The tropical ocean is a giant collector of solar energy. Surface waters have temperatures around 24 °C, and deeper waters have temperatures around 4 °C. This temperature differential can be used to run engines that drive electrical generators.
(a) Estimate the amount of solar energy Qh − Qc stored in the ocean by means of this temperature differential; the warm surface layer is typically 200 m thick and the tropical ocean covers about 1/3 of the Earth’s surface area. (Earth’s radius is 6400 km.)
(b) The world consumes energy at a rate of about 9 billion kilowatts. How many joules of energy is this per year?
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(c) What fraction of the solar energy stored in the oceans would have to be harvested annually to meet the world’s energy needs?
(d) Answer part (c) for the case where 90% of the energy is lost during conversion.
(e) What is the Carnot efficiency for engines running between these two temperatures?
(f) What is the actual efficiency for engines running between these two temperatures if the coefficient of utility is 0.1?