(a)
To analyze: That the average density of Earth is
(a)
Answer to Problem 18Q
Solution:
Explanation of Solution
Given data:
Diameter of Earth is
Mass of Earth is
Formula used:
Write the expression for finding the volume of a spherical object.
Here,
Write the expression for finding the density of an object.
Here,
Explanation:
Radius of Earth (
To find the volume of Earth, refer to the expression for finding the volume of a spherical object.
Upon substituting
Mass of Earth (
Refer to the expression for finding the density of an object.
Upon substituting
Conclusion:
Hence, the density of Earth is
(b)
The expected average density of the core assuming that the average density of material in the Earth’s mantle is about
Earth’s Internal Structure | |||
Region | Depth Below surface (km) | Distance from center (km) | Average density (kg/m3) |
Crust (solid) | 0-5 (under oceans) 0-35 (under continent) | 6343-6378 | 3500 |
Mantie (plastic, solid) | From bottom of crust to 2900 | 3500-6343 | 3500-5500 |
Outer core (liquid) | 2900-5100 | 1300-3500 | 10,000-12,000 |
Inner core (solid) | 5100-6400 | 0-1300 | 13,000 |
(b)
Answer to Problem 18Q
Solution:
Average density of the core is calculated to be
Explanation of Solution
Given data:
Average density of material in the Earth’s mantle is
Formula used:
Write the expression for finding the density of an object.
Here,
Explanation:
Total mass of Earth is composed of core, mantle and crust. The mass of any object is the product of its density and its volume. Therefore, mass of crust and mantle is the product of their density
The volume of core is 17% of that of Earth. Hence, the volume of core in terms of the volume of Earth is given as,
Here,
The volume of mantle is 83% of that of Earth. Hence, the volume of mantle in terms of the volume of Earth is given as,
Here,
Write the expression for the mass of Earth in terms of the mass of mantle and the mass of core.
Here,
It is known that mass is the product of density and volume. Hence, in terms of density, the above expression can be rewritten as,
Upon substituting
Substitute
Conclusion:
Hence, the density of core is
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