$4$Y$7.$ Ponchon$-$Savarit $($Prob$.19-10$ in McCabe and Smith. Unit Operations of Chemical Engineering. $3^{rd}$ Ed$.)$ A saturated liquid feed containing $40$ mole percent $n-$hexane and $60$ mole percent $n-$ octane is fed to a small distillation column at a rate of $100$gmo$\frac{l}{h}.$ A reflux ratio, $L\frac{a}{D}=1\mathrm{.}2,$ is maintained. The overhead product is $95$ mole percent hexane, and the bottom product is $10$ mole percent hexane. If each theoretical plate loses $80,000ca\frac{l}{h},$ step off the plates on a Ponchon diagram, taking into account the column heat loss. Physicochemical data are given in Tables $19-12$ and $19-13.($a$)$ Determine the heat added to the reboiler in calories per hour, $($b$)$ Find the number of theoretical plates excluding the reboiler. Assume that a total condenser is used. DO This PROBLEM $1)$ WITHOUT HEAT LOSSES $2)$ WITH HEAT LOSSES

Table $19-12$ VAPOR$-$IIQUID EQUIIIBRIUM DATA, $1$ atm MOLE FRACIION HEXANE

$\backslash$table$[[x,$ in liquid,$0,0\mathrm{.}1,0\mathrm{.}3,0\mathrm{.}5,0\mathrm{.}55,0\mathrm{.}7,1\mathrm{.}0],[y,$ in vapor,$0,0\mathrm{.}36,0\mathrm{.}70,0\mathrm{.}85,0\mathrm{.}90,0\mathrm{.}95,1\mathrm{.}0]]$

Table $19-13$ ENTHALPY$-$CONCENTRATION DATA

$\backslash$table$[[\backslash$table$[[$Concentration$,],[$mole fraction$],[$hexane$]],$Enthalpy, cal$/$g mol$],[,\backslash$table$[[$Saturated$],[$liquid$]],\backslash$table$[[$Saturated$],[$vapor$]]],[0,7000,15,700],[0\mathrm{.}1,6300,15,400],[0\mathrm{.}3,5000,14,700],[0\mathrm{.}5,4100,13,900],[0\mathrm{.}7,3400,12,900],[0\mathrm{.}9,3100,11,600],[1\mathrm{.}0,3000,10,000]]$