As dry air moves upward it expands and in doing so cools at a rate of 1 degrees Celsius for each 100 m rise up to about 12 km
If the ground temperature is 20 degrees Celsius find an expression for the temperature T as a function of the height H
the answer is T=20-10h(h in kilometers) please show and explain steps thanks
nothing to show.
They said T started out at 20 and decreased by 10 for each km.
just subtract 10 for each km, starting from 20.
If that's not clear, make a table for values of h from 0 to 12:
h 0 1 2 3 4 ...
T 20 10 0 -10 ...
To find the expression for the temperature T as a function of the height H, we first need to convert the height H from meters to kilometers.
We know that the temperature cools at a rate of 1 degree Celsius for every 100 m rise. Since there are 1000 meters in a kilometer, this means that for each kilometer rise, the temperature cools by 10 degrees Celsius.
Let's represent the height in kilometers as h. Since we know that the temperature cools at a rate of 10 degrees Celsius per kilometer, we can express the change in temperature, ΔT, as 10h.
Given that the ground temperature is 20 degrees Celsius, we can write the equation:
T = Ground temperature - ΔT
Substituting ΔT with 10h, the expression becomes:
T = 20 - 10h
Therefore, the expression for the temperature T as a function of the height H is T = 20 - 10h, where h is the height in kilometers.