Problems

7-1 Develop the equations necessary to describe a column in which each stage is regarded as a unit of a system. Apply the capital 0 method to each stage and solve the equations by use of the Newton-Raphson method.

7-2 Describe the differences in the method described in Prob. 7-1 and the 2N Newton-Raphson method described in Chap. 4.

7-3 For the case where the reflux ratio LJD and the boilup ratio Vs /B are specified in lieu of the reflux rate L1 and the distillât^ rate D for a conventional distillation column having a partial condenser, formulate the g functus of the 6 method where the variables x are taken to be x = [07i T2 Tv., TS QC <2J'

7-4 (a) Formulate the functions needed to solve a typical absorber problem by the 0 method when the variables of the 0 method are taken to be

(b) Formulate the equations necessary to compute the temperatures T2, T3,..TN_, by the Kb method and the flow rates L2, by the constant-composition method.

7-5 Formulate the functions for the capital 0 method for the case where the absorber is subdivided into two columns8 as shown in Fig. P7-5. The independent variables of the capital 0 method are taken to be x = [0, ©2 Tx Tm Tm + i

Figure P7-5 Division of a single column into a system of two columns.

7-6 Show that the function gx given in Table 7-1 for a conventional distillation column is a mono-tonic decreasing function of 0 and has one zero lying between 0 = 0 and 0 = oo.