CHALLENGE PROBLEM: The Earth cools by radiating energy into space (at ~0 K). Whi
ID: 159144 • Letter: C
Question
CHALLENGE PROBLEM:
The Earth cools by radiating energy into space (at ~0 K). While it was once an entirely molten ball, luckily it is now quite habitable.
A.) Using the following data, estimate the age of the Earth (in solid phase).
In this crude approximation, you should:
- estimate that the Earth has a uniform temperature throughout at any given time.
- NOT use the Newton's cooling approximation (exponential)-- think about a better limit to use.
Physical data:
Mass of Earth = 5.97x1024 kg
Radius of Earth = 6.38x106 m
Approximate specific heat of Earth (average) = 728 J/(kg·K)
Approximate minimum melting temperature of Earth (silicate rock) = 1687 K
Current average crust temperature (seen in many caves) = 15 oC
emissivity of the Earth's surface (varies by surface conditions) = 0.95
Estimated age of the Earth (as a solid) = ????????? years
B.) Below is a series of advanced corrections that can be made to the above result. While I will not have you address them quantitatively, you should be able to reason how each of these factors will affect the above result.
the core of the Earth is still molten: ---Select ONE ---
increases it
decreases it
has no effect on it
heat must be transferred from the interior to the surface to radiate into space: ---Select ONE---
increases it
decreases it
has no effect on it
the Earth has an internal heat source (radioactivity): ---Select ONE---
increases it
decreases it
has no effect on it
the atmosphere absorbs/re-radiates some heat back to the Earth: ---Select ONE---
increases it
decreases it
has no effect on it
Explanation / Answer
CHALLENGE PROBLEM: The Earth cools by radiating energy into space (at ~0 K). Whi