Anonymous
Anonymous asked in Science & MathematicsPhysics · 10 years ago

# What is the approximate mass of a column of air 1sq cm in area that extends from sea level to upper atmosphere?

And what is the weight of this amount of air?

Please provide an explanation as well, because this concept is above me.

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Air pressure at sea level is about 101 000 Pa. A Pa (pascal), by definition, is a newton per square meter.

So the weight, force of that column which is 1 square meter in cross-section area is 101000 newtons.

There are 10000 cm² per m², so we get

the weight, force of that column 1 square cm in cross-section area is 10.1 newtons ⬅

Using F = ma or Weight = mass x acceleration of gravity,

10.1 newtons corresponds to a mass of 10.1 N / 9.8 = 1.03 kg ⬅

that is approximate and does not account for the weight decreasing as you go up in altitude. But most of the air is at low altitudes, so it's close.

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• What is the approximate mass of a column of air 1sq cm in area that extends from sea level to upper atmosphere?

And what is the weight of this amount of air?

Please provide an explanation as well, because this concept is above me.

The web site above states that standard air pressure at sea level = 101325 pascals = 101325 Newton per meter^2

1 meter = 100 cm

1m^2 = (100 cm)^2 = 10,000 cm^2

101325 N/m^2 ÷ 10,000 cm^2/m^2 = 10.1325 N/cm^2

This air pressure is caused by the weight of the air above the surface of the earth. The earth attracts the mass of the air above the surface, like the earth attracts objects in the air above the earth. The gravitational force attracts all objects toward the earth.

You may wonder why the air does not fall to the surface!

I say, “The air has fallen to the surface!”

The atmosphere is similar to the ocean! When a diver goes 100 meter under water, the pressure is caused by the weight of the volume of water above the diver.

The density of water = 1000 kg/m^3. The pressure is directly proportional to the depth.

Pressure = Density * g * depth = 1000 * 9.8 * 100 = 9.8 * 10^5 N/m^2

This pressure is caused by the weight of a column of water which is 100 m high with cross-sectional area of 1 m^2

The weight of the column of water is caused by the gravitational force.

The gravitational force is caused by the mass of the earth and the mass of the volume of water in the column.

The volume of water in the column = cross-sectional area * height = 1 m^2 * 100 m = 100 m^3

The mass of water in the column = Volume * density 100 m^3 * 1000 kg/m^3 = 100,000 kg of water

The weight of water in the column = 100,000 kg * 9.8 m/s^2 = 980,000 N = 9.8 * 10^5 N

As we sit on surface of the earth and look upward, we are sitting on the bottom of an ocean of air. The pressure that we measure with a barometer is caused by the weight of a column of air that is directly above us. The standard pressure at sea level = 10.1325 N/cm^2 So, the weight of the air on a 1 cm^2 = 10.1325 N

Weight= mass * g

10.1325 = mass * 9.8

mass = 10.1325 ÷ 9.8 = 1.0339 kg

This is the mass of air in a column with 1 cm^2 cross-sectional area and as high as the atomosphere.