One day air at sea level, has a pressure of p = 1020mb and a temperature of T i = 310.00K. A small plume of

One day air at sea level, has a pressure of pı = 1020mb and a temperature of T_i = 310.00K. A small plume of dry air is released at ground level. This small plume (air parcel) has a temperature of T_p = 311.00K. The buoyancy force on the plume causes it to slowly convect upwards. The temperature profile of the air on this particular day is T(z) = 310.00 - 8.800z. Here the temperature is in Kelvin degrees and z is in km. Numerically calculate the following by using the appropriate equations. Assume that the dry adiabatic lapse rate is T_d = 9.800K/km.

(a) Calculate the potential temperature of the plume at 1020mb.

(b) Calculate the height where the plume stops convecting upward.

(c) What is the potential temperature of the plume at its maximum height? Why?