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AUGUSTANA PH 202 - Internal Energy

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Internal EnergyPAL #15 Kinetic TheoryPAL #16 Internal EnergyIdeal GasSlide 5Molar Specific HeatsSpecific Heat and Internal EnergySpecific Heat at Constant PressureDegrees of FreedomRotational MotionsSlide 11Equipartition of EnergyOscillationInternal Energy of H2Adiabatic ExpansionIsothermsIsobaric ProcessSummary: Ideal Gas ProcessesAdiabatic ProcessIsochoric ProcessIdeal Gas ProcessesFour Thermodynamic ProcessesP-V DiagramProcessesThe Arrow of TimeEntropyDetermining EntropyIsothermal Reversible ProcessIsothermal ExpansionClosed SystemsInternal EnergyPhysics 202Professor Lee CarknerLecture 16PAL #15 Kinetic TheoryWhich process is isothermal? Since T is constant, nRT is constant and thus pV is constant A is isothermal3 moles at 2 m3, expand isothermally from 3500 Pa to 2000 Pa Need T, Vf Vf = nRT/pf = (3)(8.31)(281)/(2000) = 3.5 m3 Since T is constant, E = 0, Q = W = 3917 JPAL #16 Internal Energyp,V and T for nitrogen Pressure increases (since lid pops off) Heat flow How do you find work?Assume all work is contained in lifting the lid  Ideal GasWe will approximate most gases as ideal gases which can be represented by: vrms = (3RT/M)½ dVVnRTWVfViInternal EnergyWe have looked at the work of an ideal gas, what about the internal energy?If the internal energy is the sum of the kinetic energies of each molecule then: Eint = (3/2) nRT  Strictly true only for monatomic gassesMolar Specific HeatsHow does heat affect an ideal gas? The equation for specific heat is: From the first law of thermodynamics:Consider a gas with constant V (W=0), But Eint/T = (3/2)nR, so:CV = 3/2 R = 12.5 J/mol KSpecific Heat and Internal EnergyIf CV = (3/2)R we can find the internal energy in terms of CV Eint = nCVTChange in internal energy depends only on the change in temperatureSpecific Heat at Constant PressureWe can also find the specific heat at constant pressure:Eint = Q - WQ = nCpT Solving for Cp we find:Cp = CV + RMolar specific heat at constant pressureDegrees of FreedomOur relation CV = (3/2)R = 12.5 agrees with experiment only for monatomic gases  Kinetic energyFor polyatomic gasses energy can also be stored in modes of rotational motionRotational MotionsMonatomicNo RotationPolyatomic2 Rotational Degrees of FreedomDegreesofFreedomEquipartition of EnergyEquipartition of Energy:  We can now write CV asCV = f/2 R = 4.16f J/mol KOscillationAt high temperatures we also have oscillatory motion So there are 3 types of microscopic motion a molecule can experience:   If the gas gets too hot the molecules will disassociateInternal Energy of H2Adiabatic ExpansionLets consider a process in which no heat transfer takes place (adiabatic)It can be shown that the pressure and temperature are related by: where  = Cp/CVYou can also write: IsothermsIsobaric ProcessSummary: Ideal Gas ProcessesIsothermalConstant temperature W = nRTln(Vf/Vi)IsobaricConstant pressure W=pV Adiabatic ProcessIsochoricProcessIdeal Gas ProcessesAdiabaticNo heat (pV = constant, TV-1 = constant) W=-Eint IsochoricConstant volume W = 0Four Thermodynamic ProcessesP-V DiagrampVIsobaric (p=const.)Isochoric (V=const)Isothermal (T=const)Adiabatic (Q=0)ProcessesFor each type of process you should know:    First law and ideal gas law always applyThe Arrow of TimeIf you see a film of shards of ceramic forming themselves into a plate you know that the film is running backwards  Examples: EntropyWhat do irreversible processes have in common? The degree of randomness of system is called entropyDetermining EntropyIn any thermodynamic process that proceeds from an initial to a final point, the change in entropy depends on the heat and temperature, specifically:Isothermal Reversible ProcessIsothermal ExpansionConsider an example, isothermal expansionA cylinder of gas rests on a thermal reservoir with a piston on top  The temperature is constant so:S = Sf-Si=(1/T)dQClosed SystemsConsider a closed system  The entropy change in the gas is balanced by the entropy change in the reservoir


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AUGUSTANA PH 202 - Internal Energy

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