Consider the distillation of a mixture of ethane, propane, n$-$butane, n$-$pentane, and n$-$

hexane as shown in the figure below. Entalpy and entropy values are given as

The column has a condenser duty of $3431\mathrm{.}88kW$ and a reboiler duty of $3395\mathrm{.}34kW.$

The condenser and the reboiler temperatures are $319\mathrm{.}3K$ and $400\mathrm{.}2K,$ respectively.

Assuming $T_0=300K,$ calculate,

a$)$ The lost work,

b$)$ The minimum work of separation,

c$)$ The efficiency.