Question

Puffy cumulus clouds, which are made of water droplets, occur at lower altitudes in the atmosphere. Wispy cirrus clouds, which are made of ice crystals, occur only at higher altitudes. On a typical day and at altitudes less than 11 km, the temperature at an altitude y is given by T=T0−αy, where T0 = 24.5 ∘C and α=(6.00∘C)/(1000m). Find the altitude y (measured from sea level) above which wispy cirrus clouds can start to occur. (Ignore supercooling of water droplets.)

Answer 1

Answer:

4083.33 m

Explanation:

$T_0$ = 24.5°C

$\alpha$ = Constant = $\dfrac{6^{\circ}C}{1000\ m}$

The equation of temperature at a height is given by

$T=T_0-\alpha y$

The temperature at which the water will form clouds is 0°C

$0=24.5-\dfrac{6}{1000}\times y\\\Rightarrow y=\dfrac{-24.5}{-\dfrac{6}{1000}}\\\Rightarrow y=4083.33\ m$

The altitude is 4083.33 m