Due to heat sources (e.g. radioactivity) and remnant heat associated with Earth's accretion and differentiation, the interior of the Earth is continually transmitting heat up to the surface, ultimately to be dissipated into space. Measurements in sea-floor sediments confirm that, on average, 1.8´10-6 cal of heat cross each cm2 of the surface of the sea floor every second.
(By the way, in the past, the heat flow was likely to have been greater....)
(a) If the oceans cover 70% of Earth's surface, how much heat in total is leaving the Earth's interior every second and entering the oceans?
(b) How long (in years) would it take the oceans to heat up to 100°C? You can assume that they start out at about 2°C. Take the heat capacity of seawater to be the same as pure water.
(The heat capacity of water is 1 calorie per gram, i.e. 1 gram of water will absorb 1 calorie of heat if its temperature is raised by 1°C.)
(c) To cause the oceans to boil, an additional 542 cal of heat - called the latent heat of evaporation - must be added to each gram of water. How long would it take (in years) for the heat flow out of the sea floor to heat the oceans to boiling, once they've reached 100°C?
(d) Why haven't the oceans boiled away as a result of the heat emanating from Earth's interior?