A distillation column is separating methanol and water with the reflux returned to the column at its bubble point. A larger condenser is now installed, significantly cooling the reflux stream. Control devices keep the apparent (or external) reflux ratio constant. If the same amount of product is to be withdrawn as before, what will happen to 

(a) The slope of the operating line,

(b) The reboiler heat duty, and 

(c) The purity of the overhead product?