Draw and label a flowchart and determine the number of

QUESTION:

Draw and label a flowchart and determine the number of degrees of freedom for each of the given systems. Give a feasible set of design variables and, if possible, an infeasible set. The solution to part (a) is given as an example.

(a) An aqueous solution of sulfuric acid at temperature \(T_0\) is diluted with pure water at the same temperature in an adiabatic mixer. Calculate the final mixture temperature.

Solution:

\(\begin{aligned} & 7 \text { variables }\left(m_{1}, x_{1}, m_{2}, m_{3}, x_{3}, T_{0}, T\right) \\ - & 3 \text { relations }(2 \text { material balances and } 1 \text { energy balance }) \\ \hline= & 4 \text { degrees of freedom } \end{aligned}\)

One feasible set of design variables (there are others) is

\(\left\{m_1,\ x_1,\ m_2,\ T_0\right\}\)

If you are given values of these variables you can calculate \(m_3\) (total mass balance), \(x_3\) (\(\mathrm{H}_{2} \mathrm{SO}_{4}\) balance), and T (energy balance). An infeasible set is

\(\left\{m_1,\ m_2,\ m_3,\ T_0\right\}\)

Once \(m_1\) and \(m_2\) have been specified, \(m_3\) is fixed by a total material balance and may not be independently assigned a value.

(b) A natural gas containing methane, ethane, and propane at temperature \(T_1\) is mixed with preheated air at temperature \(T_2\), and the mixture is heated to \(200^{\circ} \mathrm{C}\). Calculate the required heat input.

(c) A stream containing hexane vapor in nitrogen at temperature \(T_1\) is cooled at constant pressure, condensing 95% of the hexane. Calculate the product temperature.