 # Using Python calculate numerically the change of the specific internal energy of the superheated steam as it passes through the turbine

Using Python calculate numerically the change of the specific internal energy of the superheated steam as it passes through the turbine, which operates at steady state and reversibly, but  non-adiabatically. Assume the steam to obey the Peng-Robinson equation  of state

P = RT/(V-b) – a/(V(V+b)+ b(V-b))

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where a = 0.5542 Pa m6/mol2 and b = 3.049 m3/mol.

The specific volume of the steam (V) changes from 7.123 to 12.312 m3/mol  when passing through the turbine. At the same time, the steam temperature in this process remains constant. Your code should generate the answer for the change of the specific internal energy in SI units.  Please submit this homework by uploading your script file (Python file).

(Comment: you can solve the problem by deriving an expression that  needs to be integrated, and then computing a definite integral using the  quad function from scipy  (https://docs.scipy.org/doc/scipy-1.1.0/reference/integrate.html))