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A stack 100m tall emits a plume whose temperature is 20C. The temperature at the ground is 19C. The ambient lapse rate is -4.5C/km up

A stack 100m tall emits a plume whose temperature is 20C. The temperature at the ground is 19C. The ambient lapse rate is -4.5C/km up to an altitude of 200 m. Above this the ambient lapse rate is +20C/km. Assuming perfectly adiabatic conditions, how high will the plume rise and what type of plume will it be?

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