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Mobile App Chapter 6: Q87GP (page 138)
Estimate the total mass of the Earth’s atmosphere, using the known value of atmospheric pressure at sea level.
Short Answer
The total mass of the Earth’s atmosphere is \(5.28 \times {10^{18}}\;{\rm{kg}}\).
Step by step solution
Understanding the air pressure
The weight of the atmosphere produces air pressure with an area equivalent to the surface area of the Earth. Use the pressure force relation to find the total mass.
Calculating the total mass
The relation of air pressure is given by,
\(\begin{array}{c}P = \frac{F}{A}\\P = \frac{{mg}}{A}\\m = \left( {\frac{{P \times A}}{g}} \right)\\m = \left( {\frac{{P \times 4\pi {r^{^2}}}}{g}} \right)\end{array}\)
Here, \(A\) is the area, \(F\) is the weight of the atmosphere, \(P\) is the atmospheric pressure, \(m\) is the total mass, \(r\) is the radius of the Earth and \(g\) is the gravitational acceleration.
On plugging the values in the above relation,
Thus, the total mass of the Earth’s atmosphere is \(5.28 \times {10^{18}}\;{\rm{kg}}\).
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