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Thermodynamics: turbine, steady-state, how to find the necessary mass flow?

  1. Nov 22, 2011 #1
    The problem (tried my best to translate it):
    A small high speed turbine is operating on compressed air. It deliveres dW/dT=100 W. At the inlet, the pressure is 400 kPa and the temperature 50*C.

    At the exit, the pressure is 150 kPa and the temperature -30*C.

    Neglect the velocity and assume an adiabatic process. Find the necessary mass flow of air through the turbine.


    My attempt at a solution:
    I have derived the first law for a control volume:
    dE/dt=(dQ/dt)-(dW/dt)+∑m_i (h_i+0.5v_i^2+gz_i)-∑m_e (h_e+0.5v_e^2+gz_e)

    Where t is time, and m_i og m_e is rate of change of mass flow at the inlet and exit, respecitively.
    Assumed steady state: dE/dt=0.
    Adibatic dQ/dt=0.
    Also m_e´=m_i´=m´

    By neglecting kinetic and potential energy associated with gravity, i end up with:

    dW/dt=m(h_i-h_e) <=> m=(dW/dt) / (h_i-h_e)

    So far so good, but now I need to find the change of enthalphy. We were supposed to solve this task without the use of steam tables. I have tried to use the definition of constant volume heat capacity, but no luck so far. Any input?

    Thanks in advance. :)

    e: sorry, this was supposed to go in the homework section. Could a mod please move it? Thanks. :)
     
  2. jcsd
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