Question

What is the approximate mass of the atmosphere of the earth? Assume the radius of the earth to be $6370$ km.

Answer 1

Let the mass of the atmosphere be $m_a$.

By balancing the force due to the weight of atmosphere and force due to atmospheric pressure.

$m_{a}g={Area}_{Earth}\times AtmosphericPressure$

$⟹m_a=\frac{4\pi (6370\times {10}^3{)}^2\times 101325}{10}$

$m_a=5.27\times {10}^{18}kg$

So, the mass of atmosphere is $5.27\times {10}^{18}kg$