Consider an isothermal atmosphere at rest. (a) Using hydrostatic balance, show that pressure p and potential temperature are respectively given by and 0 = 0e²/Hs where the isothermal and isentropic scale heights are given by H = RT。/g and H₂ = CpTo/g and To is the temperature. How is o related to po and To? (b) Show that the Brunt-Vaisala frequency squared N² = g/H、 for an isothermal atmosphere. (c) Calculate H, H, and N for To = 250K. e-²/ H P = Poe

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