1Climate Sciences:Atmospheric ThermodynamicsInstructor: Lynn Russell, NH343http://aerosol.ucsd.edu/courses.htmlText: Curry & WebsterThe Greenhouse EffectSolar radiationLong-waveradiationCapeTown below Devil’sPeak and Table Mountain2Of course, the phenomenon is also supported by a meteorological explanation. The moisture-laden south-easter blowsagainst Table Mountain from over the False Bay and rises. At a height of approximately 900 meters the winds reach thecolder layers of air and thick clouds form. These clouds roll over the mountain and down towards the City Bowl. Thecharacteristic tablecloth forms when the clouds reach the warmer, lower air layers and dissolve once more.Review from Ch. 1• Thermodynamic quantities• Composition• Pressure• Density• Temperature• Kinetic Theory of GasesCurry and Webster, pp. 1-17Feynman, Book I, ch. 39Thermodynamic Quantities• Classical vs. Statistical thermodynamics• Open/closed systems• Equation of state f(P,V,T)=0• Extensive/intensive properties• Thermal, engine, heat/work cyclesIntensive quantities: P, T, v, nExtensive quantities: V, NConcentration: n=N/VVolume: v=V/NSystemEnvironment<-- ClosedOpen -->Composition• Structure– Comparison to other planets• N2, O2, Ar, CO2, H2O: 110 km constitute 99%• Water, hydrometeors, aerosol3Pressure• Force per unit area• 1 bar = 105 Pa; 1 mb = 1 hPa; 1 atm = 1.013 bar• Atmosphere vs. OceanAtmosphereOceanDensity• Specific volume: v=V/m• Density: ρ=m/V– 1.29 kg/m3• Mean free path– frequency of intermolecular collisionsTemperature• “Zeroeth” Law of Thermodynamics– Equilibrium of two bodies with third– Allows universal temperature scale• Temperature scale– Two fixed points: Kelvin, Celsius– Thermometer• Lapse Rate Γ = -∂T/∂z– Change in temperature with altitude– Typically Γ=6.5 K/km• Temperature inversion Γ<0– Boundary layer “cap”– Tropopause between troposphere and stratosphereKinetic Theory of Gases• Pressure of a gas• Kinetic energy• Internal energy• Temperature of a gas• Pressure-volume-temperature relationship• The “fine print”4Initial Momentum: mvxFinal Momentum: -mvxIf all atoms had same x-velocity vx:Momentum Change for one Atom-Collision: [Initial]-[Final] = mvx-(-mvx) = 2mvxNumber of Atom-Collisions-Per-Time: [Concentration]*[Volume] = [n]*[vxA]Force = [Number]*[Momentum Change] = [nvxA]*[2mvx] = 2nmAvx2Pressure = [Force]/[Area] = 2nmvx2For atoms with average velocity-squared of <vx2>:Pressure = [Force]/[Area] = nm<vx2>Force: FArea: ACollision Distance-Per-Time: vxt/t=vxIndividual collisionsPerfect reflectionIdeal gas Monatomic gasPopulation-averaged Velocity: <v2>=[vi2 + vii2 + viii2 +…+ vn2]/nScalar multipliers: <mv2/2>=[mvi2 + mvii2 + mviii2 +…+ mvn2]/2nHow many will hit “right” wall? n/2viiviiivi3D velocity: <v2>=<vx2>+<vy2>+<vz2>Random motion (no preferred direction): <vx2>=<vy2>=<vz2><vx2>= <v2>/3vvxvzvyP = nm<vx2>=[2/2]*[nm]*[<v2>/3]=[2/3]n*<mv2/2>=[2/3]n*[kinetic energy of molecule]PV =[2/3]*[N*<mv2/2>]=[2/3]*U=[2/3]*EkConcentration: n=N/VTotal “internal” energy: UKinetic energy of gasPV =[2/3]*EkEk =[3/2]* PVDefine T = f(Ek)For scale choose T=(2/3Nk)*Ek Ek =(3/2)*NkT Then PV = NkT = nR*TKinetic energy of gasRHS is independent of gas--> so scale can be universalMean k.e.: Ek/N=(3/2)kTk=1.38x10-23 J/KR*=N0k=8.314 J/mole/KTemperatureis defined to beproportional to the averagekinetic energy of the
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