Question

As the result of a thermal inversion the prevailing air temperature profile increases 1 degree C/100 m above ground level. To what maximum height will polluted air rise if it is released at ground level 12 degrees C warmer than the atmosphere? The adiabatic lapse rate is -0.65 degrees C/100 m. Enter the answer in meters, but do not enter the units.

Answer 1

727.273 m

Step-by-step explanation:

Rate of temperature increase with 100 m elevation = 1°C

h = Maximum Height

Adiabatic lapse rate = -0.65°C/100 m

Initial temperature = 12°C

We have the relation

`(1^(\circ)C)/(100)=(12^(\circ)C)/(h)+\left(-(0.65)/(100)\right)\\\Rightarrow (1^(\circ)C)/(100)+\left((0.65)/(100)\right)=(12^(\circ)C)/(h)\\\Rightarrow h=(12^(\circ)C)/(1.65^(\circ)C)* 100\\\Rightarrow h=727.273\ m`

The maximum height is 727.273 m