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.
First law for control volume
Definition ofg enthalpy
The 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.
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. :)