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Spring 2004 PHY 2053C: College Physics A

L15—Ch13Ch14. Spring 2004 PHY 2053C: College Physics A. Motion, Forces, Energy, Heat, Waves Dr. David M. Lind Dr. Kun Yang Dr. David Van Winkle. Today: Kinematic Theory of Gas Ideal Gas Law PV=nRT Maxwell distribution Internal energy Heat Heat: definition Specific Heat

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Spring 2004 PHY 2053C: College Physics A

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  1. L15—Ch13Ch14 Spring 2004PHY 2053C: College Physics A • Motion, Forces, Energy, Heat, Waves • Dr. David M. Lind • Dr. Kun Yang • Dr. David Van Winkle Today: • Kinematic Theory of Gas • Ideal Gas Law PV=nRT • Maxwell distribution • Internal energy • Heat • Heat: definition • Specific Heat • Thermal conductivity • \\

  2. Temperature, Heat, & Thermodynamics:Introduction So far we have looked at properties of macroscopic objects. • In order to study the subjects of temperature, heat and thermodynamics, we need to understand what happens microscopically. • The correct understanding of these subjects depends on the knowledge of the micro-structure of matter and leads to the atomic theory of matter. • The building blocks of matter are the atoms of the chemical elements, molecules of the chemical compounds, and crystalline solids.

  3. Atomic Theory of Matter Democritos: Matter can be divided into very small units, which are indivisible: atoms. • All atoms of a given chemical element are identical. • Z ProtonsZ Electrons(here 2) • N Neutronsadd to atomic mass • Zis chemical element number(here 2=Helium) • A = Z+Nis mass number(here 4 =>4He) • Atomic Mass ≈ (Z+N) * 1u(here 4u) • where 1u=1.66 x 10 -27kg “atomic mass unit” • Mole: definition 1 mole contains1 NA= 6.022x1023atoms. “Avagadro’s number” 1 moleweighsAgrams.(4g He = 1 mole)

  4. Question: Atoms • A slightly irritated Taxi-Driver tells you that the solution to all health problems lies in a certain powder (which you can mail-order) containing “activated micro-hydrogen”. • You reply:1) You ask him if his finances have improved since he is taking the powder2) You answer: There is only one type of hydrogen, all “hydrogen” atoms are of the same size and he might just as well drink clear water. 3) You ask him if he is talking about tritium (a radioactive isotope of hydrogen), in which case you call the CIA4) You tell him that you have had better experiences with fat-dissolving hydrocarbons (if you're over 21, that is).5) All of the above

  5. Brownian Motion Atomic Theory: Temperature is connected tounordered (random) motion of atoms and molecules. • Observation: (Thermal Equlibrium) Bring hot and cold objects in contact and they will eventually equalize their temperatures.

  6. Thermal Expansion expansion joint in roadway. Most substances expandwith increasing Temp. • The expansion is a result of increased vibrational motion at the atomic level. • We write • , where α is a material constant. • typical values (around 20° C) • Glass α= 9 x 10-6 (°C)-1 • Aluminum α= 25 x 10-6 (°C)-1 • Water α= 210 x 10-6 (°C)-1 Eiffel Tower gains about 1/5th cm for each Celcius degree of temperature rise.

  7. Thermometers Most materials expandwith higher Temperature  can be used to measure temperature • (a) Liquid-in-glass thermometer:as liquid in reservoir expands(by a few %), the level varies in narrow tube. • (b) bi-metallic strip-therm.two metals with different expansion properties bend with temperature • (c) Thermocouple (electric voltage function of temperature)

  8. Temperature Scales Temperature was measured long before people understood brownian motion. Historic units are arbitrary: Fahrenheit: • lowest Temp. that winter = 0°F • his body Temp.: = 100°F (he had a fever!) Celsius scale: (“centigrade”) • water freezing temp. = 0°C(= 32°F) • water boiling temp. = 100°C (= 212°F) TC = 5/9(TF - 32°) TF = (9/5TC) + 32°

  9. Absolute Temperature • How cold can things get? Both Celsius and Fahrenheit defined 0° to be some arbitrary point. • If we think about the analogy: temperature <=> random motion zero temperature <=> NO random motion then there must be anabsolute zero Temperature! • This point is reached at -273°C (-459°F). • There can never be anything colder than this. Absolute Temperature: Kelvin scale • Degrees Kelvin = degrees Celsius above absolute zero T(K) = T(°C) – 273 Lord Kelvin, born William Thompson (1824-1907)

  10. Ideal Gas Law Pressure*Volume = no.moles * R * Temp. • R=8.315 J/(mol Kelvin) “universal gas constant” =0.0821 (L atm)/(mol K) • absoluteTemperature is used ! • absolutePressure is used ! What is an “ideal” gas T?-- well above liquefication point • We use: PV (=P1V1 = P2V2) = constant(if T and n constant) “Boyle's law” P/T (=P1/T1 = P2/T2) = constant(if V and n constant) “Gay-Lussac law”

  11. Question • You have 1 mole of Hydrogen (atomic mass 2) and 1 mole of O2 (molecular mass 32), both at atmospheric pressure and room temperature. • 1.) Oxygen occupies a larger volume • 2.) They occupy the same volume • 3.) Helium occupies a larger volume • 4.) That depends on the density of the surrounding gas.

  12. Kinetic Gas Theory • Atoms/Molecules bounce off the walls: • The pressure exerted by a gas comes from the rate at which atoms/molecules bounceper surface area timestheir average momentum • Many, many atoms are in the air around you  you “feel” no bouncing, but constant pressure. • Temperature is related to average kin. energy

  13. 1 3 2 KE m v k T B 2 2 Kinetic Gas Theory Temperature: unordered (random) motion of atoms. definition:“average kinetic energy of one atom/molecule” ~temperature wherekB=1.38 x 10-23 J/K The atoms/molecules have a wide range of different speeds. (called theMaxwell distribution) Notice: this is dependent both on atomic/molecular mass and on temperature.

  14. 1 3 2 KE m v k T B 2 2 3 J 23 1.38 10 297 K KE 2 K 1 1 21 2 2 = 6.14 10 J m v m v rms 2 2 27 26 32 1.67 10 kg 5.3 10 kg m O 2 2 m KE => 481 214 mph v rms s m O 2 example:Speed of Molecules • speed of air-molecules around you. • for air (O2) at 24 °C = 297 K,

  15. 1 3 2 KE m v k T B 2 2 Ideal Gases:Temperature, Heat, and Internal Energy Let's first look at gas of single atoms (He, Ar, Kr ..) • Here: the kinetic energy is the only energy an atom can have where kB=1.38 x 10-23 J/K • The total internal energy U in this case is: the number of atoms times kinetic energy per atom • Heat transferred increases internal Energy Q U

  16. Questions • Question A 100-g piece of steel (A) is at 200°C (473 K) and a 200-g piece of steel (B) is at 100°C (373 K). Which one has higher average KE per atom? 1) A 2) B 3) same • Question Which object has the higher internal energy? 1) A 2) B 3) same

  17. example:Heat capacity of Helium How much heat is required to raise the temperature of 1 kg of Helium by 1 °C? • For the single-atom gas Helium: How many moles is 1kg? • (Mass number 4: 4g He is one mole) • 250 moles! 3 Q U n R T 2 J 3 250 mol 8.315 1 3118 Q K J mol 2 K

  18. Internal Energy:Molecular Gases Different materials have different forms of internal energy: (“degrees of freedom”) • In addition to linear KE, • Molecules may have rotational KE • Molecules may have elastic Potential E. • The more degrees of freedom, the higher the specific heat capacity! U N KE rot.KE P.E 3 2 1 = k T k T k T B B B 2 2 2 1 k T = number of dimensions x B 2 energy forms

  19. V P=F/A Real Gases, Condensation:Water and Vapor • Raise Pressure, lower Temp=> • condensation. (gas to liquid) • gas and liquidco-exist (vapor) until all is converted. P P T=high T=low T(°C) V

  20. Heat Originally, heat was thought to be a separate quantity, connected to Temperature. Heatisenergy. Mechanical energy can become heat through friction. symbol: Q unit: 1 J = “1 Joule” unit: 1 cal = Heat required to raise 1g of Water: Temp +1 C° (1 kcal = 1 Cal) James Prescott Joule (1818-1889): showed that you can raise temperature by mechanical work KE Q mgh

  21. demo: “melting races” Al, Fe, Pb Specific Heat Different materials require different amount of Q to change their temperature! The difference is called: • Specific Heat c:the amount of Heat required to raise the temperature of 1 kg of given material by 1 °C. • positive Q “heats up”, negative Q “cools down” • Several examples:cWater= 4186 J/(K kg) cGlass= 840 J/(K kg) cIron= 450 J/(K kg) cProtein= 1700 J/(K kg) cAluminumn= 900 J/(K kg) clead= 128 J/(K kg) Q c m T

  22. Heat and Temperature • Heat will flow from higher to lower temperature. • Heat is transfer of energy, and energy is conserved,so: Q2 = -Q1 • +Q will raise T2, while-Q will lower T1=> until T1=T2 and Heat stops flowing. • Heat is the change of the internal energyU !

  23. Heat and Temperature: Thermal conductivity • The rate of heat flow is proportional to the thermal conductivity of the materials. Q/t = kA (T1-T2)/l • several examples:kcopper= 380 J/(s m °C) kice= 2 J/(s m °C) kAluminum= 200 J/(s m °C)kGlass= 0.84 J/(s m °C) ksteel= 40 J/(s m °C) kstyrofoam= 0.010 J/(s m °C)

  24. Question • A 100-g piece of steel (A) is at 200°C and a 200-g piece of steel (B) is at 100°C. • Which object gains internal energy when the two are in contact? • 1) A • 2) B • 3) none

  25. Stay tuned... • Friday:CAPA10/Recitation Monday:Chapter 14 (cont.): • More Calorimetry • Latent Heat • Heat Exchange Wednesday:Mini-Exam#5 (chapters 9, 13)

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