$(15$ POINTS$)$ Exergy analysis of the melting of a piece of ice

In this exercise you are asked to evaluate the exergy changes $($lost work$)$ associated with

the melting of an ice lump of mass of $1kg$ and an initial temperature of $245K$ as it

becomes in contact with the environment assumed at a temperature of $293K.$ The

whole process can be assumed to be at $1$ bar of pressure.

You can use the following information:

Enthalpy of fusion of water: $h_w=333\mathrm{.}4k\frac{J}{k}g$

Isobaric specific heat capacity of ice: $c_{P,i}=2\mathrm{.}07k\frac{J}{kgK}$

Isobaric specific heat capacity of water: $c_{P,w}=4\mathrm{.}20k\frac{J}{kgK}$

Melting temperature for ice under $1$ bar of pressure: $T_m=273\mathrm{.}16K$