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The potential density D is defined as the density that air would attain if it was adiabatically transformed to a pressure p=1000 mbar.

a)Show that D=density(p/P)^Cv/Cp

b)Calculate D for a sample of air with pressure 600 mbar and temperature -15 degree centigrade.

c) Show that (dD/dz)/D=-1/T(g/Cp+dT/dz)