General Science / Re: How good would a diameter of 111 Km be for a cylinder of diamond 111 Km high?« on: 13/03/2023 14:53:52 »
By the way, what would be, theoretically, the size of the mentioned column if we used all carbon atoms available on air, around us?
What size would be a cube of same structure as diamond made of carbon with all the cabon on the air atmosphere nowadays on our planet?
To determine the size of a cube made of carbon with the same structure as a diamond, we need to know the total amount of carbon available in the Earth's atmosphere.
However, it's important to note that most of the carbon on Earth is not in the form of diamonds. In fact, the vast majority of Earth's carbon is in the form of carbon dioxide (CO2) in the atmosphere, dissolved in the oceans, or stored in the Earth's crust as fossil fuels.
To estimate the amount of carbon in the Earth's atmosphere, we can refer to data from the United States Environmental Protection Agency (EPA), which estimates that the total amount of carbon in the Earth's atmosphere is about 3.1 trillion metric tons.
Now, we need to calculate the volume of a diamond cube with the same mass as 3.1 trillion metric tons of carbon. The density of diamond is about 3.5 grams per cubic centimeter, so the mass of a diamond cube can be calculated as:
mass = density x volume
Solving for volume, we get:
volume = mass / density
Plugging in the values, we get:
volume = (3.1 x 10^12 metric tons) / (3.5 g/cm^3 x 1 x 10^6 metric tons/g)
volume = 8.86 x 10^17 cubic centimeters
Taking the cube root of the volume, we get:
size = (8.86 x 10^17)^(1/3) cm
size = 4,735 km
Therefore, a cube made of carbon with the same structure as a diamond and containing all the carbon in the Earth's atmosphere would have a side length of approximately 4,735 kilometers (2,944 miles).
What would be the diameter of a cylinder like that instead of a cube if it had altitude 100 km (Karman Line) ?
If we assume that the cylinder has a height of 100 km (the Karman Line, which is commonly regarded as the boundary between Earth's atmosphere and outer space), we can calculate the diameter of the cylinder with the same mass as 3.1 trillion metric tons of carbon.
First, we need to calculate the volume of the cylinder. The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
To find the radius of the cylinder, we can rearrange the formula as:
r = √(V / πh)
We know the volume of the cylinder is the same as the volume of the diamond cube we calculated earlier, which is approximately 8.86 x 10^17 cubic centimeters. We also know the height of the cylinder is 100 km, or 10^8 centimeters.
Plugging in these values, we get:
r = √(8.86 x 10^17 / π x 10^8)
r = 1.19 x 10^6 cm
So the radius of the cylinder would be approximately 1.19 million centimeters.
To find the diameter of the cylinder, we simply double the radius:
d = 2r
d = 2 x 1.19 x 10^6 cm
d = 2.38 x 10^6 cm
Therefore, the diameter of the cylinder would be approximately 2.38 million centimeters, or 23,800 kilometers (14,800 miles).
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