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

To find the altitude where wispy cirrus clouds can form, use the temperature equation T = T0 - αy with T = 0°C, T0 = 24.5°C, and α = 6.00°C/1000m. Solving for y gives approximately 4083 meters.

Step-by-step explanation:

To find the altitude y above which wispy cirrus clouds can start to occur, we need to determine the temperature at which water remains frozen as ice crystals. Knowing the temperature at any given altitude can be calculated using the linear equation T = T0 - αy, where T0 is the initial temperature at sea level, α is the temperature lapse rate, and y is the altitude.

Since cirrus clouds are made up of ice crystals, we consider the temperature at which water freezes, 0°C, to find the altitude where cirrus clouds occur. Substituting T = 0°C and the given values T0 = 24.5°C and α = 6.00°C/1000m into the temperature equation and solving for y gives the following:

0 = 24.5 - (6.00/1000)y

Multiplying both sides by 1000 to clear the fraction gives:

0 = 24500 - 6y

Solving for y we get:

6y = 24500

y = 24500 / 6

y ≈ 4083.33 meters

So, wispy cirrus clouds can start to occur at an altitude of approximately 4083 meters above sea level.

Answer 2

4083.33 m

Step-by-step explanation:

`T_0` = 24.5°C

`\alpha` = Constant =
`(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-(6)/(1000)* y\\\Rightarrow y=(-24.5)/(-(6)/(1000))\\\Rightarrow y=4083.33\ m`

The altitude is 4083.33 m