A steam engine consists of a boiler tank connected to a turbine. The boiler tank

Question

A steam engine consists of a boiler tank connected to a turbine. The boiler tank has a volume of 100 L and initially contains saturated liquid with a very small amount of vapor at 100 kPa. Heat is now added by the burner, and the pressure regulator does not open before the boiler pressure reaches 700kPa, which it keeps constant. The vapor leaving the boiler tank passes through a turbine and is discharged to the atmosphere as saturated vapor at 100kPa. The burner is turned off when no more liquid is present in the boiler. Find the total turbine work and the total heat transfer to the boiler for this process. Assume the turbine is adiabatic and the change in the kinetic and potential energy across the turbine is negligible.
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Explanation / Answer

Assuming all the pressures are in absolute units: Heat Transfer = m(h2-h1) m = V1/v1 V1 = 100L v1 = vf at 100 kPa = 0.001043 m3/kg m = 100/(0.001043*1000) = 95.9 kg h1 = hf at 100 kPa = 417.4 kJ/kg s2 = s3 = sg @ 700 kPa = 7.359 kJ/kg-K h2 = h @ 700 kPa & s2=s3=7.359 kJ/kg-K h2 = 3094.0 kJ/kg Heat Transfer = 95.9*(3094.0-417.4) = 256,686 kJ Turbine Work = m*(h2-h3) h3 = hg @ 700 kPa = 2675.0 kJ/kg Turbine Work = 95.9*(3094.0-2675.0) = 40,182.1 kJ

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