A solar pond operates on the principle that heat losses from a shallow layer of water, which acts as a solar absorber, may be minimized by establishing a stable vertical salinity gradient in the water. In practice such a condition may be achieved by applying a layer of pure salt to the bottom and adding an overlying layer of pure water. The salt enters into solution at the bottom and is transferred through the water layer by diffusion, thereby establishing salt-stratified conditions. As a first approximation, the total mass density P and the diffusion coefficient for salt in water (DAB) may be assumed to be constant, with D_AB = 1.2 x 10^-9 m²/s.

(a) If a saturated density of PA.s is maintained for salt in solution at the bottom of the water layer of thickness L = 1 m, how long will it take for the mass density of salt at the top of the layer to reach 25% of saturation?

(b) In the time required to achieve 25% of saturation at the top of the layer, how much salt is transferred from the bottom into the water per unit surface area (kg/m²)? The saturation density of salt in solution is p_A,s = 380 kg/m³.

(c) If the bottom is depleted of salt at the time that the salt density reaches 25% of saturation at the top, what is the final (steady-state) density of the salt at the bottom? What is the final density of the salt at the top?

Transcribed Image Text:

Water (Quiescent) Salt