A solar pond operates on the principle that heatlosses

Chapter 14, Problem 14.46

(choose chapter or problem)

A solar pond operates on the principle that heatlosses from a shallow layer of water, which acts as asolar absorber, may be minimized by establishing astable vertical salinity gradient in the water. In prac-tice such a condition may be achieved by applying alayer of pure salt to the bottom and adding an overly-ing layer of pure water. The salt enters into solutionat the bottom and is transferred through the waterlayer by diffusion, thereby establishing salt-stratifiedconditions.As a first approximation, the total mass density ? andthe diffusion coefficient for salt in water (DAB) may beassumed to be constant, with DAB?1.2?10?9m2/s.(a) If a saturated density of ?A,sis maintained for saltin solution at the bottom of the water layer ofthickness L?1 m, how long will it take for themass density of salt at the top of the layer to reach25% of saturation? b) In the time required to achieve 25% of saturation atthe top of the layer, how much salt is transferredfrom the bottom into the water per unit surface area(kg/m2)? The saturation density of salt in solutionis ?A,s?380 kg/m3.(c) If the bottom is depleted of salt at the time that thesalt density reaches 25% of saturation at the top,what is the final (steady-state) density of the saltat the bottom? What is the final density of the salt at the top?