1!Lecture Ch. 5a!• Surface tension (Kelvin effect)!– Hygroscopic growth (subsaturated humidity)!– Saturation!• Chemical potential (Raoult effect)!• Nucleation!– Competition between surface and chemical effects!– Köhler curves!• Aerosol-cloud interactions!Curry and Webster, Ch. 5 (skip 5.6, 5.7); also 4.5.1!Pruppacher and Klett, Ch. 6!For Thursday: Homework Problem 3 and 7 (Ch. 5) (optional!)!Tuesday, Oct. 27: Midterm!Thursday, Oct. 29: meet to work on ROAST!!Macro-Thermodynamics!• Hot air rises!• Rising air cools!• Cooled moist air saturates!• (Sub & Super)-saturated water vapor condenses!• Condensation liberates heat!Water Saturation!• Saturation concentration of water over a flat water surface !Seinfeld and Pandis, Fig. 15.1 N.B. Equilibrium is in but is NOT the same as “steady state.”!Micro-Thermodynamics!• Saturation has the most possible dissolved species!• Equilibrium means two phases are balanced!• Supersaturated states are not stable!• Nucleation initiates a change of “phase” (from particle to droplet)!Bohren, 1987!2!Surface Thermodynamics!• Surfaces require energy to form !• Smaller particles have !– higher surface-to-volume ratios!– higher curvature!• Higher curvature requires more energy per mass!€ Sv,w≡ea,wesat,w= exp4 Mwσw / aRTρwDp Hygroscopic Growth of Particles!• Normalized diameter change (growth factor) of sulfate species !– Relative to particle size at 0% RH!Seinfeld and Pandis, Fig. 9.3 Free Energy Equation!• Surface energy!• Free energy at constant T, P!• Liquid (H2O/EtOH) supersaturated with vapor (CO2) nucleates on salt to form bubbles Bubbles • Vapor (air) supersaturated with liquid (H2O) nucleates on particles to form droplets Clouds3!Kelvin Equation!• vapor pressure over a curved interface always exceeds that of the same substance over a flat surface!– vapor pressure of a liquid = energy necessary to separate a molecule from the attractive force of its neighbors!– curvature - increases the distance between a molecule and its neighbors so it has fewer neighbors -- therefore it is easier for molecules to break free!• for pure water Kelvin effects are important <0.05 µm diameter droplets!4.1 ==pwwwwwsatwwDRTMxPPRHρσγ4expParticle composition xw mole fraction of water γw activity coefficient for water σw surface tension of solution ρw density of aqueous solution Mw molecular weight Dp particle diameter Ambient conditions RH relative humidity T temperature Pw vapor pressure Pwsat saturation pressure • NaCl solution reservoir • Simulates a grand canonical (constant RH) ensemble • Equilibrates with humid air • Ambient pressure fixed by nitrogen molecules Simulating Atmospheric Humidity using Molecular Dynamics Time = 2 ns Time = 5 ns • Humidity as controlled by solutions of differing concentrations • Fluctuations/noise introduced due to individual evaporation/condensation events but overall RH is held constant • Due to the small number of water molecules removed, reservoir concentration does not change. • Humidity is controlled closely to value expected from bulk thermodynamics, within a small margin of error. Raoult’s "Law!Raoult’s "Law!4!Chemical Potential!• From Maxwell’s equations!• Integrating from vapor to liquid!Measured Hygroscopic Growth!• Particle balance for levitating particles (Tang et al., 1987)!• Growth compensated by change in electric field!• Deliquescence occurs at transition from dry to wet!Seinfeld and Pandis, Fig. 9.7 Condensed Water Molecules!• Change in number of liquid molecules!Critical Radius and Supersaturation!• Integrate then find maximum!5!Cloud Droplet Nucleation!• particle activation - process by which droplets (several micron in size) are formed (or activated) from primarily submicron particles; also called heterogeneous nucleation or just nucleation by cloud physicists!– process illustrates the conditions required for growth to droplets!– the approach used assumes that this formation is an equilibrium process!Activation on Particles!• Soluble salts dissolve! Sv,w= exp2Mwσs /aRTρwa−υΦsmsMw/ Ms4πa33 ρs"− ms Kelvin effect! Raoult effect!Activation of CCN to Droplets!• Variation of the equilibrium vapor pressure of an aqueous solution drop containing ammonium sulfate and insoluble material !– Initial dry particle diameter 0.1 µm !– Soluble mass fractions 0.2, 0.4, 0.6, 1.0 at 293K!7.1 Seinfeld and Pandis, Fig. 15.8 Kelvin effect!Raoult effect!Köhler Curves!• Köhler curves for sodium chloride and ammonium sulfate !– Dry diameters 0.05, 0.1, 0.5 µm!– Supersaturation of 1% is equivalent to 101% relative humidity!Seinfeld and Pandis, Fig. 15.5 Pressure Altitude Calculator!http://www.csgnetwork.com/pressurealtcalc.html!€ p = p0TT0 gRdΓ,T = T0− Γz → p = p0T0− ΓzT0 gRdΓLet’s compare the hydrostatic equation to the atmosphere!6!Pressure-Altitude Dependence!Latitudinal and Seasonal Variability of Pressure-Altitude!Radiation Balance Example!It has been estimated from satellite observations that variations in solar radiance duringthe last 20 years amounted to ≤0.2 W m-2, or less than 0.1% of the incoming shortwaveradiation. Calculate the approximate change in the temperature at the Earth’s surface fora 0.1% decrease in solar luminosity for a simplified climate model. State allassumptions, simplifications, and equations used. Values of constants that you may needare Earth’s albedo 0.31, solar luminosity 3.92x1026 W, Earth-sun distance 1.50x1011 m, Stefan-Boltzmann constant 5.67x10-8 W m-2 K-4.Definition Example!Define the following terms, briefly and clearly, in light of their use in the kinetic theoryof gases and the first and second laws of thermodynamics:a) an ideal gasb) temperaturec) entropyd) exact differentiale) enthalpyTerminology Review!• Synoptic!– large phenomena, hundreds of kilometers in length!• Isentropic !– Adiabatic+reversible!• For adiabatic, ideal: !– p determines T and vice versa!• Potential temperature!– temperature that air would have if raised/lowered to a
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