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 TheoryWhich process is isothermal? Since T is constant, nRT is constant and thus pV is constant A is isothermal3 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 Energyp,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 GasWe will approximate most gases as ideal gases which can be represented by: vrms = (3RT/M)½ dVVnRTWVfViInternal EnergyWe 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 gassesMolar Specific HeatsHow 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 KSpecific Heat and Internal EnergyIf CV = (3/2)R we can find the internal energy in terms of CV Eint = nCVTChange in internal energy depends only on the change in temperatureSpecific Heat at Constant PressureWe can also find the specific heat at constant pressure:Eint = Q - WQ = nCpT Solving for Cp we find:Cp = CV + RMolar specific heat at constant pressureDegrees of FreedomOur relation CV = (3/2)R = 12.5 agrees with experiment only for monatomic gases Kinetic energyFor polyatomic gasses energy can also be stored in modes of rotational motionRotational MotionsMonatomicNo RotationPolyatomic2 Rotational Degrees of FreedomDegreesofFreedomEquipartition of EnergyEquipartition of Energy: We can now write CV asCV = f/2 R = 4.16f J/mol KOscillationAt 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 ExpansionLets 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/CVYou can also write: IsothermsIsobaric ProcessSummary: Ideal Gas ProcessesIsothermalConstant temperature W = nRTln(Vf/Vi)IsobaricConstant pressure W=pV Adiabatic ProcessIsochoricProcessIdeal Gas ProcessesAdiabaticNo heat (pV = constant, TV-1 = constant) W=-Eint IsochoricConstant volume W = 0Four Thermodynamic ProcessesP-V DiagrampVIsobaric (p=const.)Isochoric (V=const)Isothermal (T=const)Adiabatic (Q=0)ProcessesFor each type of process you should know: First law and ideal gas law always applyThe Arrow of TimeIf you see a film of shards of ceramic forming themselves into a plate you know that the film is running backwards Examples: EntropyWhat do irreversible processes have in common? The degree of randomness of system is called entropyDetermining EntropyIn 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 ExpansionConsider an example, isothermal expansionA cylinder of gas rests on a thermal reservoir with a piston on top The temperature is constant so:S = Sf-Si=(1/T)dQClosed SystemsConsider a closed system The entropy change in the gas is balanced by the entropy change in the reservoir
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