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Determine the Turbine Work

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A nitrogen line 300 K and 0.5 Mpa, shown in figure below, is connected to a turbine that exhausts to a closed initially empty tank of 50 m?3. The turbine operates to a tank pressure of 0.5 MPa, at which the temperature is 250 K. Assuming the entire process is adiabatic, determine the turbine work.

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The solution determines the turbine work assuming the entire process is adiabatic.

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We approximate the nitrogen by an ideal gas with adiabatic index gamma= 5/3.
As the process is adiabatic, the work equals (-) the change of internal energy of the gas,

W = -gamma*N*k*(Delta T), ...

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