$(20$ points$)$ For air$-$conditioners and refrigerators, hydrocarbon coolants are being considered as a candidate for future coolant because using them can reduce the greenhouse gas effects. However, hydrocarbon coolants are very flammable. Thus, when we design air$-$conditioners and refrigerators with a new coolant, we need to consider flammability once leaked.

Say, this is for your home. How much coolant can you have in the air$-$conditioners and refrigerators without flammability issues if you want to use propane as the coolant?

Your report will be evaluated by the following criterion.

Is the analysis based on a scientific approach?

Does a student explain the governing equations and thermodynamic$/$combustion analysis concepts used in the report in detail?

Are both rich and lean conditions considered?

Is the report readable?

The page limits for each problem are $5$ and $2$ pages for problems $1$ and $2,$ respectively. Please use additional assumptions if needed. Again, keep in mind that there are no definitive answers to these problems as they are very open problems. What I want to see from you is your logical thinking for modeling the problem, applying governing equations, calculating thermodynamic properties, and explaining them in the report. Good luck.