Calculating Time to Heat Earth to 100°C

[djk628]

Homework Statement

The Earth intercepts 1.27 x 10^17 W of radiant energy from the Sun. Suppose the Earth, of volume 1.08 x 10^21 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?

Homework Equations

Q=mc*deltaT

The Attempt at a Solution

I just want to make sure that I did this correctly because the answer choices are all similar and vary by degrees of magnitude and I would like to avoid a simple mistake. Multiply the volume by 1000 to get the weight in kilograms, then multiply by 100, the temperature change. Multiply this by the specific heat. So:

1.27 x 10^17 = 1.08 x 10^24 kg * 4186 * 100

divide both sides by Q, gives a value in seconds. Convert to years which is approximately 113 years. Is this correct?

 

[rock.freak667]

your equation should be

(1.27 x 10^17)*t = 1.08 x 10^24 kg * 4186 * 100

But other than that, it looks like it should be correct.