An adiabatic air compressor is to be powered by a direct coupled adiabatic steam turbine that is also driving a generator. Steam enters the turbine at 12.5 MPa and 500-degree C at a rate of 25 Kg/s and exits at 10 kPa and a quality (or dryness factor) of 0.92. Air enters the compressor at 98 kPa and 295 K at a rate of 10 Kg/s and exits at 1 MPa and 620 K. determine the net power delivered to the generator by the turbine.

1)First we apply the first law of thermodynamics in the turbine that states that the energy must always be conserved, then we find in the energy balance that the power generated by the turbine must be equal to the power consumed by the compressor and the power consumed by the generator

Wt=Wc+Wg

Wg=Wt-Wc

where

Wt= turbine power

Wc=compresor power

Wg=generator power

2) we find the power generated by the turbine, for this we apply the first law of thermodynamics and find the enthalpies in the two states using the thermodynamic tables.

Through laboratory tests, thermodynamic tables were developed, these allow to know all the thermodynamic properties of a substance (entropy, enthalpy, pressure, specific volume, internal energy etc ..)

through prior knowledge of two other properties

h1= enthalpy at the entrance at 12.5Mpa and 500C

h1=3342KJ/kg

h2=enthalpy at the exit at 10kpa and quality=0.92

h2=2151KJ/kg

Wt=m(h1-h2)

Wt=25(3342-2151)=29775Kw

2) Now we do the same as we did in step two for the compressor remembering that to calculate the power the following equation is used considering that it operates with air

Wc=m Cp (T2-T1)

Where

m=mass flow=10kg/S

Cp=specific heat for air=1.012KJ/Kg

T2= oulet temperature=620K

T1=inlet temperature=295K

solving

Wc=10(1.012)(620-295)=3289Kw

finally we apply the equation found in step 1 to find the power in the generator

Wg=Wt-Wc =29775Kw-3289Kw=26486Kw

the net power delivered to the generator by the turbine. is 26486Kw