ANS:C - total cost first decreases and then increases.

As the reflux ratio in a distillation column is increased from the minimum, the slope of the operating line in the stripping section decreases. Explanation:

1. Reflux Ratio:
   • Reflux ratio is the ratio of the amount of condensed overhead vapor (reflux) returned to the column to the amount of vapor taken off as distillate.
   • It plays a significant role in the separation efficiency and energy consumption of a distillation column.
2. Operating Line in Stripping Section:
   • In a distillation column, the stripping section is where the liquid enters and moves countercurrently to the rising vapor.
   • The operating line in the stripping section represents the relationship between the concentrations of components in the liquid and vapor phases as they change along the height of the stripping section.
   • As the reflux ratio increases from the minimum, more reflux liquid is returned to the column, resulting in a greater liquid flow rate in the stripping section.
   • This increased liquid flow rate leads to greater dilution of the volatile components in the liquid phase, causing a decrease in the slope of the operating line in the stripping section.
3. Effect on Number of Plates:
   • Increasing the reflux ratio from the minimum generally leads to an increase in the number of plates in the column.
   • However, the rate of increase in the number of plates may vary, and it typically decreases very slowly at first and then more rapidly as the reflux ratio increases further.
4. Total Cost:
   • The total cost of a distillation column operation may vary with changes in the reflux ratio due to alterations in energy consumption, equipment size, and other factors.
   • The relationship between reflux ratio and total cost can be complex and depends on factors such as energy prices, equipment costs, and operating conditions.
5. Liquid and Vapor Flows:
   • Increasing the reflux ratio generally leads to an increase in liquid flow and a decrease in vapor flow within the column, as more liquid is returned to the column as reflux.