A student tries to dissolve a congealed mass of $\mathrm{NaOH}$ by adding water to the beaker. The concentration profile of $\mathrm{NaOH}$ in the water above it was measured and found to be:

\[1-x_{a}=(1.143)^{z / L-1}\]

The initial and reference temperature of the water is $0^{\circ} \mathrm{C} . c_{t}=63055 \mathrm{~mol} / \mathrm{m}^{3} ; D_{a b}=1.0 \times$ $10^{-9} \mathrm{~m}^{2} / \mathrm{s} ; L=5 \mathrm{~cm}$. Assume the water properties are constant at the reference temperature values. Data on the partial molar enthalpies of solution as a function of temperature and hence the partial molar heat capacities can be obtained crudely from the enthalpy concentration diagram [14]. What is the temperature profile?