Question 2 20 % Max Problem Statement An adiabatic turbine operates on an ideal

Question

Question 2 20 % Max Problem Statement An adiabatic turbine operates on an ideal gas (Gas constant, R-0.30kJ/kg.K). At the inlet port to the turbine, T-1200K and P(abs)-900kPa. The gas exists the turbine at 800K. The turbine produces 650kW and the following parameters may be used where relevant: Cp-1.13 kJ/kg.K and Cv-0.83 kJ/kg.K. Your task is to: (2-A). Apply the first law of thermodynamics and calculate the mass flowrate (units: kg/s) across the turbine. (7% Max] (2-B). Use the ideal gas equation and calculate the specific volume (units: [7% Max] (2-C). Calculate the volume flowrate (units: m3/s) for the ideal gas at the turbine inlet port. [6% Max)

Explanation / Answer

Work done in an adiabatic process:

Power = m' R x (T1 - T2) / (? - 1)

? is the ratio Cp / Cv and n' is mass flow rate. Plugging in values,

? = 1.13/0.83 = 1.3614

Now, since no heat is added, the temperature change i.e. change i internal energy manifests as the rate of work done. Hence, the electrical work output equals the wrok obtained.

650 = m' x 0.3 x 400 / 1.3614

m' = 7.374 kg/s -- A

Inlet = 1200 K and P = 900 kPa = 900 kJ /m3

By ideal gas equation, v = RT/P = 0.3 kJ/kg-K x 1200 K / (900 kJ /m3) = 0.4 m3 /kg -- B

Mass flow rate = Volumetric flow rate / Specific volume

or Volumetric flow rate = Mass flow rate x Sp. Vol = 7.374 kg/s x 0.4 m3/kg = 2.9496 m3/s -- C

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