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SJSU METR 60 - Lecture 7

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Lecture 7Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Saturation – Technical DefinitionWater Vapor FluxesSaturationSaturation Vapor PressureClausius-Clapeyron EquationTeten’s FormulaExerciseGraph of Clausius-Clapeyron EquationSystem of Dry Air + Water VaporSaturation, Sub-Saturation, Super-SaturationSuper-Saturation and CondensationSupersaturationHumidity VariablesSlide 21Slide 22Slide 23Slide 24Cooling a Parcel -- Constant PressureReminderSlide 27Start with Sub-Saturated AirCool at Constant PressureSlide 30Slide 31Slide 32Slide 33Saturation AchievedSuper-Saturation!DewDEWDew Point (Td)Temperature and Dew PointNoteFrostRelative Humidity (RH)Relative Humidity ApproximationSlide 44Increased AccuracySlide 46Adiabatic CoolingSlide 48RH of Expanding Parcele and es for a rising parcele and es for a sinking parcelRH and Adiabatic ProcessesLifting Condensation Level (LCL)LCLLecture 7Lecture 7Water VaporWater VaporWater Vapor amount in the air is variable.Water Vapor amount in the air is variable.Concentration of water vapor can be Concentration of water vapor can be quantified by:quantified by:Vapor pressureVapor pressureMixing ratioMixing ratioSpecific humiditySpecific humidityAbsolute humidityAbsolute humidityRelative humidityRelative humidityDew point depressionDew point depressionWet-bulb temperatureWet-bulb temperatureWarmer air can hold more water vapor at Warmer air can hold more water vapor at equilibrium than colder air. equilibrium than colder air. Air that holds this equilibrium amount is Air that holds this equilibrium amount is saturated.saturated.If air is cooled below the saturation If air is cooled below the saturation temperature, some of the water vapor temperature, some of the water vapor condenses into liquid, which releases latent condenses into liquid, which releases latent heat and warms the air.heat and warms the air.Thus, temperature and water vapor interact in Thus, temperature and water vapor interact in a way that cannot be neglected.a way that cannot be neglected.Saturation Vapor Pressure Saturation Vapor Pressure Vapor pressure:Vapor pressure:Air is a mixture of gases. All of the gases Air is a mixture of gases. All of the gases contribute to the total pressure. The pressure contribute to the total pressure. The pressure associated with any one gas in a mixture is associated with any one gas in a mixture is called the called the partial pressurepartial pressure..Water vapor is a gas, and its partial pressure in Water vapor is a gas, and its partial pressure in air is called the air is called the vapor pressurevapor pressure..Symbol Symbol ee is used for vapor pressure. Units are is used for vapor pressure. Units are pressure units: kPa. pressure units: kPa.SaturationSaturationAir can hole any proportion of water vapor. Air can hole any proportion of water vapor. For humidities greater than a threshold called the For humidities greater than a threshold called the saturation humidity, water vapor tends to condense saturation humidity, water vapor tends to condense into liquid faster than it re-evaporates. into liquid faster than it re-evaporates. This condensation process lowers the humidity This condensation process lowers the humidity toward the equilibrium (saturation) value. toward the equilibrium (saturation) value. The process is so fast that humidities rarely exceed The process is so fast that humidities rarely exceed the equilibrium value. the equilibrium value.SaturationSaturationThus, while air Thus, while air cancan hold any portion of water vapor, hold any portion of water vapor, the threshold is the threshold is rarely exceededrarely exceeded by more than 1% in by more than 1% in the real atmosphere.the real atmosphere.Air that contains this threshold amount of water vapor Air that contains this threshold amount of water vapor is is saturatedsaturated..Air that holds less than that amount is Air that holds less than that amount is unsaturatedunsaturated..SaturationSaturationThe equilibrium (saturation) value of vapor The equilibrium (saturation) value of vapor pressure over a flat surface of pure water is pressure over a flat surface of pure water is given the symbol:given the symbol:eessFor unsaturated air,For unsaturated air, ee < < eessAir can be slightly Air can be slightly supersaturatedsupersaturated ( (ee > > eess). ). When there are no surfaces upon which water When there are no surfaces upon which water vapor can condense.vapor can condense.Saturation – Technical DefinitionSaturation – Technical DefinitionSealed ContainerLiquid WaterWater VaporWater Vapor FluxesWater Vapor FluxesFlux of water molecules from liquid to vaporFlux of water molecules from vapor to liquidSaturationSaturationFlux of water molecules from liquid to vaporFlux of water molecules from vapor to liquidSaturation exists when these two fluxes of water vapor are equalSaturation Vapor PressureSaturation Vapor PressureFormula for eFormula for ess(T) called the (T) called the Clausius-Clapeyron EquationClausius-Clapeyron EquationApproximation:Approximation:TTRLeevs11exp00Where e0 = 0.611 kPa, T = 273 K, Rv = 461 J K-1 Kg-1 is the gas constant for water vapor. Absolute temperature in Kelvins must be used for T.Clausius-Clapeyron EquationClausius-Clapeyron EquationThis equation describes the relationship This equation describes the relationship between temperature and saturation vapor between temperature and saturation vapor pressure.pressure.Because clouds can consist of liquid droplets Because clouds can consist of liquid droplets and ice crystals suspended in air, we must and ice crystals suspended in air, we must consider saturations with respect to water consider saturations with respect to water and ice. and ice.Teten’s FormulaTeten’s FormulaIs an empirical expression for saturation vapor Is an empirical expression for saturation vapor pressure with respect to liquid water that includes pressure with respect to liquid water that includes the variation of latent the variation of latent heatheat with temperature. with temperature.210)(expTTTTbeesB = 17.2694, T1 = 276.16 K, T2 = 35.86 KExerciseExerciseCalculate eCalculate ess(T) for T = 0(T) for T = 0C, 10C, 10C, 20C, 20C, 30C, 30C, C, 4040CCGraph of Clausius-Clapeyron EquationGraph of Clausius-Clapeyron EquationSystem of Dry Air + Water VaporSystem of Dry Air +


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SJSU METR 60 - Lecture 7

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