Copyright © 2013 R. R. Dickerson11 Professor Russell Dickerson Room 2413, Computer & Space Sciences Building Phone(301) web site AOSC 620 PHYSICS AND CHEMISTRY OF THE ATMOSPHERE, I Lecture 5A, Moist Air
Copyright © 2013 R. R. Dickerson & Z.Q. Li 2 Dew Point Temperature T d Temperature to which moist air may be cooled with pressure and mixing ratio held constant to just reach saturation with respect to H 2 O. The “frost point” is the saturation temperature with respect to ice.
Copyright © 2013 R. R. Dickerson & Z.Q. Li 3 At the dewpoint w = w s (T d, P) As in Henry’s Law, at a given temperature
Copyright © 2013 R. R. Dickerson & Z.Q. Li 4 e T gas solid liquid T0T0
Copyright © 2013 R. R. Dickerson & Z.Q. Li 5 Phase Diagram of Water
Copyright © 2013 R. R. Dickerson & Z.Q. Li 6
7 Wet-Bulb Temperature T w dry air, Temperature to which air may be cooled by evaporating water into it at constant pressure. When water is evaporated into air, energy is added to the water. This energy comes at the expense of the dry air, which is cooled.
Copyright © 2013 R. R. Dickerson & Z.Q. Li 8 Consider 1. Isobaric process 2. Mixing ratio increased by evaporating water into air: w => w s (T w,p) The heat necessary to evaporate dw grams of water per kilogram of dry air is: dq = L v dw
Copyright © 2013 R. R. Dickerson & Z.Q. Li 9 To find the heat lost to dry air alone due to evaporation of water, we must correct for the mass of the water that the dry air now contains: Integrate from T to T w w => w s (T w,p)
Copyright © 2013 R. R. Dickerson & Z.Q. Li 10 Useful for isobaric condensation. Measure using a Sling Pychrometer or aspirated wet and dry bulbs: We measure T and T w. Since w s is a known function of T w and p, you can determine w from w s and the above equation.
Copyright © 2013 R. R. Dickerson & Z.Q. Li 11 Alternatively, if w and T are known, one can calculate the wet bulb temperature T w. Example: We may now apply the Clausius Clapeyron equation.
Copyright © 2013 R. R. Dickerson & Z.Q. Li 12
Copyright © 2013 R. R. Dickerson & Z.Q. Li 13 From Isobaric Condensation: The Clausius Clapeyron Equation gives: Solve for T w : (f = w/w s (T) )
Copyright © 2013 R. R. Dickerson & Z.Q. Li 14 After extensive algebra:
Copyright © 2013 R. R. Dickerson & Z.Q. Li 15 Also note:
Copyright © 2013 R. R. Dickerson & Z.Q. Li 16 Equivalent Temperature T e Temperature a sample of moist air would reach if all the moisture were condensed out at constant pressure (i.e., latent heat converted to sensible heat).
Copyright © 2013 R. R. Dickerson & Z.Q. Li 17
Copyright © 2013 R. R. Dickerson & Z.Q. Li 18 Isentropic Condensation Temperature T c T c is the temperature at which saturation is reached when moist air is cooled adiabatically with w held constant. See R&Y Figure 2.3 or W&H Figure T c can be determined by the intersection of the adiabatic equation (Poisson’s) and the Clausius Clapeyron equation and found on a SkewT.
Copyright © 2013 R. R. Dickerson & Z.Q. Li 19 p SkewT Dry adiabat Constant H 2 O mixing ratio
Copyright © 2013 R. R. Dickerson & Z.Q. Li 20 For completeness Absolute humidity, v, density of water vapor. Specific humidity, q, g H 2 O /kg air (not dry air). Same as [H 2 O] .
Copyright © 2013 R. R. Dickerson & Z.Q. Li 21 Conservative Properties of Air Parcels CNC ee CC ww CC TdTd TwTw wC T*T* TeTe TcTc C f C qq CC Variable dry adiabatic saturated/pseudo adiabatic