Calculate the adiabatic change in entropy when $3g$ of ice at $-12C$ is added to $55\mathrm{.}0g$ of hot water at $77C$ in an isolated system.

Given the following information:

Heat capacity of ice $c_p[H_{2}O(s)]=37\mathrm{.}17J{K}^{-1}mo{l}^{-1}$

Heat capacity of water $c_p[H_{2}O(l)]=75\mathrm{.}29J{C}^{-1}mo{l}^{-1}.$

Molar enthalpy of fusion of ice $D{H}_m[H_{2}O(s)]=+6\mathrm{.}008kJmo{l}^{-1}$

$[18$ marks$]$

With the aid of a diagram, describe how the Gibbs$-$Helmholtz equation allows for the determination of thermodynamic data from equilibrium measurements.

$[14$ marks$]$