As dry air rises, it expands, and this causes it to cool about 1 degree Celsius for every 100 meter rise, up to a height of 12 Km. If the ground temperature is write a formula for the temperature T in terms of the height h (in meters) above ground.
As dry air rises, it expands, and this causes it to cool about 1 degree Celsius for every 100 meter rise, up to a height of 12 Km. If the ground temperature is write a formula for the temperature T in terms of the height h (in meters) above ground.
Let h denote the height measured in metres.
Then the temperature can be calculated by:
$\displaystyle T(h) = T(0) +\frac{-1^\circ C}{100} \cdot h$
Plug in the given value:
$\displaystyle T(12,000) = 22^\circ C +\frac{-1^\circ C}{100} \cdot 12,000 = -98^\circ C$
A personal remark: The last time I travelled by plane the temperature outside at an altitude of 13 km was around -60°C.
I only want to point out that your model isn't very accurate.