Puffy cumulus clouds. which are made of water droplets, occur at lower altitudes

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 = T_0 - alpha y, where T_0 = 26.0 degree C and alpha = (6.00 degree C)/(1000 m). Find the attitude-y (measured from sea level) above which wispy cirrus clouds can star to occur (Ignore super cooling of water droplets.) Express your answer numerically in kilometers, using three significant figures.

Explanation / Answer

Given

equation is

   T = T0 - alpha*y

the cloud contains the ice crystals so the temperature T is 0 0C at the clounds

and the tempeature T0 = 26 0C ,

   alpha = 6 0c/1000 m

   T0-T = alpha*y

   y = (T0-T)/alpha
  
   y = (26-0)/(6/1000)
   y = 26000/6 m

   y = 4333.33 m

   y = 4.333 km

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