- #1

- 32

- 0

**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. :)