In$-$Class Example $27$:

Carbon$-$Dioxide at $100$ kPa and $1600$ K is flowing into a mixing chamber at a rate of $\backslash (1\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The mixing chamber is also receiving super$-$heated steam at $100$ kPa and $800$ K at a rate of $\backslash (2\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The mixture exits the mixing chamber at $100$ kPa and $500$ K $.$ Find the rate of cooling required to achieve the exit temperature and the entropy generated by this mixing and cooling process.