Consider the distillation of a mixture of ethane, propane, n$-$butane, n$-$pentane, and nhexane as shown in the figure below. Entalpy and entropy values are given as

$\backslash$table$[[,$Feed,Distillate,Bottoms$],[\backslash$table$[[$Entalpy$],[($kJ$/$kmol$)]],134570,102840,143460],[\backslash$table$[[$Entropy$],[$ kmol.K$)]],-403\mathrm{.}93,-277\mathrm{.}61,-443\mathrm{.}76]]$

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.

Figure $1.$ Distillation column