An adiabatic turbine is operating with an ideal gas working fluid of fixed inlet temperature and pressure,

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An adiabatic turbine is operating with an ideal gas working fluid of fixed inlet temperature and pressure, T1 and P1, respectively, and a fixed exit pressure, P2. Show that 

a. The minimum outlet temperature, T2, occurs when the turbine operates reversibly, that is, when Sgen = 0. 

b. The maximum work that can be extracted from the turbine is obtained when Sgen = 0.

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