1Homework Ch. 2 Problem 2due Tuesday!Reversible ProcessesReversible ProcessesReversible€ Wrev= − pdvFrictionlessmass is conserved• Always at or infinitesimally close to equilibrium• Infinitesimally small steps• Infinite number of steps• Each step can be reversed with infinitesimal forcegrain of sandReversible-Adiabatic-WorkReversible-Adiabatic-WorkAdiabaticFirst LawReversibleInternal EnergyIdeal Gasp1v1T1= R =p2v2T2Δu = cvdTW = − pdvΔu = Q + WQ = 0thick wallsLow P, Low TFrictionlessReversible, Adiabaticmass is conserved€ T2T1=P2P1 RcpReversible-Adiabatic-WorkReversible-Adiabatic-WorkAdiabaticFirst LawReversibleInternal EnergyIdeal Gasp1v1T1= R =p2v2T2Δu = cvdTW = − pdvΔu = Q + WQ = 0€ T2T1=P2P1 Rcpthick wallsLow P, Low TFrictionlessReversible, Adiabaticmass is conserved€ −pdv = cvdT−RTv dv = cvdT− R12∫dvv= cv12∫dTTLecture Ch. 2b• Entropy• Second law of thermodynamics• Maxwell’s equations• Heat capacity• “Meteorologist’s entropy”Curry and Webster, Ch. 2 pp. 47-62Van Ness, Ch. 5-72Entropy• Is there a way to quantify “useful” energy?• Need a measure that is conserved, exact,unique• While Q is not exact, Qrev is exact– Reversible heat is limit of maximum work done– Since path is specified, cyclic integral is 0Curry and Webster, Ch. 2 pp. 47-62Van Ness, Ch. 5-7Second Law ofThermodynamics• Heat cannot pass of itself from a colder body to a hotter body.• A system left to itself cannot move from a less ordered state to a moreordered state.• The entropy of an isolated system cannot decrease.19oC 21oC10oC 30oCnotpossibleroom containingairnotpossibleO2hereN2hereΔSsystem≥ 0ΔSsystem=dQrevTsystemstate1state2∫Rudolf JE Clausius 1822-1888The 2nd Law•Energy spontaneously tends to flow onlyfrom being concentrated in one place tobecoming diffused or dispersed and spreadout.http://www.secondlaw.com/two.htmlThe 2nd law in practice• All types of energyspread out• A sinking ship losesits potential energyto the water itpushes away fromitself as it sinks.• A tire pops. The airnever spontaneouslyfills up the tire.www.creators.com/ 0305/LK/LK0310bg.gif3Clausius’ InequalityMaxwell’s EquationsPotential TemperatureReview: Virtual Temperature€ Tv≥ T, Tv≈ T + [0 → 3K]Virtual Potential Temperature• Potential Temperature (for moist air)• Virtual Potential Temperature€ θv= T 1+ 0.608qv( )p0p RdcpdMeteorologists’ Entropy€ η2−η1cp= lnθ2θ1θ2θ1= expη2−η1cp = expΔηcp 4Example: NOAA HYSPLITModel• Trajectories• * Single or multiple (space or time) simultaneous trajectories• * Optional grid of initial starting locations• * Computations forward or backward in time• * Default vertical motion using omega field• * Other motion options: isentropic, isosigma, isobaric, isopycnic• * Trajectory ensemble option using meteorological variations• * Output of meteorological variables along a trajectoryhttp://www.arl.noaa.gov/ready/hysplit4.htmlExample: NOAA
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