How to weigh the mass of the atmosphere
The Sunday Nation
Nairobi,
26 December 2010
After reading last week’s article, Moses Otieno wonders how anybody can measure the mass of all the air in the atmosphere. He says: “If I’m not wrong, the atmosphere thins off gradually as one goes higher and higher above the earth’s surface. Ideally, the atmosphere doesn’t end. So, how can one weigh it?”
Quite true, Moses; but actually, the mass of the atmosphere is one the easier things to determine about our planet. This is how it can be evaluated.
Suppose we have a cubic container measuring one metre on each side and we filled it with water. How would we measure its mass? Simple: we just place it on a weighing scale! And it should come to about 1,000kg.
Now, since all the sides are one metre long, it is obvious that the flat base of the container sits on an area of one square metre. Therefore, the distribution of weight is 1,000kg-force per square meter.
Knowing this distribution; we can work out the total weight of any number of similar containers placed side by side. If there are three, for example, they shall weigh 3,000kg; and so on.
The weight distribution actually gives us the amount of pressure “felt” at the base of the container. This gives us an idea about measuring the weight (and, therefore, the mass) of the atmosphere.
The atmosphere “sits” on the whole surface of the Earth. The air pressure at the surface must therefore be equal to the weight distribution of the atmosphere. If we multiply the pressure by the surface area of the planet we should get the total weight of the atmosphere.
Air pressure is measured using a simple gadget know as a barometer – most secondary schools have one. At sea-level, the pressure is about 10,000kg-force per square metre. That’s a lot of weight: why doesn’t it crush everything on the Earth’s surface? I will leave you to figure that one out!
The Earth is spherical in shape to a good approximation. The average diameter (distance from one point, through the centre, to another point at the opposite side) is about 12,740km while the highest mountain is only 8.8km tall and the deepest sea goes only 11km below.
We can therefore use the geometry of a sphere to calculate the total surface area of the planet. This comes to about 500 million square km; which is equal to 500 trillion square metres.
On each of these 500 trillion square metres, there is 10,000kg of air sitting on it. Therefore, to get the mass of the atmosphere, we multiply the total are of the planet by the mass per unit area.
The answer is 500 billion-billion kilograms; that is, the number 5 followed by 20 zeroes (I hope your calculator has enough space!). Since one tonne is equivalent to 1,000kg, we can write that a little more conveniently as 500 million billion tonnes…QED
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