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Solved: A barometer having a cross-sectional area of 1.00
Chapter 5, Problem 106P(choose chapter or problem)
A barometer having a cross-sectional area of 1.00 \(\mathrm{cm}^{2}\) at sea level measures a pressure of 76.0 cm of mercury. The pressure exerted by this column of mercury is equal to the pressure exerted by all the air on 1 \(\mathrm{cm}^{2}\) of Earth’s surface. Given that the density of mercury is 13.6 g/mL and the average radius of Earth is 6371 km, calculate the total mass of Earth’s atmosphere in kilograms. (Hint: The surface area of a sphere is 4𝜋\(r^{2}\) where r is the radius of the sphere.)
Questions & Answers
QUESTION:
A barometer having a cross-sectional area of 1.00 \(\mathrm{cm}^{2}\) at sea level measures a pressure of 76.0 cm of mercury. The pressure exerted by this column of mercury is equal to the pressure exerted by all the air on 1 \(\mathrm{cm}^{2}\) of Earth’s surface. Given that the density of mercury is 13.6 g/mL and the average radius of Earth is 6371 km, calculate the total mass of Earth’s atmosphere in kilograms. (Hint: The surface area of a sphere is 4𝜋\(r^{2}\) where r is the radius of the sphere.)
ANSWER:Step 1 of 2
Here, we are going to calculate the total mass of the earth’s atmosphere in kg.
The mass of the earth’s atmosphere
= (surface area of the earth in 
(mass per
Given that
Density = 13.6 g/mL = 13.6 g/
Mass of a single column of surface area 1
= 76.0 cm 13.6 g/
