$1.$ Consider a converging$-$diverging nozzle whose exit and throat area ratio is equal to $6.$ During an experiment, the reservoir pressure and temperature are kept constant and equal to $1$ MPa and $500$ K$,$ respectively, while the pressure environment is varied. Suppose that the experiment is carried out in a steady state and that the gas used is helium $($ $=1\mathrm{.}67$; R $=2078\mathrm{.}5$ J$/$kgK; cp $=5180\mathrm{.}7$ J$/$kgK$).$ Characterize the flow $($informing: the Mach number at the exit; the position of the normal shock, if such occurs; presence of oblique shocks or expansion waves; the type of flow $-$ totally subsonic, blocked, partially supersonic; and the flow rate flow entropy generation, if applicable$)$ for the following static pressures at the outlet: $995$ kPa; $900$ kPa; $500$kPa; $100$ kPa; $5$kPa.