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

Answer:

727.273 m

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

$\dfrac{1^{\circ}C}{100}=\dfrac{12^{\circ}C}{h}+\left(-\frac{0.65}{100}\right)\\\Rightarrow \dfrac{1^{\circ}C}{100}+\left(\frac{0.65}{100}\right)=\dfrac{12^{\circ}C}{h}\\\Rightarrow h=\dfrac{12^{\circ}C}{1.65^{\circ}C}\times 100\\\Rightarrow h=727.273\ m$

The maximum height is 727.273 m