Mars has a diameter that is approximately half that of Earth. If the interiors of these planets are heated by radioactive decays, how does the heating rate of the interior of Mars compare to that of Earth? a. The heating rate of Mars is 0.125 times that of Earth. b. The heating rate of Mars is 8 times that of Earth. c. The heating rate of Mars is 0.5 times that of Earth. d. The heating rate of Mars is 4 times that of Earth. e. The heating rates are about the same.

Md Ariful Islam

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Heating Rate Comparison

The heating rate of a planet's interior due to radioactive decay is proportional to its volume, which is determined by its radius cubed. Since Mars has a diameter that is approximately half that of Earth, its radius is also approximately half that of Earth's. Therefore, the volume of Mars is approximately $ \left(\frac{1}{2}\right)^3 = \frac{1}{8} $ times that of Earth.

Since the heating rate is proportional to volume, the heating rate of Mars is $ \frac{1}{8} $ times that of Earth.

Therefore, the correct answer is:

a. The heating rate of Mars is 0.125 times that of Earth.

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