The total mass of the earth's atmosphere is 5×[tex]10^{8}[/tex] kg.
To calculate the total mass of the earth's atmosphere we use the expression
[tex]P=\frac{F}{A}[/tex]
or, [tex]F=P\times A[/tex]
or,[tex]M\times g=P\times A[/tex]
or,[tex]M=\frac{P\times 4\times \pi\times r^{2} }{g}[/tex]
Here, P= Atmospheric pressure at the surface = [tex]10^{5}[/tex] N/m2
F= Force at the earth surface.
A= Area of the earth.
r= Radius of the earth=6.4 × [tex]10^{6}[/tex] m
g= Acceleration due to gravity. = 9.8 m/s2 ≈ 10 m/s2
Let, M be the total mass of the earth's atmosphere.
Now, [tex]M=\frac{10^{5}\times4\times\pi\times(6.4\times10^{6} )^{2} }{10}[/tex]
M= 5×[tex]10^{8}[/tex] kg.
Thus from the above calculation we can show that, the total mass of the earth's atmosphere is 5×[tex]10^{8}[/tex] kg.
Learn more about earth's atmosphere: brainly.com/question/200658
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