One thousand $K\frac{g}{h}$ of an alcohol$-$water solution containi $50$ weight percentage alcohol is separated in a distillate containing $85$ weight percentage alcohol and a lotboms containing $3$ weight $\%$ alcohol in a plate column at $101.3$Kpa. A total condensor is employed and reflux ratio used is one. The feed enters the columm as satwrated liquid. The equilibrium data $($weight fraction ethanol$)$ are

$\backslash$table$[[x^{\text{'}},0,0\mathrm{.}02,0\mathrm{.}05,0\mathrm{.}10,0\mathrm{.}20,0\mathrm{.}30,0\mathrm{.}40],[y^{\text{'}},0,0\mathrm{.}192,0\mathrm{.}377,0\mathrm{.}527,0\mathrm{.}656,0\mathrm{.}713,0\mathrm{.}746],[x^{\text{'}},0\mathrm{.}50,0\mathrm{.}60,0\mathrm{.}70,0\mathrm{.}80,0\mathrm{.}90,0\mathrm{.}94,0\mathrm{.}96],[y^{\text{'}},0\mathrm{.}771,0\mathrm{.}794,0\mathrm{.}822,0\mathrm{.}858,0\mathrm{.}912,0\mathrm{.}942,0\mathrm{.}959]]$

The Enthalpy data $($weight Fraction ethanol$)$ are:

$\backslash$table$[[x^1,0,0\mathrm{.}10,0\mathrm{.}30,0\mathrm{.}50,0\mathrm{.}70,0\mathrm{.}90,1\mathrm{.}0],[H_1,K\frac{J}{k}g,419,372,314,286,258,225,207],[H_{G,}K\frac{J}{k}g,2675,2517,2193,1870,1544,1223,1064]]$

Using ponchon savaric method$/($c$)$ The number of theoretical plate

Determine: when reflux rakio used is $1km$ ol kmol product

$($a$)$ The minimum number of plates$/($D$)$ The condenser duty and

$($b$)$ The minimum reflun ratio the reboibr heat load per $100$kmo$\frac{l}{h}$ of beed