the molecules in an ideal gas is directly proportional to the temperature T of the gas 1871 The Ideal Gas Law and the Molecular Interpretation ofTemperature Example 137 Molecular kinetic energy hat is the avaage cranslatinnal kinetic Kitty at mnlecnles in an idtal gas at 37 C rml snLunoN Mme T l 39anlK metwt Nan m4 x cl n v t v m t m mm k 1871 The Ideal Gas Law and the Molecular Interpretation ofTemperature mn nnw calculate the avera in a pszsz function nftanp ge speed at mnlecnles 21392er m t rms rnntrmmnrsqllare 1871 The Ideal Gas Law and the Molecular Interpretation ofTemperature Example 132 Speeds nfair mnlecules c t w t istherms speed nfair mnlecllles01 and N1 atmm temperature zlrc 293K sman 39m t n than N e m m n w 39va mm n for nicntgen vm 5m ms 1871 The Ideal Gas Law an Molecular Interpretation of Temp erature Example 1amp4 Average sp eed and rms speed 8 particles have the following speeds given in ms 1116 4uzu6u3 zusu Calculate a the zvm nd h the rms speed saumnN m up t t t l n am me quot7 let 7 xt quotmmcm Nu m Relative number 182 Distribution of Molecular Speeds The molecules in a gas will not all have the same speed random motion their distribution of speeds fv is called the Maxwell distribution of speed 3 fv 47TNlt 2 2T 196 5 W 7T g Distribution of speeds of molecules i3 in an ideal gas N that vav and e peak of the E l This is because the curve is as l skewed to the right it is not l symmetrical The speed at the 0 7JP lvrms Speed 0 peak of the curve is the most 1 probable speed Vp 182 Distribution of Molecular Speeds The Maxwell distribution depends only on the absolute temperature This gure shows distributions of molecular speed for two different temperatures at the higher temperature the whole curve is shifted to the right T 273 K 0 C T 310 K 37 C lulu m fv 47TNlt 277kTgt Relative number of molecules Speed 1 E A 182 Distribution of Molecular Speeds Example 185 Determining v and vp l 0 In N Determine formulas for a the average speed v and b the most probable speed vp of molecules in an ideal gas at temperature T SOLUTION 11 We are given a eontintlotts distribution of speeds Eq 18 6 so the sum over the speeds becomes an integral over the product of N and the number n I that have speed 2 e v It t u l 4 m 3 I r r r I 139 N 27 l We can integrate by parts or look tip the definite integral in a Table and obtain 4 m ti2k i7 i quot8 kT 160 1 2 3977 1 7 r I 7 277ij nr I 17 m m 182 Distribution of Molecular Speeds Example 185 Determining v and vp Determine formulas for a the average speed v and b the most probable speed vp of molecules in an ideal gas at temperature T IThe most probable speed is that speed which occurs more than any others and thus is that speed where f139 has its maximum value At the maximum ot the curve the slope is Zero dfvfdu 0 Taking the derivative of Eq 18 6 gives 10 in Zuni 47rN 2m 3H 7 e w 0 do 27rer 2kT SolvingI for t39 we find l 2T l k T 1 L i 11 l m m Relative number 182 Distribution of Molecular Speeds In summary kT IL WWII II II39I 1 I Z 3 l4l Iquot 39 1 m m l kT 10 H l V L 39 1 Tr In m and from liq 18 5 I k39l39 v I3 vs 17 1 I 1quotquot m I m 3 K S 39 I I 4 I I a I 39I o I II a I I a I I LI I I I o I I I 39I 0 Up vrms Speed 1 183 Real Gases and Changes of Phase The curves A B C D represent the same substance at different temperatures T A gt TB gt TC gt TD A L iq uid B A I West C rlegmn D In curve D the gas becomes liquid it begins condensing at b and is entirely liquid at a The point c is called the critical point 183 Real Gases and Changes of Phase Below the critical temperature the gas can liquefy if the pressure is suf cient above it no amount of pressure Will suf ce BA39 TABLEIB l Critical Temperatures and Pressures P Critical Temperature Critical Pressure Substance C K atm Water 374 647 218 C02 31 304 728 A Oxygen 118 155 50 D 0d B Nitrogen 147 126 335 A gig C Hydrogen 72399 333 128 1 gm 8 D Helium 2679 53 23 183 Real Gases and Changes of Phase APT diagram is called a phase diagram it shows all three phases of matter The solidliquid transition is melting or freezing the liquidvapor one is boiling or condensing and the solidvapor one is sublimation S id Critical point a 218 7 w r r w 5 I Liqmd Phase dIagram of e 10 I water I i iGas 0006 Vaporl a I Triple I I 5 I I point I I 0 00 001 100 374 183 Real Gases and Changes of Phase The triple point is the only point where all three phases can coexist in equilibrium Critical point 73 Solid i Phase diagram of carbon diox1de a 56 3 l Critical Q4 13011quot1t I I A 511 I i l g 218 Vapor l E 10 1 1 1 l l l I 0006 5660 20 31 T C 000 001 HOC 100 374 184 Vapor Pressure and Humidity An open container of water can evaporate rather than boil away The fastest molecules are escaping from the water s surface so evaporation is a cooling process as well The inverse process is called condensation When the evaporation and condensation processes are in equilibrium the vaporjust above the liquid is said to be saturated and its pressure is the saturated vapor pressure 184 Vapor Pressure and Humidity TABLE 18 2 Saturated Vapor Pressure of Water Temp erature 3 7 50 7 10 0 5 10 15 20 E 30 40 50 60 70 80 90 1 00t 120 150 torr mmHg 0030 195 458 654 921 128 175 238 318 553 925 149 234 355 526 760 1489 3570 Saturated Vapor Pressure Pa Nmz 40 260 x 102 611 x 102 872 x 102 123 x 103 171 x 103 233 x 103 317 x 103 424 x 103 737 x 103 123 gtlt 104 199 x 10 312 x 104 473 x 104 701 x 104 101 x 105 199 x 105 476 x 105 TBoiling paint on summit of Mt Everest iBoiJjng point at sea level The saturated vapor pressure increases with temperature 184 Vapor Pressure and Humidity A liquid boils when its saturated vapor pressure equals the external pressure 18 4 Vapor Pressure and Humidity Partial pressure is the pressure each component ofa mixture of gases would exertifitwere the only gas present The partial pressure ofwater in the air can be as low as zero and as high as the saturated vapor pressure at that temperature Relative humidity is a measure of the saturation of air X 100 Rclnuvc humidity 18 4 Vapor Pressure and Humidity Example 1876 Relative humidity On a particular hot day the temperature is 30 C and the partial pressure of water vapor in the air is 210 torr Whatis the relative humidity at riJI pimuic of H20 shire of H10 1 mm Relative humidity saturated apm39j APPROMN Fluff Tii39nlu i372 we we ihhi the wwmltd pm pressure of wmr at 30 C l 1 m SDLUI IO remit hum am is thus zioion x i vii Jvi 39S lerr 0 M 18 4 Vapor Pressure and Humidity When the humidity is high it feels muggy it is hard for any more water to evaporate The dew point is in temperature at which the air If the temperature goes below rain may occur would be saturated with water the dew point dew fog or even Summary of Chapter 18 I The average kinetic energy of molecules in a gas is proportional to the temperature I Below the critical temperature a gas can liquefy if the pressure is high enough I At the triple point all three phases are in equilibrium I Evaporation occurs when the fastest moving molecules escape from the surface ofa liquid I Saturated vapor pressure occurs when the two phases are in equilibrium I Relative humidity is the ratio of the actual vapor pressure to the saturated vapor pressure

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