Write a linear equation that describes the energy balance, using Table $1$ and the same

concept that energy in must equal energy out.

$Q+{\displaystyle \underset{?}{\overset{?}{}}}{n}_{in}$widehat$(H_{in})={\displaystyle \underset{?}{\overset{?}{}}}\frac{n_{\text{o}\text{u}\text{t}}}{b}ar(H_{\text{o}\text{u}\text{t}})$

Table $1.$ Substance Enthalpies $($accounting for difference in stream

temperatures and changes of state$)$

You now have a linear system with $3$ equations and $3$ unknowns.

Put the equations in matrix form.

Solve the system of equations using Python, then solve them in Excel to check your

answer.

Finally, calculate the fractional conversion $(x)$ for the reaction using the following

equation:

$x=\frac{(n^{})(C_2{H}_{5}OH{)}_{in}-(n^{})(C_2{H}_{5}OH{)}_{\text{o}\text{u}\text{t}}}{(n^{})(C_2{H}_{5}OH{)}_{in}}$

In your memo to Dr$.$ Richards, include $1)$ the system of equations, $2)$ the solution giving the

unknown flow rates in the outlet stream, and $3)$ the fractional conversion $(x).$ Attach your

Python code as an appendix to the memo and submit your Excel file.