Which of the following best describes why the smaller terrestrial worlds have cooler interiors than the larger

Question

Which of the following best describes why the smaller terrestrial worlds have cooler interiors than the larger ones?

a)They had more volcanic eruptions in the past, which released their internal heat.
b)They were cooler when they formed.
c)They have relatively fewer radioactive elements.
d)The smaller ones are farther from the Sun.
e)They have relatively more surface area compared to their volumes.

Answer 1

Of your choices, (e) is the best. (a) is no good because it fails to account for the continuing generation of heat, as, for example, by the earth. (b) is no good because they were all about the same temperature when they formed. As the protoplanets grew larger, their interiors began to heat up. (c) is no good because what matters more is density, and there's no reason to believe there are significant differences in the density of radioactive elements. (d) is just plain false: Earth is farther from the sun than Mercury.

That leaves (e). Surface area of a sphere is 4pr^2, where p is pi, and volume is (4/3) pr^3, so the ratio of surface area to volume varies as 1/r ... it varies inversely with radius, so the ratio for smaller planets is greater than that for larger ones.

The key connection, though, is internal , which is a direct function of r. Larger planets have more pressure at their centers, and that means more heat. In fact, if the "planet" were big enough, it would become a star.

Conclusion: Big means hot.

Answer 2

I think "e" is the best answer but really it has to do with mass and gravity. The internal heat comes from the pressure exerted by gravity. Larger planets have more gravity.

Answer 3

a