To determine the net power produced by the gas turbine power station, we need to calculate the work done by the turbine and the work done by the compressor. The net power produced is the difference between these two values.
The simple Brighton cycle consists of four processes:
Isentropic compression in the compressor.
Constant pressure heat addition in the combustion chamber.
Isentropic expansion in the turbine.
Constant pressure heat rejection to the surrounding environment.
Given data:
Inlet conditions:
Pressure at turbine inlet (P1) = 1 MPa
Temperature at turbine inlet (T1) = 1000 K
Exit conditions:
Pressure at turbine exit (P2) = 125 kPa
Temperature at turbine exit (T2) = 600 K
Heat expelled to the surrounding environment (Q_out) = 7922 kJ/s
Mass flow rate of air (m_dot) = 2.5 kg/s
First, let's calculate the specific enthalpy at state 1 (h1) using the air properties at the given temperature and pressure. You can refer to the air tables for this purpose.
Next, we need to calculate the specific enthalpy at state 2 (h2). We can use the temperature and pressure at state 2 and the air properties tables to determine h2.
Now, we can calculate the work done by the turbine (W_turbine) using the equation:
W_turbine = m_dot * (h1 - h2)
Since the compressor is assumed to be an isentropic process, the work done by the compressor (W_compressor) can be determined using the isentropic efficiency of the compressor (η_compressor) and the enthalpy difference between states 1 and 2:
W_compressor = (h2s - h1) / η_compressor
Where h2s is the specific enthalpy at state 2s, which can be determined using the temperature and pressure at state 2 and the air properties tables.
Finally, the net power produced (P_net) is given by:
P_net = W_turbine - W_compressor
Calculate the values using the above steps, and you will find the net power produced by the gas turbine power station.