Question $4$d

A solar still is a device used to desalinate sea water using energy from the sun. It works by evaporating sea water and condensing the fresh water, leaving the salt behind in the solution.

Below you see a solar still in Kenya, where the maximum solar irradiance at midday is approximately $\backslash (600\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}2\backslash ).$ The initial temperature of the water is $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Your still has a water height of $0\mathrm{.}01$ m $,$ in a container with a length of $3$ m and a width of $2$ m $.$ For efficient operation, the water in the still should be heated to $\backslash (65^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

You can assume that the water is only heated by the sun and the still is $\backslash (100\backslash \%\backslash )$ efficient.

At midday, how long does it take to heat the water in the still?

Show your working $-$ marks are awarded not just on the basis of the final answer, but also the method used and equations presented.

Density of water $-\backslash (1000\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$

Heat capacity of sea water $\backslash (-4\mathrm{.}2\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash$cdot $\backslash$mathrm$\{$K$\}\backslash )$