$100$ mol$/$h of a liquid mixture containing $69$ mol $\%$ methanol and the rest is water at $30$oC and $1$ atm is to be separated in a distillation column at the same pressure. It is desired that the top vapor product contains $98$ mol $\%$ methanol and the bottom liquid product $96$ mol $\%$ water. The temperatures of the top and bottom product are $64\mathrm{.}7$oC and $93\mathrm{.}5$oC$,$ respectively. Calculate the required heat rate $($kW$)$ that must be transferred to the liquid mixture.