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

In summary, the problem involves a small high speed turbine operating on compressed air, with specific values for pressure and temperature at the inlet and exit. Neglecting velocity and assuming an adiabatic process, the necessary mass flow of air through the turbine can be calculated using the first law for a control volume. However, the change in enthalpy must be determined without the use of steam tables, and the constant pressure heat capacity for air can be used.
  • #1
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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. :)
 
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  • #2
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.
 

1. What is a turbine in thermodynamics?

A turbine is a device that converts the energy of a moving fluid, such as gas or steam, into mechanical energy. In thermodynamics, turbines are commonly used to generate electricity by harnessing the energy from steam produced by a heat source.

2. What is steady-state in thermodynamics?

Steady-state in thermodynamics refers to a condition where a system's properties, such as temperature and pressure, do not change over time. This means that the system is in a state of equilibrium and is not experiencing any net change in energy.

3. How do I find the necessary mass flow in a thermodynamic system?

To find the necessary mass flow in a thermodynamic system, you can use the equation: mass flow rate = power / (specific enthalpy change * efficiency). This equation takes into account the power output, specific enthalpy change of the fluid, and the efficiency of the system.

4. What is the first law of thermodynamics?

The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or converted from one form to another. In other words, the total energy of a closed system remains constant.

5. How does a turbine work in a thermodynamic system?

A turbine works in a thermodynamic system by using the pressure and velocity of a fluid to turn a rotor, which is connected to a generator. The rotor's movement generates electricity, and the fluid is then released, completing the cycle. This process is known as a Rankine cycle and is commonly used in power plants to generate electricity.

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