1Lecture Ch. 4b• Homework Problem Ch. 4 Prob. 5• Hydrostatic equilibrium– Special cases– Pressure altitude dependence• More Midterm Review problems– Terminology reviewCurry and Webster, Ch. 4 (pp. 96-115; skip 4.5, 4.6)For Thursday: Read Ch. 5Tuesday: Study for midterm, extra problems at end of each chapterMore Reminders• Virtual Temperature: The temperature air would have at the given pressure and density if therewere no water vapor in it• Potential Temperature: The temperature a parcel would have if it were brought adiabatically andreversibly to p0 (usually 1 atm)• Virtual Potential Temperature: The temperature a parcel would have if there were no water vaporin it (only condensed water) and if it were brought adiabatically and reversibly to p0 (usually 1 atm)• Equivalent Temperature: The temperature that an air parcel would have if all of the water vaporwere to condense in an adiabatic isobaric process• Equivalent Potential Temperature: The temperature a parcel would have if all of the water werecondensed in an adiabatic isobaric process and if it were brought adiabatically and reversibly to p0(usually 1 atm)Ch. 4: Problem 5Consider moist air at a temperature of 30°C, a pressure of 1,000 hPa, and a relativehumidity of 50%. Find the values of the following quantities:a) vapor pressureb) mixing ratioc) specific humidityd) specific heat at constant pressuree) virtual temperatureHydrostatic Equilibrium ExampleConsider a planet with an atmosphere in hydrostatic equilibrium. Assume that theatmosphere is an ideal gas. Also assume that the temperature is a maximum at thesurface of the planet, and, as height increases, the temperature in the atmospheredecreases linearly (in other words, temperature decreases with height at a constant rate).Derive a formula for atmospheric density as a function of height in this atmosphere.Special Cases of HydrostaticEquilibrium• 1. rho=constant (homogeneous)– H=8 km =RT/g=scale height eq. 1.39– DT/dz=-g/R=-34/deg/km• 2. constant lapse rate– -dT/dz=constant• 3. isothermal T=constant– p=p_0*exp(-z/H)Pressure Altitude Calculatorhttp://www.csgnetwork.com/pressurealtcalc.html€ p = p0TT0 gRdΓ,T = T0− Γz → p = p0T0− ΓzT0 gRdΓLet’s compare the hydrostatic equation to the atmosphere2Pressure-Altitude DependenceLatitudinal and SeasonalVariability of Pressure-AltitudeDefinition ExampleDefine the following terms, briefly and clearly, in light of their use in the kinetic theoryof gases and the first and second laws of thermodynamics:a) an ideal gasb) temperaturec) entropyd) exact differentiale) enthalpyTerminology Review• Synoptic– large phenomena, hundreds of kilometers in length• Isentropic– Adiabatic+reversible• For adiabatic, ideal:– p determines T and vice versa• Potential temperature– temperature that air would have if raised/lowered to areference
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