1kg/s of nitrogen enters the turboexpander of a nitrogen liquefaction plant at 8 bar and 310 K with a velocity of 1.5 m/s and expands with pressure ratio of 6, exiting from the turbine with a velocity...

1kg/s of nitrogen enters the turboexpander of a nitrogen liquefaction plant at 8 bar and 310 K with a velocity of 1.5 m/s and expands with pressure ratio of 6, exiting from the turbine with a velocity of 30 m/s. The environment is at 10 °C and 1 atm. The turbine is poorly insulated and energy is transferred as heat from the environment to the turbine at a rate of 8 % of its power output. The overall thermodynamic transformation undergone by the working fluid can be modeled as a polytropic process with n = 1.2. Nitrogen in the thermodynamic region of interest can be treated as a perfect gas with a constant isobaric specific heat cP = 1.05 kJ/(kg · K). Assuming that the heat transfer from the environment to the turbine casing occurs at the uniform temperature of −10 °C, calculate the rate of exergy destruction and the exergy efficiency of the turbine.