A $60$:$40$ liquid mixture of ethanol and water is fed to a distillation column which produces both a liquid and vapor stream. The vapor leaves the top of the distillation column where it is completely condensed and split into two equal fractions. One fraction is taken off as a product stream and the other is fed back to the column. The liquid leaving the bottom of the column is fed to a partial reboiler in which $40\%$ of its vaporized. The vapor from the reboiler is recycled back to the distillation tower and the liquid is taken off as bottoms product. The partial reboiler is at $500$mm Hg and $90$C$.$ We have inlet feed rate mixture of $20$kg$/$h

$80\%$ of the ethanol fed to the column leaves the condenser in the product stream. Perform mass balance and energy balance.