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

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SUMMARY

The discussion focuses on calculating the necessary mass flow of air through a small high-speed turbine operating under adiabatic conditions. The turbine delivers power at a rate of 100 W, with inlet conditions of 400 kPa and 50°C, and outlet conditions of 150 kPa and -30°C. The first law of thermodynamics is applied to a control volume, leading to the equation m=(dW/dt) / (h_i-h_e) for mass flow, where h_i and h_e represent the specific enthalpy at the inlet and outlet, respectively. The challenge lies in determining the change in enthalpy without using steam tables, utilizing the constant pressure heat capacity for air instead.

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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. :)
 
Science news on Phys.org
The constant pressure heat capacity for air is supposed to be used. This is equal to the constant volume heat capacity plus the universal gas constant.
 

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