Lecture07

Lecture07 - Physics 7A-2 (C/D) Professor Chertok Fall, 2008...

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Unformatted text preview: Physics 7A-2 (C/D) Professor Chertok Fall, 2008 Lecture 7 Original presentations copyright M. Chertok 2008. All rights reserved. Questions? Outline for today Veterans Day Quick recap from DLM12 What’s ahead this week Reading / Quiz M. Chertok, Physics 7A 3 Veterans Day As I’ve added to the website: Veterans Day schedule: No DLs meet on 11/11 No Office Hours Held on 11/11 DLM14 starts on Friday, 11/14 You will have 1 fewer DLM than usual “this” week Next quiz: Friday, Nov. 14 Only covers through DLM 12 plus its FNTs followed up in DLM 13 M. Chertok, Physics 7A 4 Veterans Day Teaching schedule for DLM13: 1 Chance: 11/7 2 Pat: 11/7 3 Pat: 11/10 4 Ruggero: 11/12 5 Ruggero: 11/13 6 Peter: 11/12 7 Nicholas: 11/12 8 Kevin: 11/13 9 Sergey: 11/13 10 Guillermo: 11/13 11 Nicholas: 11/13 Some of these are changed. The other DLM is not held (double check with your TA!) M. Chertok, Physics 7A 5 In DLM 12 You probably got through Addenda with additional FNTs from DLM11 available on website if you didn’t get these 3.3.1 Modes and Equipartition 25 cyan atoms + 15 red atoms... 3.3.2 Using Modes to Interpret Data Etot vs T graph for 50 atoms 3.3.3 Follow up of rest of FNTs from DLM11 Which has greater Ethermal... ? M. Chertok, Physics 7A 6 Using modes to interpret data Now in DLM 13 compartment of your refrigerator? How do the algebraic relationships relate to the graph? Which parts? What is the relationship? These are the kinds of questions you need to be asking yourself and getting confident about. You want to practice using this representation enough so that it really does become a useful tool to make sense of thermal phenomena and to be comfortable using it to construct explanations for particular phenomena. Energy Added or Removed (at constant pressure) flip this about y=x line total energy } Temp Within one phase, what is ΔEtotal? What is slope? M. Chertok, Physics 7A 7 total energy Microscopic basis of heat cap. Temp Within one phase: Q = ΔEth Also: ΔEtot = ΔEth Slope: ΔEtot/ΔT = ΔEth/ΔT Thus, slope = Q/ΔT This means the slope is the heat capacity! M. Chertok, Physics 7A 8 total energy Microscopic basis of heat cap. Temp Assume 1 mole: slope = cvm (If the volume changes, then some Work is done by the heat, and the result changes = cmp) for 1 particle: Eth/mode = ½kBT for 1 mole: Eth/mode = ½kBNAT = ½RT Thus, ΔEth/mode = ½R ΔT cvm = ΔEth/ΔT = ½R(#modes/atom) M. Chertok, Physics 7A 9 total energy Microscopic basis of heat cap. Temp cvm = ΔEth/ΔT = ½R(#modes/atom) We’ve connected specific heat to modes and equipartition! M. Chertok, Physics 7A 10 Compare with data Examine cvm data for monoatomic gases diatomic gases triatomic gases solids By counting modes, predict (ok, verify) these using model Study graph on p. 55 Heat capacities drop at low temperature. Why? M. Chertok, Physics 7A 11 Monoatomic gases Translation in 3 spatial directions ∴3 modes M. Chertok, Physics 7A 12 Diatomic gases 3 translations, + at low temp: 2 rotations at high temp: 2 rotations plus 1 vibrational spring This means additional 1 KE + 1 PE mode M. Chertok, Physics 7A 13 Clicker question At high temperature, diatomic molecules have a) 3 active modes b) 6 active modes c) 7 active modes d) what’s a mode? M. Chertok, Physics 7A 14 Triatomic gases Additional rotation(s) depending on symmetry Many more vibrational modes M. Chertok, Physics 7A 15 Symmetry? M. Chertok, Physics 7A 16 Solids & Liquids Our 3 spring model: 3 PE + 3 KE = 6 modes M. Chertok, Physics 7A 17 capacities to the number of modes you would predict the substances to have using t thermal energy. Substance The data molar Cv 12.52 12.68 12.45 12.52 20.80 20.44 20.98 20.74 28.17 28.39 27.36 24.6 24.8 27.7 25.3 26.3 Monatomic Gases Helium Neon Argon Xenon Diatomic Gases N2 H2 O2 CO Triatomic Gases CO2 N2O H2S Solids Aluminum Copper Mercury Silver Iron What trends do you see? Why is the “mole” a good unit? M. Chertok, Physics 7A 18 vaporization presented in Chapter 1, we would expect our models to provide us with the capability of explaining the heat capacity values, both at constant pressure and at constant volume for a large range of substances. Several of these data patterns are presented on this and the next page. Heat capacities vs. T CH4 NH3 Cvm R 9.5 8.5 7.5 6.5 5.5 4.5 3.5 N2 2.5 1.5 H2 Monatomic gases (He, Ar, Ne, etc.) 1000 1500 5 2 3 2 CO2 Cl2 7 2 This first graph shows the constant volume molar heat capacity of several gases from room temperature up to several thousand kelvin. The values of the heat capacities have been divided by the gas constant, R. There are several obvious trends. The monatomic vm gases have the lowest molar constant-volume heat capacity at 3/2 R and the values are independent of temperature. Diatomic gases seem to have higher values starting at about 5/2 R, while polyatomic gases have significantly larger values, but also a much more pronounced temperature dependence. These are some of the trends our models should enable us to provide explanations for. Clicker question: What is C /R ? a) #modes b) #modes*2 c) #modes/2 d) (1/2)mv2 e) NA 300 500 2000 T [Kelvin] M. Chertok, Physics 7A 19 vaporization presented in Chapter 1, we would expect our models to provide us with the capability of explaining the heat capacity values, both at constant pressure and at constant volume for a large range of substances. Several of these data patterns are presented on this and the next page. Heat capacities vs. T CH4 NH3 Cvm R 9.5 8.5 7.5 6.5 5.5 4.5 3.5 N2 2.5 1.5 H2 Monatomic gases (He, Ar, Ne, etc.) 1000 1500 5 2 3 2 CO2 Cl2 7 2 This first graph shows the constant volume molar heat capacity of several gases from room temperature up to several thousand kelvin. The values of the heat capacities have been divided by the gas constant, R. There are several obvious trends. The monatomic gases have the lowest molar constant-volume heat capacity at 3/2 R and the values are independent of temperature. Diatomic gases seem to have higher values starting at about 5/2 R, while polyatomic gases have significantly larger values, but also a much more pronounced temperature dependence. These are some of the trends our models should enable us to provide explanations for. -y displacement from equilibrium Energy +y 300 500 2000 T [Kelvin] Some modes get frozen out at low Temp M. Chertok, Physics 7A 20 Reading / Quiz Continue reading Chapter 4 Next quiz: Friday, Nov. 14 Only covers through DLM 12 plus its FNTs followed up in DLM 13 Thanksgiving will also affect our schedule Stay tuned! M. Chertok, Physics 7A 21 ...
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This note was uploaded on 05/30/2009 for the course PHY 7A taught by Professor Pardini during the Fall '08 term at UC Davis.

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