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Lecture08

# Lecture08 - 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 8 Original presentations copyright M. Chertok 2008. All rights reserved. Outline for today Announcements Chertok’s ofﬁce hours cancelled, Tues, Nov. 18 Quarter winding down. After today, 2 more lectures + quizzes. Hang in there! This week: DLM 14 + 15 Thermodynamics Enthalpy Quiz 8 / Reading assignment M. Chertok, Physics 7A 2 Questions? DLM 14: CG3.4 3.4.3 FNTs from DLM 12/13 H2 versus N2 Lead vs. Aluminum @ low T -- freezing out Gas mixture at 1000K: 2 moles N2 + 1 mole CH4. Translational KE, active modes. M. Chertok, Physics 7A 4 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 5 Freezing out - example Lead (Pb) and Aluminum (Al) have similiar cvm at room temperature However, at LN temp (T=77K): Al’s speciﬁc heat < Pb’s speciﬁc heat What does this tell us about energy levels? M. Chertok, Physics 7A 6 Freezing out of modes Which is Pb and which is Al? Energy ... E2 kBT300 ½kBT77 Immersed in LN: E1 kBT = (1.38 x 10-23 J/K)(77 K) ~ 1 x 10-21 J < E1Al M. Chertok, Physics 7A ... E3 E2 E1 7 2 moles N2 + 1 mole CH4 What affects Ethermal? Amount (2 moles vs. 1 mole) Temperature Active modes M. Chertok, Physics 7A 8 2 moles N2 + 1 mole CH4 My (clicker) questions Which substance has greater KEtrans at T=1000K? a) N2, b) CH4, c) both same How many total rotational modes does the mixture have? a) 2, b) 3, c) 5, d) NA, e) 7NA Which substance contributes more to the heat capacity of the mixture? a) N2, b) CH4, c) both same M. Chertok, Physics 7A 9 Heat capacities vs. T Cvm R 9.5 8.5 NH3 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 vaporization presented in Chapter 1, we would expect our mo with the capability of explaining the heat capacity values, pressure and at constant volume for a large range of substances data patterns are presented on this and the next page. CH4 CH : 1 mole * 15 modes CO2 Cl2 7 2 N2: 2 moles * 6 modes This first graph shows the constant v capacity of several gases from room several thousand kelvin. The val capacities have b4 en divided by the e There are several obvious trends. gases have the lowest molar cons capacity at 3/2 R and the values ar temperature. Diatomic gases seem values starting at about 5/2 R, while have significantly larger values, but pronounced temperature dependence of the trends our models should ena explanations for. 300 500 2000 M. Chertok, Physics 7A T [Kelvin] 10 Thermodynamics DLM14 - Thermo 4.1.1- Learn about U, ΔU, process, state function, state diagram, work 4.1.2 - Cv heat capacity measurement Using AIM simulation M. Chertok, Physics 7A 12 CG 4.1 FNTs (a) What contributes to internal energy, U? At T<1000 K, which energy systems change, and thus contribute to ∆U? (b) In the equation “∆U = Q + W” why does the U have a “∆” in front of it, but Q and W do not have “∆”s? (c) What is a state function? Which of the following are state functions and which are processes? Eth Ebond Q U P T W KE PE M. Chertok, Physics 7A 13 CG 4.1 FNTs (d) How are states and processes represented on state diagrams? (e) When the volume of a gas is changed, the work done is: W = -∫P(V)dV How can this work be found on a PV state diagram? M. Chertok, Physics 7A 14 Changes in U Q Eth ↑ T↑ W ∆Eth = Q = ∆U ΔEth = Q + W = ΔU 1st Law of Thermodynamics M. Chertok, Physics 7A 15 DLM 15 4.1.3 - FNTs from DLM14 4.1.4 - Cp measurement compare with Cv results from last time 4.2.1 - New state function: H, enthalpy M. Chertok, Physics 7A 16 Ideal gas state diagrams PV = nRT P P P V V V What are the dots? What are the paths? Which of these involve work? M. Chertok, Physics 7A 17 Sign (+/-) of Work W = -∫P(V)dV If Volume increases, W<0 If Volume decreases, W>0 Think about compressing the air in a piston. M. Chertok, Physics 7A 18 Work What is the work in each case? P [J/m3] 5 P [J/m3] 5 1 3 V [10-3 m3] 1 3 V [10-3 m3] W = -∫P(V)dV = -[5(3-1)]x10-3 J = - 0.01 J W = -∫P(V)dV = -[5(1-3)]x10-3 J = + 0.01 J M. Chertok, Physics 7A 19 Cpm measurement Do you expect constant pressure heat capacity to be larger or smaller than that at constant volume? Remember, C = Q/∆T and the 1st Law M. Chertok, Physics 7A 20 Enthalpy H = U + PV (deﬁnition) ΔH = ΔU + PΔV + VΔP At constant pressure: ΔH = ΔU + PΔV But ΔU = ΔEth = Q + W = Q -PΔV Thus, ΔH = Q at constant pressure M. Chertok, Physics 7A 21 Enthalpy So, ΔH = Q at constant pressure Relates a state function change to a process Use this to generalize ΔHvap and ΔHmelt from Chapter 1 Model of sweating: since H is state function, the path taken from state 1 to state 2 doesn’t matter Use this to ﬁgure out ΔHvap of water at skin temperature M. Chertok, Physics 7A 22 Quiz 8 / Reading assignment Read through section 4-5 Quiz 8 Nov. 21 DLM 12-14 and FNTs from 14 covered in 15 M. Chertok, Physics 7A 23 ...
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