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Problem on ideal gas law

A stream of steam at 1 bar and 400 K enters a compressor through a pipe with cross-sectional area of 0.1 m2 at a velocity of 5 m/s. The pressure of the outlet stream is at 5 bar, temperature is at 500 K, and velocity is 1 m/s. Assume the steam can be described by the ideal gas law with constant Cp = 2.08 kJ/kg/K for parts (a) and (b) of this problem.

a. Assuming the ideal gas law, what is the mass flow rate at the inlet stream?

b. The compressor is not perfectly efficient, and some heat is lost through it. If 55 kJ/s is the work required to operate the compressor, how much heat is lost through the compressor? Assume water is an ideal gas for this problem.

c. Now, without assuming the ideal gas law, how much heat is lost through the compressor if 55 kJ/s is the work required to operate the compressor?

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