Numerical Estimation problem

[hasan_researc]

Homework Statement

"Estimate the mass of water in all the World’s oceans."

Homework Equations

I know the following:
Two-thirds of the Earth is sea.
The density of seawater is 1025 kg/m³.
Radius of the Earth = 6.3*10⁶m.

The Attempt at a Solution

Let's assume that the Earth's crust is a spherical shell that has a thickness of 0.001 times the radius of the earth.
So, the volume of the crust = (4$$\pi$$r²)(r_outer-r_inner) = 3.1*10¹⁸ m³.
So, volume of seawater = 2.1*10¹⁸ m³.
So, mass of seawater = 2.1*10²¹ kg.

Is the answer reasonable? How might I improve it?

 

[zhermes]

no no, ~2/3 of the SURFACE of the Earth is ocean. much much less of the entire Earth is ocean. I'd recommend using the average depth of the ocean, and the surface area of the earth.

 

[hasan_researc]

"no no, ~2/3 of the SURFACE of the Earth is ocean. much much less of the entire Earth is ocean.": I am reading the 'surface' as the crust (or the outer layer) of the earth. I think that's what I have used in the calculation, not ~2/3 of the entire volume of the earth.

" I'd recommend using the average depth of the ocean, and the surface area of the earth. ":
I think that's what I did above.

I'd be glad if you could offer some genuine help.

 

[lzkelley]

I'd be glad if you could offer some genuine help.

Very sorry! I took, "Two-thirds of the Earth is sea" to mean that you thought that 'two-thirds of the Earth was sea.' I clearly should have known you meant something completely different.

Your numbers look good; your radius is a little big, but your density a little small (for sea-water), you should be within a factor of two.

 

[rwisz]

I would suggest that the answer provided is a reasonable estimation based on the given information. However, there are several ways we can improve the accuracy of this estimation.

1. Consider the actual shape of the Earth: While assuming the Earth's crust to be a spherical shell is a good approximation, it is not entirely accurate. The Earth's shape is more accurately described as an oblate spheroid, which means it is flattened at the poles and bulging at the equator. This can affect the volume and mass calculations.

2. Consider the depth of the oceans: The given information only mentions the two-thirds of the Earth's surface is covered by oceans, but it does not specify the average depth of the oceans. Accounting for the varying depths of the oceans can significantly impact the estimation of the mass of water.

3. Use more precise measurements: The given radius of the Earth is rounded to one significant figure. Using a more precise measurement, such as 6,371 km, can improve the accuracy of the estimation.

4. Account for salt content and temperature: The density of seawater varies based on the salt content and temperature. The given density of 1025 kg/m3 is an average value. Taking into account the variations in density can result in a more accurate estimation.

5. Use more data points: The given information only mentions the two-thirds of the Earth's surface and the density of seawater. Including more data points, such as the average depth of the oceans and the actual shape of the Earth, can lead to a more accurate estimation.

Overall, while the provided estimation is reasonable, incorporating more precise measurements and data points can result in a more accurate answer. As a scientist, it is important to continuously improve and refine our estimations and calculations to increase the accuracy of our results.