General Physics II
General Physics II PHYS 408
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This 12 page Class Notes was uploaded by Cayla Kilback on Thursday October 29, 2015. The Class Notes belongs to PHYS 408 at University of New Hampshire taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/231704/phys-408-university-of-new-hampshire in Physics 2 at University of New Hampshire.
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Date Created: 10/29/15
Lec rure 12 Kine ric Theory Chap rer39 20 Announcements 0 This weeks LAB You will be asked to do an evaluation off your understanding of ElectroMagnetism This is for research purposes You will get 10 bonus points towards your Lecture participation Transla rional KineTic Energy 3RT 3kT RMS veIOCIty vrms M m Average Kinetic K 1 2 1 3 energy avg 2 ms 2 2 m A 2 J57de NV Mean free path Distribution of Speeds Not all the molecules in a gas will have the same velocity Even if they started with the same velocity collisions will soon spread the velocities so that there is a distribution of speeds 1852 James Clerk Maxwell Maxwell s speed distribution law va4 Mv2 36 2 2RTJ ve Z RT The fraction of molecules with a Properties of a distribution function velocity between v1 and v2 is equal to the probability of finding a particular molecule with a velocity between v1 IPvdv1 and v2 v 0 fracwz IP02 dv OO Pv10393 sm Dis rribu rion of Speeds II Speed Distribution for 02 T 00K 4 35 3 25 2 39L5 1 05 0 0 200 400 600 800 1000 1200 Vn Average RMS Mos r Probable v We can now make several interesting conclusions The probability of nding a molecule with v0 is O The probability of nding a slow molecule is not zero it gets larger for lower temperatures The probability of nding a molecule with very large V say v2000ms is not zero It gets larger for higher temperatures P0ooTPvdvl 3 8RT 8kT vavg vPvdv 2 TM 2 Tm 3 3RT 3kT 2P d vIms v v v M m dPv 2RT 2kT VP gt 0 gt VP 2 dv M m Internal Energy of a 605 A gas can store energy in 1 Translational Kinetic Energy 2 Rotational Kinetic Energy 3 Molecular Excitations vibration modes A monatomic gas is the simplest case Quantum mechanics tells us that it can not store energy in rotation and having only one molecule limits possibilities for excitation So the energy is stored in kinetic energy For N molecules we get T E NKan gva m Nmi gNkT gnRT m 1nt Molecular Specific Heat at constant volume The molar specific heat C is defined by Q nCAT Capita39 quot We ase It does not matter as long as you keep track For constant volume we use CV and using the 1st law of thermodynamics and WO we can write AEmt Q W Note that the result AEth is general as long as you use the correct CV 3 3 For a monatomic gas we then have 3 3 CV 3 R Molecular Specific Heat at constant pressure At constant pressure the heat that is added to the gas Will not only increase the internal energy of the gas but also do work The amount of work done is just W pAV nRAT Combining this with the 1st Law of Thermodynamics and the previous result AEint Q W 2 Q nCVAT nRAT Definition of molar specific heat at constant pressure Q quotCPAT nCpATanVATnRAT gt Cp CVR Monatomic Gas C R Equipor ri rion Theorem The available energy to be stored in a gas will distribute itself equally over the available degrees of freedom 0 Each degree of freedom will have on average 121ltTof energy associated with it Monatomic gas 3 degrees of freedom Eint NkT gt CV R Diatomic gas 5 degrees of freedom Eint 3 translation 2 rotation NkT gtCV R Diatomic gas 6 degrees of freedom Eint 3NkT gt CV 2 3R 3 translation 3 rotation Adiobo ric Expansion of Gas We can now find an equation for adiabatic expansion Using dEQrWand setting Q0 Wdeand using our previous results plus some math wed in pV constant 3 TV 1 constant Admmx iQ 0 Pressure Immenm 70 K A solid copper cylinder of lengTh L and cross secTional area A has one end aT 100 C and The oTher end aT 0 C The heaT flow Through The pipe is 50 WaTTs The pipe is now cuT in half and The Two halves are placed side by side beTween The same 2 TemperaTures The ToTal heaT flow is now a25W b50W c100Wd200We400W The heat ow through a material isP kALi so if L is 12 and A is 2 times larger the resulting ow is 4 times as large Two flasks in The laboraTory are filled wiTh gas in Thermal equilibrium wiTh The environmenT Gas A has molecular weighT of 4 and gas B has molecular weighT of 64 I Which gas has The higher TemperaTure a A b B c Same Temp d NoT enough Info The gasses are in equilibrium with the same environment so the temperatures are the same II On average which gas molecules are moving fasTer a A b B c Same molecular speed d NoT E Info The molecular speed vms is given byvRMS so the smaller the mass the m higherthe rms speed forthe same temperature III WhaT is The raTio VAVB a14 b1c4 d8 e16 l3k7 Using the equation above V A m4 4 VB 31 m V 4 m8
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