# c b N/m 2 (0.120 m m 3 ), = J. W total = W a b + W b c 2.00

Save this PDF as:

Size: px
Start display at page:

Download "c b 5.00 10 5 N/m 2 (0.120 m 3 0.200 m 3 ), = 4.00 10 4 J. W total = W a b + W b c 2.00"

## Transcription

1 Chter 19, exmle rolems: (19.06) A gs undergoes two roesses. First: onstnt m 3, isohori. Pressure inreses from P to P. Seond: Constnt P, isori. olume omressed from m 3 to m 3. () Show oth roesses in digrm: (10 5 P) () W = 0, W = Δ (for isori roesses) = N/m 2 (0.120 m m 3 ), = J. W totl = W + W 2.00 = J. (Note: Δ = finl initil.) (m 3 ) (19.08) Biyle tire um. Nozzle losed off. Slowly deress lunger until /2. Assume ir is n idel gs. Temerture T = onstnt. () Work ositive or negtive? olume redued while ressure inresed (t onstnt T). W = Û d is negtive. Tht is, to omress the gs isothermlly, work must e done to the gs. () Het flow ositive or negtive? Q = ΔU + W. Here ΔU = 0 sine T is not hnged. So Q = W is lso negtive. Tht is, for isotherml omression, het must flow out of the system (into therml reservoir, whih is so lrge tht it n sor quite n mount of het without rising its temerture reily). If het is not llowed to flow out (y using some therml insultion), then it is lled n diti omression. ΔU must then e ositive, so tht Q n e zero. The temerture of the system must therefore go u. The ressure of the system must lso rise more thn tht of the orresonding isotherml omression y the sme Δ. () Reltive mgnitudes of the het flow nd the work: They re equl, euse ΔU = 0 when T does not hnge. (For n idel gs, U deends on T only). (19.12) A gs in ylinder. onstnt ressure N/m 2. Cooled nd Comressed from 1.70 m 3 to 1.20 m 3. Internl energy dereses y J. () Work done W = N/m 2 (1.20 m m 3 ) = J. () Q = ΔU + W = ( J) + ( J) = J. Tht is, J of het must flow out of the system to the environment. [Note: For Q, flowing in is ositive. For W, oming out (doing work to the environment) is ositive.] () The gs does not hve to e idel, sine the idel gs lw hs not een used, nd we lso did not use the ft tht U is funtion of T lone.

2 (19.22) Cylinder ontins mol of helium t T = 27.0 C. () To rise the temerture to 67.0 C, keeing the volume onstnt, the het needed is Q = nc ΔT. C = (3/2) R for montomi helium gs. Therefore Q = mol (3/2) J/mol K 40 K = J. [Note: ΔT in K is the sme s ΔT in C.] () To rise the temerture to 67.0 C, keeing the ressure onstnt, the het needed is Q = nc ΔT. C = (5/2) R for montomi helium gs. Therefore Q = mol (5/2) J/mol K 40 K = J. () The differene J J = J is due to W = Δ (for isori roesses) = ( finl initil ) = nr(t finl T initil ) = mol J/mol K 40 K = J. More het is required in the se when the ressure is ket onstnt, sine then the volume will inrese s the temerture is rised, nd therefore the system will do work to the environment. (d) The gs is idel. The hnge in U is the sme s the Q t onstnt volume, nd is equl to J, euse W = 0 in this se. Beuse ΔU is th (roess) - indeendent, so the sme hnge of U lso hens in the se when the ressure is ket onstnt. This is euse ΔU = U finl U initil deends only on the initil nd finl temertures. (For n idel gs, U deends only on T.) If you lulte ΔU using the formul ΔU = Q W for the isori roess, you get the sme nswer, nmely J J = J. You n lso use the formul U = (3/2) RT to lulte ΔU for montomi gs, nd get the sme nswer. (19.38) Cylinder ontining mol of n idel montomi gs. Initilly, = P, nd = m 3. () Initil solute temerture T = /nr = N/m m 3 / mol J/mol K = K. () 2. (i) Isotherml. T finl = T initil = K. finl = initil / 2 = P. (ii) (iii) Isori. T finl = 2T initil = K. finl = initil = P. Aditi. initil initil = finl finl. = 5/3 for montomi gs. finl = initil ( initil / finl ) = P (1/2) 5/3 = P. T finl = /nr = P m 3 / mol J/mol K = K. (You n lso lulte T finl using the formul T initil -1 initil = T finl -1 finl, nd otin T finl = T initil ( initil / finl ) -1 = K (1/2) 2/3 = K.) (19.42) 0.5 mol of idel gs tken from stte to stte : () T finl = T = N/m m 3 / mol J/mol K = K. () W totl = W + W = N/m m N/m m 3 = 500 J. () T initil = T = N/m m 3 / (10 5 P) (m 3 )

3 0.5 mol J/mol K = K. Thus ΔU = 0 etween the stte nd the stte, nd therefore Q = W = 500 J for this omosite roess. This het Q is ositive, nd is therefore flowing into the system. (Note tht we n not lulte Q or Q here, sine we do not know wht tye of idel gs is involved here (montomi, or ditomi, or olytomi), nd the roess is not ny of the known roess. But we do know tht Q = Q + Q. If we were given tht the idel gs is montomi or ditomi, we would e le to lulte Q. Then Q would follow from Q Q. But we still nnot lulte Q diretly.) (19.48) n = 3 mol. Idel gs. Cyle : C = 29.1 J/mol K, : isori exnsion. : isohori redution of ressure. : diti omression. T = 300 K. T = 492 K. T = 600 K. W yle = W + W + W. W = 0. W = ( ) = nr (T T ) = 3 mol J/mol K (492 K 300 K) = 4789 J. W = (U U ) = n C (T T ) = = n (C R) (T T ) = 3 mol (29.1 J/mol K J/mol K) (600 K 492 K) = 6735J, (where we hve used Q = ΔU + W nd C = C + R). W yle = 4789 J 6735J = 1946 J. (Another wy to do W is to use the formuls = = for n diti roess, nd otin W = Û d = Û d / = ( ) / ( + 1) = ( ) / ( 1) = nr (T T ) / ( 1) = 3 mol J/mol K (492 K 600 K) / ( ) = 6734 J. (Tht we did not get 6735 J s ove is euse the given C = 29.1 J/mol K does not hve four-signifint-digits ury. Sine this seond roh does not need C it is tully more urte if n nd the temertures given re ext.) [Note tht we hve used = C / C = C / (C R).]

4 (19.54) Thermodynmi roess in solid. Cu ue, 2.00 m on side. Susended y string. (dt on Tle 14.1, 17.2, 17.3) Heted from 20.0 C to 90.0 C. = 1 tm = N/m 2. () Δ =? β = ( C) 1. Δ = β ΔT 0 = ( C) 1 (90.0 C 20.0 C) (0.02 m) 3 = m 3. () W = Δ (for isori roesses) = N/m m 3 = J. Q = m ΔT = (ρ 0 ) ΔT = [ kg/ m 3 (0.02 m) 3 ] 390 J/kg C 70 C = J. () ΔU = Q J (d) This result shows tht nd re rtilly the sme for solid euse the volume hnge under onstnt ressure s temerture is hnged is too smll to e imortnt (euse β is in generl very smll). Thus isohori nd isori roesses rtilly involve the sme Q if the temerture hnge is the sme. This is very different from the ehvior of gs, for whih C = C + R is true, whih is equivlent to = + R / M. Note tht in this reset the ehviors of liquid nd solid re similr. (19.62) System with iston ontining mol of O N/m 2 nd 355 K. Tret O 2 s idel gs. First exnds isorilly to 2 0 (from 0 ). It is then omressed isothermlly k to 0. Finlly it is ooled isohorilly k to 0. () Show ll roesses in digrm: Isori exnsion: olume inresed from 0 to 2 0, Temerture inresed. T > T (= 355 K). Isotherml omression: olume redued from 2 0 k to 0, Temerture stys onstnt. T = T > T. Isohori ooling: Temerture dros k to T = 355 K. () T = 2 T = 710 K. T = T =710 K. () mx = = 2 = N/m 2. or P. (d) W yle = W + W (W = 0.) W = 0 (2 0 0 ) = = nrt = mol J/mol K 355 K = J W = Û ( ) d = nrt Û (1/) d = nrt ln ( / ) = mol J/mol K 710 K ln (1/2) = J W yle = J J = J.

5 (19.64) System with iston ontining mol of N N/m 2 nd 300 K. Tret N 2 s idel gs. First omressed isorilly to (1/2) 0 (from 0 ). It then exnds ditilly to 0. Finlly, it is heted isohorilly to originl ressure 0. () Show ll roesses in digrm: Isori omression: olume droed from 0 to (1/2) 0, Temerture droed. Aditi exnsion: olume exnded from (1/2) 0 to 0, Temerture droed further, Isohori heting: Temerture rised k to T = 300 K. () onstnt. T = 150 K. T 1 = T 1. = 7/5 for ditomi gses. T = T ( / ) 1 (1/2) 0 0 = 150 K (1/2) 0.4 = K. () min =. But =. = ( / ) = N/m 2 (1/2) 7/5 = N/m 2 or P. Note: n lso e omuted y using = nrt, or /T = nr/ = nr/ = /T = N/m 2 / 300 K. = K ( N/m 2 / 300 K) = N/m 2. The slight differene in the fourth signifint digit is euse T is more urtely K. The error is one rt in out 6800! This ours in the fifth signifint digit in T. Whih nswer is more urte? The first one whih used =, so it did not use the lulted T. Of ourse, if one uses the mesured vlue for, insted of the theoretil vlue 7/5, it would e even more urte.

### Isothermal process on p-v, T-V, and p-t diagrams

Isotherml roess on -, T-, nd -T digrms isotherml T = T 0 = onstnt = ( 1, 1, T 0 ) = ( 2, 2, T 0 ) = nrt 0 T 1 1 T 0 Q T 0 2 W 2 1 2 1 2 T 0 T () = nrt 0 T() = T0 (T) = multivlued PHYS 1101, Winter 2009,

### PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * challenge questions

PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * hllenge questions e The ll will strike the ground 1.0 s fter it is struk. Then v x = 20 m s 1 nd v y = 0 + (9.8 m s 2 )(1.0 s) = 9.8 m s 1 The speed

### Module 5. Three-phase AC Circuits. Version 2 EE IIT, Kharagpur

Module 5 Three-hse A iruits Version EE IIT, Khrgur esson 8 Three-hse Blned Suly Version EE IIT, Khrgur In the module, ontining six lessons (-7), the study of iruits, onsisting of the liner elements resistne,

### Density Curve. Continuous Distributions. Continuous Distribution. Density Curve. Meaning of Area Under Curve. Meaning of Area Under Curve

Continuous Distributions Rndom Vribles of the Continuous Tye Density Curve Perent Density funtion f () f() A smooth urve tht fit the distribution 6 7 9 Test sores Density Curve Perent Probbility Density

### Problem Set 2 Solutions

University of Cliforni, Berkeley Spring 2012 EE 42/100 Prof. A. Niknej Prolem Set 2 Solutions Plese note tht these re merely suggeste solutions. Mny of these prolems n e pprohe in ifferent wys. 1. In prolems

### Ratio and Proportion

Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty

### Words Symbols Diagram. abcde. a + b + c + d + e

Logi Gtes nd Properties We will e using logil opertions to uild mhines tht n do rithmeti lultions. It s useful to think of these opertions s si omponents tht n e hooked together into omplex networks. To

### Homework 10. Problems: 19.29, 19.63, 20.9, 20.68

Homework 0 Prolems: 9.29, 9.63, 20.9, 20.68 Prolem 9.29 An utomoile tire is inlted with ir originlly t 0 º nd norml tmospheric pressure. During the process, the ir is compressed to 28% o its originl volume

### excenters and excircles

21 onurrene IIi 2 lesson 21 exenters nd exirles In the first lesson on onurrene, we sw tht the isetors of the interior ngles of tringle onur t the inenter. If you did the exerise in the lst lesson deling

### D e c i m a l s DECIMALS.

D e i m l s DECIMALS www.mthletis.om.u Deimls DECIMALS A deiml numer is sed on ple vlue. 214.84 hs 2 hundreds, 1 ten, 4 units, 8 tenths nd 4 hundredths. Sometimes different 'levels' of ple vlue re needed

### 5. Molecular rotation 5.1 Moments of inertia

5. Moleulr rottion 5. Moments of inerti The key moleulr prmeter needed to desribe moleulr rottions is the moment of inerti, I, of the moleule defined s I m i r i i Definition of moment of inerti. In this

### Practice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn

Prtie Test 2 1. A highwy urve hs rdius of 0.14 km nd is unnked. A r weighing 12 kn goes round the urve t speed of 24 m/s without slipping. Wht is the mgnitude of the horizontl fore of the rod on the r?

### Chapter. Contents: A Constructing decimal numbers

Chpter 9 Deimls Contents: A Construting deiml numers B Representing deiml numers C Deiml urreny D Using numer line E Ordering deimls F Rounding deiml numers G Converting deimls to frtions H Converting

### It may be helpful to review some right triangle trigonometry. Given the right triangle: C = 90º

Ryn Lenet Pge 1 Chemistry 511 Experiment: The Hydrogen Emission Spetrum Introdution When we view white light through diffrtion grting, we n see ll of the omponents of the visible spetr. (ROYGBIV) The diffrtion

### If two triangles are perspective from a point, then they are also perspective from a line.

Mth 487 hter 4 Prtie Prolem Solutions 1. Give the definition of eh of the following terms: () omlete qudrngle omlete qudrngle is set of four oints, no three of whih re olliner, nd the six lines inident

### Answer, Key Homework 8 David McIntyre 1

Answer, Key Homework 8 Dvid McIntyre 1 This print-out should hve 17 questions, check tht it is complete. Multiple-choice questions my continue on the net column or pge: find ll choices before mking your

### State the size of angle x. Sometimes the fact that the angle sum of a triangle is 180 and other angle facts are needed. b y 127

ngles 2 CHTER 2.1 Tringles Drw tringle on pper nd lel its ngles, nd. Ter off its orners. Fit ngles, nd together. They mke stright line. This shows tht the ngles in this tringle dd up to 180 ut it is not

### The remaining two sides of the right triangle are called the legs of the right triangle.

10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right

### 11. PYTHAGORAS THEOREM

11. PYTHAGORAS THEOREM 11-1 Along the Nile 2 11-2 Proofs of Pythgors theorem 3 11-3 Finding sides nd ngles 5 11-4 Semiirles 7 11-5 Surds 8 11-6 Chlking hndll ourt 9 11-7 Pythgors prolems 10 11-8 Designing

### Simple Nonlinear Graphs

Simple Nonliner Grphs Curriulum Re www.mthletis.om Simple SIMPLE Nonliner NONLINEAR Grphs GRAPHS Liner equtions hve the form = m+ where the power of (n ) is lws. The re lle Liner euse their grphs re stright

### ISTM206: Lecture 3 Class Notes

IST06: Leture 3 Clss otes ikhil Bo nd John Frik 9-9-05 Simple ethod. Outline Liner Progrmming so fr Stndrd Form Equlity Constrints Solutions, Etreme Points, nd Bses The Representtion Theorem Proof of the

### The area of the larger square is: IF it s a right triangle, THEN + =

8.1 Pythgoren Theorem nd 2D Applitions The Pythgoren Theorem sttes tht IF tringle is right tringle, THEN the sum of the squres of the lengths of the legs equls the squre of the hypotenuse lengths. Tht

### 1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply?

Assignment 3: Bohr s model nd lser fundmentls 1. In the Bohr model, compre the mgnitudes of the electron s kinetic nd potentil energies in orit. Wht does this imply? When n electron moves in n orit, the

### An Insight into Quadratic Equations and Cubic Equations with Real Coefficients

An Insight into Qurti Equtions n Cubi Equtions with Rel Coeffiients Qurti Equtions A qurti eqution is n eqution of the form x + bx + =, where o It n be solve quikly if we n ftorize the expression x + bx

### Monopolistic competition Market in which firms can enter freely, each producing its own brand or version of a differentiated product

EON9 ring 0 & 6.5.0 Tutoril 0 hter onoolisti ometition nd Oligooly onoolisti ometition rket in whih firms n enter freely, eh roduing its own brnd or version of differentited rodut Key hrteristis: Firms

### The AVL Tree Rotations Tutorial

The AVL Tree Rottions Tutoril By John Hrgrove Version 1.0.1, Updted Mr-22-2007 Astrt I wrote this doument in n effort to over wht I onsider to e drk re of the AVL Tree onept. When presented with the tsk

### Version 001 CIRCUITS holland (1290) 1

Version CRCUTS hollnd (9) This print-out should hve questions Multiple-choice questions my continue on the next column or pge find ll choices efore nswering AP M 99 MC points The power dissipted in wire

### 1. Definition, Basic concepts, Types 2. Addition and Subtraction of Matrices 3. Scalar Multiplication 4. Assignment and answer key 5.

. Definition, Bsi onepts, Types. Addition nd Sutrtion of Mtries. Slr Multiplition. Assignment nd nswer key. Mtrix Multiplition. Assignment nd nswer key. Determinnt x x (digonl, minors, properties) summry

### The Stirling Engine: The Heat Engine

Memoril University of Newfounln Deprtment of Physis n Physil Oenogrphy Physis 2053 Lortory he Stirling Engine: he Het Engine Uner no irumstnes shoul you ttempt to operte the engine without supervision:

### not to be republished NCERT POLYNOMIALS CHAPTER 2 (A) Main Concepts and Results (B) Multiple Choice Questions

POLYNOMIALS (A) Min Concepts nd Results Geometricl mening of zeroes of polynomil: The zeroes of polynomil p(x) re precisely the x-coordintes of the points where the grph of y = p(x) intersects the x-xis.

### Maximum area of polygon

Mimum re of polygon Suppose I give you n stiks. They might e of ifferent lengths, or the sme length, or some the sme s others, et. Now there re lots of polygons you n form with those stiks. Your jo is

### Simple Electric Circuits

Simple Eletri Ciruits Gol: To uild nd oserve the opertion of simple eletri iruits nd to lern mesurement methods for eletri urrent nd voltge using mmeters nd voltmeters. L Preprtion Eletri hrges move through

### Operations with Polynomials

38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply

### Thank you for participating in Teach It First!

Thnk you for prtiipting in Teh It First! This Teh It First Kit ontins Common Core Coh, Mthemtis teher lesson followed y the orresponding student lesson. We re onfident tht using this lesson will help you

### THE PYTHAGOREAN THEOREM

THE PYTHAGOREAN THEOREM The Pythgoren Theorem is one of the most well-known nd widely used theorems in mthemtis. We will first look t n informl investigtion of the Pythgoren Theorem, nd then pply this

### Sirindhorn International Institute of Technology Thammasat University at Rangsit

Sirindhorn Interntionl Institute of Technology Thmmst University t Rngsit School of Informtion, Computer nd Communiction Technology COURSE : ECS 204 Bsic Electricl Engineering L INSTRUCTOR : Asst. Prof.

### V bulb = V/N = (110 V)/8 = 13.8 V. We find the resistance of each bulb from 2 bulb bulb 7.0 W = (13.8 V) 2 /R bulb, which gives R bulb = 27 Ω.

HPTE iruits 4. We fin the internl resistne from V = r; 9.8 V = [.0 V (60 )r], whih gives r = 0.037 Ω. euse the terminl voltge is the voltge ross the strter, we hve V = ; 9.8 V = (60 ), whih gives = 0.6

### Math 22B Solutions Homework 1 Spring 2008

Mth 22B Solutions Homework 1 Spring 2008 Section 1.1 22. A sphericl rindrop evportes t rte proportionl to its surfce re. Write differentil eqution for the volume of the rindrop s function of time. Solution

### Experiment 6: Friction

Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht

### r 2 F ds W = r 1 qe ds = q

Chpter 4 The Electric Potentil 4.1 The Importnt Stuff 4.1.1 Electricl Potentil Energy A chrge q moving in constnt electric field E experiences force F = qe from tht field. Also, s we know from our study

### Angles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example

2.1 Angles Reognise lternte n orresponing ngles Key wors prllel lternte orresponing vertilly opposite Rememer, prllel lines re stright lines whih never meet or ross. The rrows show tht the lines re prllel

### Volumes by Cylindrical Shells: the Shell Method

olumes Clinril Shells: the Shell Metho Another metho of fin the volumes of solis of revolution is the shell metho. It n usull fin volumes tht re otherwise iffiult to evlute using the Dis / Wsher metho.

### SECTION 7-2 Law of Cosines

516 7 Additionl Topis in Trigonometry h d sin s () tn h h d 50. Surveying. The lyout in the figure t right is used to determine n inessile height h when seline d in plne perpendiulr to h n e estlished

### , and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.

Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge

### Math 135 Circles and Completing the Square Examples

Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for

### Or more simply put, when adding or subtracting quantities, their uncertainties add.

Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

### and thus, they are similar. If k = 3 then the Jordan form of both matrices is

Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If

### Solutions to Section 1

Solutions to Section Exercise. Show tht nd. This follows from the fct tht mx{, } nd mx{, } Exercise. Show tht = { if 0 if < 0 Tht is, the bsolute vlue function is piecewise defined function. Grph this

### Exponents base exponent power exponentiation

Exonents We hve seen counting s reeted successors ddition s reeted counting multiliction s reeted ddition so it is nturl to sk wht we would get by reeting multiliction. For exmle, suose we reetedly multily

### Final Exam covers: Homework 0 9, Activities 1 20 and GSP 1 6 with an emphasis on the material covered after the midterm exam.

MTH 494.594 / FINL EXM REVIEW Finl Exm overs: Homework 0 9, tivities 1 0 nd GSP 1 6 with n emphsis on the mteril overed fter the midterm exm. You my use oth sides of one 3 5 rd of notes on the exm onepts

### Unit 6: Exponents and Radicals

Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -

### Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.

2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this

### Homework #6 Chapter 7 Homework Acids and Bases

Homework #6 Chpter 7 Homework Acids nd Bses 18. ) H O(l) H 3O (q) OH (q) H 3 O OH Or H O(l) H (q) OH (q) H OH ) HCN(q) H O(l) H 3O (q) CN (q) H 3 O HCN CN Or HCN(q) H (q) CN (q) H CN HCN c) NH 3(q) H O(l)

### Solutions to Physics: Principles with Applications, 5/E, Giancoli Chapter 19

Solutions to Physis: Priniples with pplitions, 5/E, Ginoli Chpter 19 CHPTE9 1 When the uls re onnete in series, the equivlent resistne is series = i = 4 ul = 4(140 Ω) = 560 Ω When the uls re onnete in

Chpter 9: Qudrtic Equtions QUADRATIC EQUATIONS DEFINITION + + c = 0,, c re constnts (generlly integers) ROOTS Synonyms: Solutions or Zeros Cn hve 0, 1, or rel roots Consider the grph of qudrtic equtions.

### Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by

### Physics 43 Homework Set 9 Chapter 40 Key

Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x

### Econ 4721 Money and Banking Problem Set 2 Answer Key

Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in

### 8. Hyperbolic triangles

8. Hyperoli tringles Note: This yer, I m not doing this mteril, prt from Pythgors theorem, in the letures (nd, s suh, the reminder isn t exminle). I ve left the mteril s Leture 8 so tht (i) nyody interested

### Lesson 18.2: Right Triangle Trigonometry

Lesson 8.: Right Tringle Trigonometry lthough Trigonometry is used to solve mny prolems, historilly it ws first pplied to prolems tht involve right tringle. This n e extended to non-right tringles (hpter

### Quick Guide to Lisp Implementation

isp Implementtion Hndout Pge 1 o 10 Quik Guide to isp Implementtion Representtion o si dt strutures isp dt strutures re lled S-epressions. The representtion o n S-epression n e roken into two piees, the

### EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

### Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

### Solving Linear Equations - Formulas

1. Solving Liner Equtions - Formuls Ojective: Solve liner formuls for given vrile. Solving formuls is much like solving generl liner equtions. The only difference is we will hve severl vriles in the prolem

### 2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

### CHAPTER 31 CAPACITOR

. Given tht Numer of eletron HPTER PITOR Net hrge Q.6 9.6 7 The net potentil ifferene L..6 pitne v 7.6 8 F.. r 5 m. m 8.854 5.4 6.95 5 F... Let the rius of the is R re R D mm m 8.85 r r 8.85 4. 5 m.5 m

### Chap.6 Surface Energy

Chp.6 urfe Energy (1) Bkground: Consider the toms in the bulk nd surfe regions of rystl: urfe: toms possess higher energy sine they re less tightly bound. Bulk: toms possess lower energy sine they re muh

### 14.2. The Mean Value and the Root-Mean-Square Value. Introduction. Prerequisites. Learning Outcomes

he Men Vlue nd the Root-Men-Squre Vlue 4. Introduction Currents nd voltges often vry with time nd engineers my wish to know the men vlue of such current or voltge over some prticulr time intervl. he men

### The following information must be known for the correct selection of current measurement transformer (measurement or protection):

P 5 Protetion trnsformers P.5.01 GB Protetion trnsformers The following informtion must e known for the orret seletion of urrent mesurement trnsformer (mesurement or protetion): The pplition for whih it

### Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd

### On the Meaning of Regression Coefficients for Categorical and Continuous Variables: Model I and Model II; Effect Coding and Dummy Coding

Dt_nlysisclm On the Mening of Regression for tegoricl nd ontinuous Vribles: I nd II; Effect oding nd Dummy oding R Grdner Deprtment of Psychology This describes the simple cse where there is one ctegoricl

### 1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator

AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.

### 1. Area under a curve region bounded by the given function, vertical lines and the x axis.

Ares y Integrtion. Are uner urve region oune y the given funtion, vertil lines n the is.. Are uner urve region oune y the given funtion, horizontl lines n the y is.. Are etween urves efine y two given

### Worksheet 24: Optimization

Worksheet 4: Optimiztion Russell Buehler b.r@berkeley.edu 1. Let P 100I I +I+4. For wht vlues of I is P mximum? P 100I I + I + 4 Tking the derivtive, www.xkcd.com P (I + I + 4)(100) 100I(I + 1) (I + I

### Right Triangle Trigonometry

CONDENSED LESSON 1.1 Right Tringle Trigonometr In this lesson ou will lern out the trigonometri rtios ssoited with right tringle use trigonometri rtios to find unknown side lengths in right tringle use

### Proving the Pythagorean Theorem

Proving the Pythgoren Theorem Proposition 47 of Book I of Eulid s Elements is the most fmous of ll Eulid s propositions. Disovered long efore Eulid, the Pythgoren Theorem is known y every high shool geometry

### . At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2

7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6

0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions

### Net Change and Displacement

mth 11, pplictions motion: velocity nd net chnge 1 Net Chnge nd Displcement We hve seen tht the definite integrl f (x) dx mesures the net re under the curve y f (x) on the intervl [, b] Any prt of the

### Finite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh

Lnguges nd Automt Finite Automt Informtics 2A: Lecture 3 John Longley School of Informtics University of Edinburgh jrl@inf.ed.c.uk 25 September 2015 1 / 30 Lnguges nd Automt 1 Lnguges nd Automt Wht is

### Lesson 2.1 Inductive Reasoning

Lesson.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 1, 16,,. 400, 00, 100, 0,,,. 1 8, 7, 1, 4,, 4.,,, 1, 1, 0,,. 60, 180, 10,

Alger Module A60 Qudrtic Equtions - 1 Copyright This puliction The Northern Alert Institute of Technology 00. All Rights Reserved. LAST REVISED Novemer, 008 Qudrtic Equtions - 1 Sttement of Prerequisite

### Example

6. SOLVING RIGHT TRINGLES In the right tringle B shwn in Figure 6.1, the ngles re dented y α t vertex, β t vertex B, nd t vertex. The lengths f the sides ppsite the ngles α, β, nd re dented y,, nd. Nte

### PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive

### Know the sum of angles at a point, on a straight line and in a triangle

2.1 ngle sums Know the sum of ngles t point, on stright line n in tringle Key wors ngle egree ngle sum n ngle is mesure of turn. ngles re usully mesure in egrees, or for short. ngles tht meet t point mke

### Answer, Key Homework 10 David McIntyre 1

Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your

### AAPT UNITED STATES PHYSICS TEAM AIP 2010

2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD

### MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. W02D3_0 Group Problem: Pulleys and Ropes Constraint Conditions

MSSCHUSES INSIUE OF ECHNOLOGY Deprtment of hysics 8.0 W02D3_0 Group roblem: ulleys nd Ropes Constrint Conditions Consider the rrngement of pulleys nd blocks shown in the figure. he pulleys re ssumed mssless

### Review guide for the final exam in Math 233

Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered

### Assuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C;

B-26 Appendix B The Bsics of Logic Design Check Yourself ALU n [Arthritic Logic Unit or (rre) Arithmetic Logic Unit] A rndom-numer genertor supplied s stndrd with ll computer systems Stn Kelly-Bootle,

### Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.

The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only

### Reasoning to Solve Equations and Inequalities

Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing

### Electric Circuits. Simple Electric Cell. Electric Current

Electric Circuits Count Alessndro olt (745-87) Georg Simon Ohm (787-854) Chrles Augustin de Coulomb (736 806) André Mrie AMPÈRE (775-836) Crbon Electrode () Simple Electric Cell wire Zn Zn Zn Zn Sulfuric

### Maths Assessment Year 4: Number and Place Value

Nme: Mths Assessment Yer 4: Numer nd Plce Vlue 1. Count in multiples of 6, 7, 9, 25 nd 1 000; find 1 000 more or less thn given numer. 2. Find 1,000 more or less thn given numer. 3. Count ckwrds through

### In the following there are presented four different kinds of simulation games for a given Büchi automaton A = :

Simultion Gmes Motivtion There re t lest two distinct purposes for which it is useful to compute simultion reltionships etween the sttes of utomt. Firstly, with the use of simultion reltions it is possile

### FEASIBILITY OF USING PRESSED SUGAR CANE STALK FOR THE PRODUCTION OF CHARCOAL. D Ffoulkes, R Elliott and T R Preston

Trop Anim Prod 1980 5:2 125 FEASIBILITY OF USING PRESSED SUGAR CANE STALK FOR THE PRODUCTION OF CHARCOAL D Ffoulkes, R Elliott nd T R Preston Fcultd de Medicin Veterinri y Zootecni, University of Yuctn,

### Real Analysis HW 10 Solutions

Rel Anlysis HW 10 Solutions Problem 47: Show tht funtion f is bsolutely ontinuous on [, b if nd only if for eh ɛ > 0, there is δ > 0 suh tht for every finite disjoint olletion {( k, b k )} n of open intervls

### Sequences and Series

Centre for Eduction in Mthemtics nd Computing Euclid eworkshop # 5 Sequences nd Series c 014 UNIVERSITY OF WATERLOO While the vst mjority of Euclid questions in this topic re use formule for rithmetic