A reaction in a poorly mixed tank leads to the following data for temperature as a function of depth:

$\backslash$table$[[$depth $z(m),0,0\mathrm{.}5,1,1\mathrm{.}5,2,2\mathrm{.}5,3],[T(C),70,70,55,22,13,10,10]]$

Compute numerical first derivatives $d\frac{T}{d}z$ and second derivatives $d^2\frac{T}{d}{z}^2$ at each point. Estimate the depth of the "thermocline", which is the depth at which the second derivative equals zero. Also compute the heat flux $Q^{}=-k(d\frac{T}{d}z)$ at each point. Use a thermal conductivity $k=0\mathrm{.}01ca\frac{l}{s}-cm-C.$