How Long Would It Take for Earth to Reach 100°C?

AI Thread Summary
To determine how long it would take for Earth to reach 100°C from 0°C using the intercepted solar energy, the relevant formula is Q=cmT, where Q is the heat energy required, c is the specific heat capacity of water, m is the mass of the Earth, and T is the temperature change. The total energy needed to heat the Earth, treated as water, is calculated as Q=4x(1.08x10^26)x100, resulting in 4.32x10^26 J. This value should then be divided by the intercepted power of 1.27 x 10^17 W to find the time in seconds. Attention to units is crucial for accurate calculations, as incorrect values can lead to erroneous results. Proper application of these formulas will yield the correct time estimate for the temperature increase.
intenzxboi
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Homework Statement



The Earth intercepts 1.27 ´ 1017 W of radiant energy from the Sun. Suppose the Earth, of volume 1.08 ´ 1021 m3, was composed of water. How long would it take for the Earth at 0°C to reach 100°C, if none of the energy was radiated or reflected back out into space?

no clue how to start.
what formulas are related to this problem
 
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intenzxboi said:
no clue how to start.
what formulas are related to this problem

What formulas has your class studied recently? I would look at those.
 
I'm not entirely sure either. But using Q=cmT to find out the energy needed to heat the water, and then dividing by the intercepted energy.

Q=4x(1.08x10^26)x100

=4.32x10^26

Then divide by the intercepted power. Which converts to J/s.

The answer comes out wrong though.
 
You used the wrong value of c. Hint: pay attention to units.
 

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