1Add an Atmosphere!• Atmosphere is transparent to non-reflected portionof the solar beam• Atmosphere in radiative equilibrium with surface• Atmosphere absorbs all the IR emissionTOA: FS = Fatm0.25*S0(1- αp) = σTatm4 Tatm = 255KFsurfFSFatmFatmAtmos: Fsurf = 2Fatm σTsurf4 = 2σTatm4 Tsurf = 303KKiehl and Trenberth, 1997 (posted on course web site)Hydrostatic Balance• Applicable to most atmospheric situations(except fast accelerations in thunderstorms)€ g = −1ρ∂p∂z∂p = −pgRdT∂zCurry and Webster, Ch. 1Homogeneous Atmosphere• Density is constant• Surface pressure is finite• Scale height H gives where pressure=0€ p0=ρgHH =pρg=RdT0g€ g = −1ρ∂p∂zdp = −ρgdzdpp00∫= −ρgdz0H∫0 − p0= −ρgH − 0( )Curry and Webster, Ch. 1Hydrostatic + Ideal Gas +Homogeneous• Evaluate lapse rate by differentiating idealgas law€ p =ρRdT∂p∂z=ρRd∂T∂z−1ρ∂p∂z = Rd−∂T∂z g = −1ρ∂p∂z € Γ = −∂T∂z=gRd= 34.1oC/kmDensity constantIdeal gasHydrostaticCurry and Webster, Ch. 1Lecture Ch. 4a• Equilibrium• Phase changes• Enthalpy changes from phase changes– Latent heat– Clapeyron equation– Clausius-Clapeyron equationCurry and Webster, Ch. 4 (pp. 96-115; skip 4.5, 4.6)For Tuesday: Homework Problem Ch.4 Prob. 52Atmospheric “Components”Phase Diagrams• Pressure-temperature diagrams• Degrees of freedom• Pressure-volume diagrams3Phase Equilibrium• Thermal equilibrium• Mechanical equilibrium• Chemical equilibriumDegrees of Freedom ExampleName the five main components of the atmosphere. (a) If all components are in the gasphase, how many degrees of freedom are there in the system? (b) If water condenses orfreezes, does that number increase or decrease? (c) If new components are added bypollution, how does that change (i) the number of possible phases and (ii) the degrees offreedom of the atmosphere?Chemical Equilibrium• Two phases in equilibrium– Constant T, P• Phase changes– Constant T, P• (What was G?)€ ΔGT ,P= 0€ ΔGT ,P= 0Gibbs (Free) EnergyEntropy Change• Entropy for phase transition• Define latent heat4Clapeyron Equation• Enthalpy change for any phase transitionExact!(Not exact but usually good)Clausius-ClapeyronEquation• Latent heat of vaporizationPhase Change Relationships• Clapeyron equation– All phase changes– Non-ideal equations of state• Clausius-Clapeyron equation– Liquid-vapor equilibrium only: vL << vV– Ideal gas law for vapor: vV = RT/pClausius Clapeyron ExampleThe saturation vapor pressure at a temperature of 30°C is 42.4 hPa. The gas constant fordry air is 287 J K-1 kg-1. The gas constant for water vapor is 461 J K-1 kg-1.In addition to the constants given above, here is one more: the saturation vapor pressureat a temperature of 40°C is 73.8 hPa. Assuming that the latent heat of vaporization isconstant, use this information to calculate the numerical value for this latent
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