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What is scale height? if the scale height of the earth is 8.6km, at what altitude on earth would the atmospheric pressure be only 10% of that at sea level?

please show all steps to get result & explain, thanks!

Respuesta :

Answer:

scale height = 19.80 km

Explanation:

given data

earth scale height = 8.6 km

atmospheric pressure = 10%

to find out

scale height

solution

we know that with the scale height we can find value of physical parameter that is change with height

and height is that value of pressure or density  [tex]\frac{1}{e}[/tex] th of ground value

so we can say

[tex](\frac{1}{e})^t[/tex]  = 10%

[tex](0.3678)^t[/tex]  = 0.1

take log both side

t log(0.3678) = log 0.1

t = 2.3025

so

scale height for 10% is

scale height = 2.3025 × 8.6

scale height = 19.80 km

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