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CSU AT 540 - Course Outline

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Focus3. Atmospheric Thermodynamics3.1 The Gas LawsConcepts and DefinitionsConcepts and Definitions (cont)Dry AirWater VaporGas ConstantsDalton’s Law of Partial PressuresExample (Wallace and Hobbs)Virtual TemperatureEquation of State: Summary3.2 Hydrostatic EquationHydrostatic Equation Notes3.3 Geopotential and Geopotential Height3.4 ThicknessSome Uses of ThicknessExamplesA Basic Introduction to FrontsFronts (cont)Fronts (cont)Fronts (cont)Fronts (cont)Fronts (cont)Fronts (cont)3.5 First Law of ThermodynamicsState VariablesJoule’s Law3.6 Specific Heats3.7 EnthalpyForms of the First Law of ThermodynamicsSome Definitions and ConceptsDefinitions and Concepts (cont)3.8Potential Temperature3.9 Dry Adiabatic Lapse Rate3.10 Water Vapor and Moisture ParametersMixing Ratio (w)Specific Humidity (q)Relationship between Vapor Pressure and Mixing RatioSaturation Vapor PressureSaturation Mixing RatiosRelative HumidityDew Point and Frost PointLifting Condensation LevelWet-Bulb Temperature (Tw)3.11 Saturated-Adiabatic and Pseudoadiabatic ProcessesDerivation of Saturated Adiabatic Lapse Rate3.12 Equivalent Potential Temperature3.13 Static StabilityStatic Stability in terms of TemperatureStatic Stability in terms of Γ and ΓdStatic Stability in terms of θConditional InstabilityConvective or Potential InstabilityCourse OutlineSection Instructor Time123456789Atmospheric Variables Cotton 1 classCommunication with the atmosJirak 1 classAtmospheric Thermodynamicsvd Heever ~4 weeksAtmospheric Dynamicsvd Heever ~4 weeksExtratropical CyclonesJirak ~2 weeksNumerical Weather Predictionvd Heever ~1 weekConceptual Models of CumulonimbiCotton 1-2 classesConceptual Models of MCSsCotton 1-2 classesTropical CyclonesCotton 1-2 classesFocus• Practical application of basic meteorological principles and laws• Brings together aspects of many classes – dynamics, thermodynamics, synoptic meteorology• Forecasting techniques and ability to interpret weather maps• Introduce new terminology for students not having previously taken any meteorology / atmospheric science classes• Some derivations• Notes based on Wallace and Hobbs, Cotton’s notes, Pielke’s notes and my own notes3. Atmospheric Thermodynamics1. The gas laws2. The hydrostatic equation3. Definition of geopotential and geopotential height4. Thickness5. First law of thermodynamics6. Specific heats7. Enthalpy8. Potential temperature9. The adiabatic lapse rate 10. Water vapor and moisture parameters11. Saturated-adiabatic and pseudo adiabatic processes12. Equivalent potential temperature13. Static Stability3.1 The Gas LawsmRTpV=• Lab experiments: pressure, volume and temperature of any material can be related by an Equation of State• All gases follow approximately the same equation of state –Ideal Gas Equation• Ideal gas equation or Equation of State for gases:where p is pressure (Pa)V is volume (m3)m is mass (kg)T is temperature (K)R is the gas constant (J K-1kg-1)• R is dependant on the gas typeRTp volumespecific theis 1 and 1m kg), (1 massunit For RTpgas theofdensity theis Vm Now mRTpV=α∴αρ=α=ρ=∴ρρ==Atomic weight of hydrogen 1.00794 AMUAtomic weight of oxygen 15.9944 AMUConcepts and Definitions• Atomic weight and atomic mass are used interchangeably, as are molecular weight and molecular mass• On the periodic table, atomic masses are relative and are given in atomic mass units (AMU)•Examples: Hydrogen: 1.0079Oxygen: 15.9994Water: 18.0153Concepts and Definitions (cont)•A gram-molecular weight or mole (mol) of any substance is the molecular weight of the substance expressed in grams• A mole of a gas therefore contains enough molecules to give the molecular mass in grams•Examples: 1 mol of hydrogen weighs 1.0079 g1 mol of oxygen weighs 15.9994 g1 mol of water weighs 18.0153 g• As molecular masses are relative, 1 mol of any substance must contain the same number of molecules as 1 mol of any other substance. • The number of molecules in 1 mol of any substance is a universal constant, which is called Avagadro’s number, NA. The value of NAis 6.022x1023per mole. • The number of moles in the mass of a substance is given by:• Example: For 18 g of hydrogen we have ~18 mol of hydrogen, whereas for 18g of water we have ~1 mol of water• Avagadro’s hypothesis: Gases containing the same number of molecules occupy the same volumes at the same temperature and pressure. (g/mol) massmolecular :M (g) mass :m moles ofnumber :n Mmn =Universal Gas ConstantAssume that we have x molecules of gas A and x molecules of gas B at some temperature T and some pressure P. We can then write the equation of state for x molecules of each gas as:TRpVTRpVBBAA==But from Avagadro’s hypothesis, gases containing the same number of molecules occupy the same volumes at the same temperature and pressure:BABARRVV=∴=⇒So for the same number of molecules of any gas, the constant R will be the same!• As 1 mol of gas contains the same number of molecules as 1 mol of any other gas → R for 1 mol is the same for all gases•Called the Universal Gas Constant (R*)• R* = 8.3145 J K-1mol-1• The ideal gas law for 1 mol of any gas:TRpV*=and for n moles of any gas is:TnRpV*=mRTpV=So for some mass of gas we have:where R is the gas constant for that particular gas (JK-1kg-1)TnRpV*=and for some number of moles we have:where R*is the Universal Gas Constant (8.3145 JK-1mol-1)MRRRMRnMRTpVnMmMmn** Now=⇒=⇒=∴=⇒=For a gaseous mixture the molecular mass is:∑∑=iiiiiMmmMwhere miand Miare the mass (g) and molecular mass of the ithconstituentDry Air1-1-**ddkgK J 28797.281000100097.28M a hasair dry of mol 1 97.28 air.dry for constant gas theis R whereor :massunit for stateofEquation ===⇒=∴===RMRRgMTRpTRpdddddddddραWater Vapor1-1-*v*vvvvvvvvkgK J461016.18R1000MR1000Rg016.18M a hasor water vapof mol 1 016.18Mpressure vapor is e and vapor for water constant gas theis R whereTReor TRe:massunit for stateofEquation ===⇒=∴=ρ==αGas Constants• So we have:Rd= 287 J K-1kg-1Rv= 461 J K-1kg-1R* = 8.3145 JK-1mol-1• Define:622.0MMRRdvvd===εDalton’s Law of Partial Pressures• The total pressure exerted by a mixture of gases that do not interact chemically is equal to the sum of the partial pressures of the gases• The partial pressure of a gas is the pressure that that gas would exert if it alone occupied the volume that the mixture occupies (at the same temperature)'' :airmoist For


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