Final answer:
To estimate the total mass of the Earth's atmosphere above a 5-m2 area, multiply the atmospheric pressure at sea level by the area to get the weight, and then divide by the acceleration due to gravity to get the mass, resulting in approximately 51,478 kg.
Step-by-step explanation:
To estimate the total mass of the Earth's atmosphere above a 5-m2 area using the atmospheric pressure at sea level, we use the relationship that a column of air above 1.00 m2 of the Earth's surface weighs 1.01 × 105 N at sea level, which is equivalent to 1 atm.
Given that atmospheric pressure (P) is the force exerted per unit area, and weight (W) is the force due to gravity on a mass (m) near the surface of the earth (W = mg, where g is the acceleration due to gravity), we can use the equation P = W/A, where W is the weight of the air column and A is the area over which the pressure is distributed. To find the weight of the atmosphere above 5 m2, we multiply the pressure by the area:
W = P × A = 1.01 × 105 N/m2 × 5 m2 = 5.05 × 105 N. Since weight is the product of mass and gravity, to find the mass we divide by the gravitational acceleration:
m = W/g = 5.05 × 105 N / 9.81 m/s2 = 51,478 kg (approximately)
Therefore, the estimated atmospheric mass above a 5 m2 area at sea level is approximately 51,478 kg.