Download Understanding Saturation Processes in Atmospheric Thermodynamics - Prof. Jefferson R. Snid and more Assignments Meteorology in PDF only on Docsity! Processes Leading to Saturation in the Atmosphere 1. Isentropic processes (a.k.a., reversible/adiabatic processes, entropy is conserved (s=const.) and so is vapor mixing ratio) a. Unsaturated ascent 2. Isenthalpic processes (a.k.a., isobaric/adiabatic processes, enthalpy is conserved (h=const.), but vapor mixing ratio is not conserved) a. Wet bulb process 3. Isobaric cooling a. Dew point process (vapor mixing ratio is conserved (r=const.), and so is total pressure) Saturation vapor Curve Unsaturated State T e h = const. (process 2a) r = const. (process 3a) s = const. (process 1a) The temperature (T) /Specific volume (v) projection: Phase Descriptions are indicated by the following subscripts: - Compressed liquid w - Saturated liquid v - Saturated vapor Specific volume (v) Temperature (T) v / w mixture v Similarly for "system-wide" expressions for specific entropy, enthalpy, internal energy, and Gibb's free energy )( wvw ssss )( wvw hhhh )( wvw uuuu )( wvw gggg Keep in mind that these equations are only valid for saturated liquid/vapor mixtures. Now, if we maintain constant pressure (and therefore constant temperature), only the amount of vapor and liquid (via ) is free to vary, hence: dvvdv wv )( dssds wv )( dhhdh wv )( duudu wv )( dggdg wv )( The derivation of the Clausius-Clapeyron equation starts with a generalized Maxwell relationship (see page 40 in Iribarne and Godson): TV V S T P (1) For the specific case of a saturated vapor-liquid mixture we have Tv w v s T e (2) For a vapor-liquid mixture, it can be shown that the left-hand side of (2) is a total derivative, i.e., dT de T e w v w (3) Also for a vapor-liquid mixture, the term on the right hand side (RHS) of (2) can be simplified via the relationships developed on the previous page Tv s = Twv wv dvv dss )( )( = Twv wv vv ss Combining the LHS and the RHS of the Maxwell relation (2) we get the differential form of the Clausius-Clapeyron equation: Twv wvw vv ss dT de (4) Equation (4) is the differential form of the Clausius-Clapeyron equation. This relationship is useful for the following reasons 1. If integrated, we obtain the desired relationship between saturation vapor pressure and temperature. The integrated form of (4) will be exploited to define the terminal states corresponding to the three mechanisms of air parcel saturation (i.e., expansion, evaporation, isobaric cooling). 2. From measurements of dTdew / and wv vv ( ), the entropy of vaporization can be inferred. 3. Useful property relationships (e.g., relation of Twvwv vvss ))/()(( to temperature) are developed in going from (4) to )(Tfew .
