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### thermo_problems

Course: PHYSICS 141, Fall 2010
School: SUNY Stony Brook
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Word Count: 270

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In 1 Problems . chapter 20. 4, 6, 7, 20, 63, 69, 77, 71part a (1) 1. Adiabatic Expansion (a) Starting from dW = pdV show that the work done during an adiabatic expansion is W= 1 [P1 V1 P2 V2 ] 1 (2) where is the adiabatic index (b) For an ideal gas expansion explain why dU = nCv dT . Use this to show that U = nCv (Tf Ti ) (3) (c) Show that for an adiabatic expansion U = W . Show that the expressions...

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In 1 Problems . chapter 20. 4, 6, 7, 20, 63, 69, 77, 71part a (1) 1. Adiabatic Expansion (a) Starting from dW = pdV show that the work done during an adiabatic expansion is W= 1 [P1 V1 P2 V2 ] 1 (2) where is the adiabatic index (b) For an ideal gas expansion explain why dU = nCv dT . Use this to show that U = nCv (Tf Ti ) (3) (c) Show that for an adiabatic expansion U = W . Show that the expressions given in Eq. 2 and Eq. 3 are consistent with this 2. Internal Combustion Engines: Briey explain how an internal combustion engine works. Draw a PV cycle. Indicate the dierent piston strokes work in conjuction with this cycle. Whats the role of the crankshaft and the camshaft? Extra Credit: What are the design constraints of the compression stroke? What are the design constraints of the ignition stroke? 3. 1 Sound At a lound concert the band plays close to the threshold of pain. The sound level is 100dB one meter away from a loundspeaker which broadcasts in all directions. (a) Determine determine the sound level 1 km away. (b) Is this soft/loud/inaudible? (c) What is the pressure deviation from equilibrium relative to atmospheric pressure (1 atm 1bar = 105 N/m2 remember!) one meter from the loadspeaker 4. Sound 2 The following picture shows the Pressure measured while beating two frequencies f1 and f2 . P Beats 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 0 2 4 6 8 10 time in units of milli sec (a) Estimate from the gure these two frequencies. You may nd it convenient to work the next problem rst. (b) Show that the sum of two sin waves sin(2f1 t) and sin(2f2 t) can be written as a product of sin and cos waves. 1
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SUNY Stony Brook - PHYSICS - 141
SUNY Stony Brook - PHYSICS - 141
1Problems.15.27, 15.37, 15.41, 15.79(1)1. (Estimates) Estimate the mass per length of a double bass string. The lowest note on the bass is anE 1, ringing in at a cool 41 Hz just above human hearing. Based on the picture below, estimate thewavelengt
SUNY Stony Brook - AST - 346
Exam # 1 SolutionsLots of partial credit given, so give at least a qualitative answer to each item. Someuseful constants are given at the end of the exam.1. Extensive spectral observations often show two peaks in high excitation emission molecular line
SUNY Stony Brook - AST - 346
Exam # 2, 10 MayLots of partial credit given, so give at least a qualitative answer to eachitem. Some useful constants are given at the end of the exam.1. In this problem, you will explore a closed box model for galacticchemical evolution in the disk.
SUNY Stony Brook - AST - 346
Homework # 1, due 10 Feb1. Show that an extinction of A = 1 magnitude leads toa ux F decrease to 40% of its original value.2. Assuming dust grains are 0.1 m in radius, that thegas density in the ISM is nH = 1 cm3, and the number density of dust grains
SUNY Stony Brook - AST - 346
Homework # 1 Solutions1. Show that an extinction of A = 1 magnitude leads to a ux F decrease to40% of its original value.1 magnitude is equivalent to a reduction of intensity of 102/5 = 0.398.2. Assuming dust grains are 0.1 m in radius, that the gas d
SUNY Stony Brook - AST - 346
Homework # 2, due 17 Feb1. Suppose the initial mass function is the Salpeter mass function with a lowmass cuto of 0.1 M and a high-mass cuto of 100M . Determine thenormalization from the local disk column mass density (i.e., the number densityintegrate
SUNY Stony Brook - AST - 346
Homework # 2 Solutions1. Suppose the initial mass function is the Salpeter mass function with a lowmass cuto of 0.1 M and a high-mass cuto of 100M. Determine thenormalization from the local disk column mass density (i.e., the number densityintegrated v
SUNY Stony Brook - AST - 346
Homework # 3, due 24 Feb1. Calculate the size of a Stromgren sphere in a gas of density 103 cm3 surrounding an O3 star. This is the volume of gas nearly completely ionized bythe star. Assume the recombination rate of protons and electrons to formneutra
SUNY Stony Brook - AST - 346
Homework # 3 Solutions1. Calculate the size of a Stromgren sphere in a gas of density 103 cm3 surrounding an O3 star. This is the volume of gas nearly completely ionized bythe star. Assume the recombination rate of protons and electrons to formneutral
SUNY Stony Brook - AST - 346
Homework # 4, due 3 Mar1. In this problem, you are asked to calculate the expected extinctionfrom a cool cloud. Assume it is spherical and located at a distanceof 100 pc from the Earth. Assume the cloud is isothermal witha temperature of 10 K. Assume
SUNY Stony Brook - AST - 346
Homework # 4 Solutions1. In this problem, you are asked to calculate the expected extinction from a coolcloud. Assume it is spherical and located at a distance of 100 pc from theEarth. Assume the cloud is isothermal with a temperature of 10 K. Assume i
SUNY Stony Brook - AST - 346
Homework # 5, due 10 Mar1. In example given in the notes describing the observations of collapsing clouds, it is indicated in some cases that there is a locusof points for which vr is constant. vr is the radial velocity seen byan observer in the z dire
SUNY Stony Brook - AST - 346
Homework # 5 Solutions1. In example given in the notes describing the observations of collapsing clouds, it is indicated in some cases that there is a locusof points for which vr is constant. vr is the radial velocity seen byan observer in the z direct
SUNY Stony Brook - AST - 346
Homework # 6, due 22 Mar1. Demonstrate that the temperature applicable to a stellar systemism &lt; v 2 (x) &gt;T=3kwhere it is assumed that the stars have equal mass m, v (x) is thevelocity of a star relative to the center-of-mass, and &lt;&gt; representsan a
SUNY Stony Brook - AST - 346
Homework # 6 Solutions1. Demonstrate that the temperature applicable to a stellar system isT=m &lt; v 2 (x) &gt;3kwhere it is assumed that the stars have equal mass m, v (x) is the velocity of astar relative to the center-of-mass, and &lt;&gt; represents an ave
SUNY Stony Brook - AST - 346
Homework # 7, due 7 Apr1. In 1959, Kopal determined that the Roche lobe radius RR withnearly the same volume as the Roche lobe surrounding the starm which is orbiting the star M isRR = 0.46D1/3m.M+mD is the distance between the stars and they are
SUNY Stony Brook - AST - 346
Solutions for Homework # 71. In 1959, Kopal determined that the Roche lobe radius RR withnearly the same volume as the Roche lobe surrounding the starm which is orbiting the star M isRR = 0.46D1/3m.M+mD is the distance between the stars and they
SUNY Stony Brook - AST - 346
Homework # 8, due 26 Apr1. Show that a simple closed-box model with instantaneous recyclingresults in the gas-phase metallicity increasing linearly with time.If this is true, what cosmic time does [Fe/H]=-3 correspond to?Also show in this model that t
SUNY Stony Brook - AST - 346
Homework # 8 Solutions1. Show that a simple closed-box model with instantaneous recycling results inthe gas-phase metallicity increasing linearly with time. If this is true, whatcosmic time does [Fe/H]=-3 correspond to?From the notes, we see that Z =
SUNY Stony Brook - AST - 346
Homework # 9, due 3 May1. Do problem 5.8 in the text.2. Do problem 5.13 in the text. Determine the ratio of the two areasof the zones in the disk where 2 and 4 armed spirals are stable.Does this depend on the value of p ?3. Do problem 5.15 in the tex
SUNY Stony Brook - AST - 346
Homework # 9 Solutions1. Do problem 5.8 in the text.Using V 2 = GM(&lt; r )/r , and using (r ) = (3a2 M/4 )(a2 + r 2 )5/2 wend3/2M (&lt; r ) = Mr 3 a2 + r 2andV (r ) =GMr a2 + r 23/4.The maximum occurs when 3r 2 /2 = r 2 + a2 or r = 2a.The spider di
SUNY Stony Brook - AST - 346
Homework # 10, due 9 May (no penalty up to 17 May)1. Compute the deection angle of a star whose light just grazes thelimb of the Sun. Also compute the deection angle of a star whoselight just grazes the limb of a 1.4M neutron star, if the neutronstar
SUNY Stony Brook - AST - 346
Homework # 10 Solutions1. Compute the deection angle of a star whose light just grazes the limb of theSun. Also compute the deection angle of a star whose light just grazes thelimb of a 1.4M neutron star, if the neutron star was at the same distancefr
SUNY Stony Brook - AST - 346
Major Topics1. IntroductionStars, the Milky Way, Other Galaxies, Cosmology2. The Galaxy and its ComponentsLuminosity/Mass Functions, Distances, Clusters, Rotation3. The Interstellar MediumGas, Dust, Emission and Absorption4. Galactic DynamicsGravi
SUNY Stony Brook - AST - 346
The Local Milky Way Color-Magnitude Diagram15,630 starsd &lt; 100 pcM0age dierencesHalf of stars withMV &gt; 10 are notdetected.metallicity dierenceswhite dwarfsJ.M. LattimerAST 346, Galaxies, Part 2red giantsF0 G0 K0 red clumpDistances from Hipp
SUNY Stony Brook - AST - 346
Importance of the Interstellar MediumGas has important diagnosticpropertiesRole in the star/gas cyclefacilitates ongoing starformationrepository for element buildup;integral for chemical evolutionGas can cool, so its collapse isdissipationalHot
SUNY Stony Brook - AST - 346
Stellar DynamicsStellar systems vs. gasesGravitational potentialSpherical and disk potentialsOrbits in the stellar neighborhoodOrbits of single starsOrbits of stars in clustersThe virial theoremMeasuring masses from motionsEective potentials and
SUNY Stony Brook - AST - 346
The Local Group and Galactic EvolutionThe Local GroupSatellite GalaxiesCepheid VariablesTides and the Roche LimitLocal SpiralsChemical EvolutionDwarf GalaxiesFuture of the Local GroupJ.M. LattimerAST 346, Galaxies, Part 5The Local GroupJ.M. La
SUNY Stony Brook - AST - 248
AST 248The Search for Life in the UniverseJames Lattimerlattimer@astro.sunysb.eduDepartment of Physics &amp; Astronomy449 ESS Bldg.Stony Brook UniversityLattimer, AST 248, Lecture 1 p.1/8Course ComponentsOfce Hours: 2:30 3:30 Tu, W, Th, ESS 449Exams
SUNY Stony Brook - AST - 248
The Sun: Example of Radiation Laws= 4 1033 erg/sLUse Wiens Law to nd the surface temperature of the Sun:T = 0.29 cm/max 6000 KInvert the blackbody luminosity formula to derive the solar radius:Yellow color means that the peak wavelength of the Suns
SUNY Stony Brook - AST - 248
Galaxies Galaxies are self-gravitating systems containing billions The observed universe has billions of galaxies. We live in a Galaxy known as the Milky Way. Galaxies dont exist randomly in space, but tend to cluster.S. Harrisof stars and having di
SUNY Stony Brook - AST - 248
Star Formation Dense cores of molecular clouds collapse into hotplasma which eventually triggers nuclear reactions. Release of gravitational energy both heats thematerial and produces infrared radiation. Conservation of angular momentum requires spin
SUNY Stony Brook - AST - 248
Radioactive DatingNucleus Sm147 Rb87 Th232 U238 K40 U235 I129 Al26 Cl36 Kr81 C14 H3 (tritium) Decay Product Nd143 Sr87 Pb208 Pb206 Ar40 Pb207 Xe129 Mg26 Ar36 Br81 N14 He3 Half Life 106 Gyr 48.8 Gyr 14.4 Gyr 4.47 Gyr 1.25 Gyr 0.70 Gyr 15.7 Myr 717,000 yr
SUNY Stony Brook - AST - 248
Determining Earth's Interior StructureSeismic (Body) Waves P waves Compressional or longitudinal (analogous to sound waves in air), can travel through fluid, solid and gaseous materials. P means primary, because they travel faster and arrive sooner. S
SUNY Stony Brook - AST - 248
Unity of LifeAll lifeforms on Earth have a common system. Examples:universal usage of DNA to store genetic informationthe ribosome technique of protein synthesisproteins serve as enzymes and catalyststhe same 20 amino acids are always used, and only
SUNY Stony Brook - AST - 248
Chemical Evolution Theory of Lifes Origins1. the synthesis and accumulation of small organic molecules, or monomers, such asamino acids and nucleotides. Production of glycine (an amino acid)energy3 HCN + 2 H2 O C2 H5 O2 N + CN2 H2 .Production of ade
SUNY Stony Brook - AST - 248
Development of ComplexityCatastrophe TheoryConsider a potential functionV (x) = x3 + ax.When a &lt; 0 there is both astable minimum (dots) and anunstable maximum in thepotential.As a is slowly increased, theequilibrium system movessmoothly to small
SUNY Stony Brook - AST - 248
Catastrophes and EvolutionExtinction was not widely accepted before 1800.Over 99% of all species that have ever existed are now extinct.Extinction was established as a fact by Georges Cuvier in 1796, and was criticalfor the spread of uniformitarinism
SUNY Stony Brook - AST - 248
Facts Concerning the Solar SystemAll the planets roughly orbit the Sun in a plane.The planets differ in composition: the planets nearest the Sun tend to be small,dense and metal-rich, whereas the planets farthest from the Sun tend to be large,light an
SUNY Stony Brook - AST - 248
Mars in HistoryLattimer, AST 248, Lecture 19 p.1/16Mars in HistoryLattimer, AST 248, Lecture 19 p.2/16Lattimer, AST 248, Lecture 19 p.3/16MarsMass (1/10), radius (1/2) and atmosphere(.7.9%) smaller than Earths.Rotation rate is nearly that of Earth
SUNY Stony Brook - AST - 248
Giant PlanetsMass, radius, rotation rate and atmosphere aresignicantly larger than Earths.Overall compositions similar to Suns except thatheavy elements are 510 times more abundant:6070% H, 2530% He, 515% C, N, O, Si, S, Fe, etc.Gaseous envelope and
SUNY Stony Brook - AST - 248
www.nineplanets.orgLattimer, AST 248, Lecture 21 p.1/17TitanOnly moon with substantial atmosphere,1.5 times EarthsSaturns largest satellite and second largestin Solar SystemAtmosphere a result of relatively coldtemperature and high gravityMajor g
SUNY Stony Brook - AST - 248
Uniqueness of Earth?Sun has sufcient Main Sequence lifetime for life to develop and evolve.The size of Earth large enoughformed with signicant but not too largeatmosphere. Varying luminosity of Sun compensated by greenhouse effect.Has large moon that
SUNY Stony Brook - AST - 248
The Drake Equationns , total number of stars in Galaxy of the right type (6 billion)f , fraction on which life actually develops (100%)L, average lifetime of civilizationsfp , fraction of these stars with planets (5%)ne , average number of planets or
SUNY Stony Brook - AST - 248
Communication by RadioAdvantages:Speed: velocity of light exceeds physical transportation speedsCost is small compared to space voyages or probesCommonly used bands in the radio spectrum.What determines the choice of communication frequency?1. Econo
Ateneo de Manila University - ACC - 101\
CHAPTER 17FINANCIAL PLANNING AND FORECASTING(Difficulty: E = Easy, M = Medium, and T = Tough)Multiple Choice: ConceptualEasy:Percent of sales method1.The percentassumptions?ofAnswer: esalesmethodisbasedonwhichoftheDiff: Efollowinga.
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CHAPTER 4THE FINANCIAL ENVIRONMENT:MARKETS, INSTITUTIONS, AND INTEREST RATES(Difficulty: E = Easy, M = Medium, and T = Tough)Multiple Choice: ConceptualEasy:Financial markets1.Answer: cDiff: EA secondary market.A physical location auction mark
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5 2008 6 2009 20%. 3 2008. . 2008 1 , 250,000 ,500,000 250,000 . 5% 30%. . = (
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ArchaeologyFrom Wikipedia, the free encyclopediaFor the magazine about archaeology, see Archaeology (magazine).Excavations at the site of Gran Dolina, in the Atapuerca Mountains, Spain, 2008Archaeology,or archeology[1] (from Greek , archaiologia , ar
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The Silver AgeRay Palmer is a physicist and professor at Ivy University in Ivy Town, New England, specializing in mattercompression as a means to fight overpopulation, famine and other world problems. Using a mass of whitedwarf star matter that he find
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Carter Corp's sales are expected to increase from \$5 million n 2008 to \$6 million in 2009or by 20%. Its assets totaled \$3 million at the end of 2008. Carter is at full capacity so itsassets must grow in proportion to projected sales. At the end of 2008
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CHAPTER2FINANCIAL STATEMENTS, CASH FLOW, AND TAXES(Difficulty: E = Easy, M = Medium, and T = Tough). Balance sheetBelow are theBoomerangs:Diff: E2001and2002year-endbalanceAssets:CashAccounts receivableInventoriesTotal current assetsNet f
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F IN3320ExamTwo;Chapters581. You plan to analyze the value of a potential investment by calculating the sum of thepresent values of its expected cash flows. Which of the following would lower thecalculated value of the investment?a. The cash flows ar
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CHAPTER 4Financial Forecasting,Planning, and BudgetingCHAPTER ORIENTATIONThis chapter is divided into two sections. The first section includes an overview of the roleplayed by forecasting in the firm's planning process. The second section focuses on
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Chapter 4Financial Planning and Forecasting FinancialStatementsANSWERS TO END-OF-CHAPTER QUESTIONS4-1a. The operating plan provides detailed implementation guidancedesigned to accomplish corporate objectives.It details who isresponsible for what p
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Chapter 4Financial Planning and Forecasting FinancialStatementsANSWERS TO END-OF-CHAPTER QUESTIONS4-1a. The operating plan provides detailed implementation guidancedesigned to accomplish corporate objectives.It details who isresponsible for what p
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Chapter 5Valuing StocksMULTIPLE CHOICE1. The first public sale of company stock to outside investors is called a/ana.|seasoned equity offering.|b.|shareholders meeting.|c.|initial public offering.|d.|proxy fight.|ANS: C DIF: E REF: 5.2 Primary Mark
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Minerals: Building Blocks of Rocks1Minerals: Building Blocks of Rocks begins with an explanation of the difference between a mineral and arock, followed by a formal definition of a mineral. Elements, atoms, compounds, ions, and atomic bondingare expla
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Chapter 1: Minerals: Building Blocks of RocksMultiple Choiceb.c.d.e.1. All silicate minerals contain the elements_.a. silicon and iron1silicon and magnesiumsilicon and calciumsilicon and sodiumsilicon and oxygen2. The most abundant element i