Steady gas flow of pressure Pin and temperature Tin is expanded in an adiabatic steam turbine to pressure Pout. The isentropic efficiency of the steam turbine is $\backslash$eta s$.$ Derive analytical equations that describe:

$$ the outlet temperature of the gas

$$ the work produced per mole of flux, and

$$ the rate of spontaneous entropy production per unit flow as a function of the problem data. You can consider the working gas to behave as a perfect gas and have a constant $($and known$)$ specific molar heat capacity at constant pressure equal to cp$.$

In a second stage, use the above general equations that you explained and calculate the values $$of the corresponding quantities in the case where: Pin $=10$ bar $=,$Tin$=550$ K $,$ Pout$=1$ bar $=,\backslash$eta s$=0\mathrm{.}65$ and cp $=37\mathrm{.}151$ J $/($mol K$).$ It gives R$=8\mathrm{.}314$ J $/($mol K $).$