Question

Steam flowing at steady state enters a turbine at 400 degrees Celsius and 7 MPa. The exit is at 0.275 MPa. The turbine is 85% efficient. What is the quality of the exiting stream? How much work is generated per kg of steam?

Answer 1

We need steam table-----

Inlet Steam Exit Steam
P1 = 7 P2 = 0.275
T1 = 400 T2 = 285.83
h1 = 3159.2 hf2 = 548.86 sf2 = 1.6408
s1 = 6.4502 hfg2 = 2172.0 sfg2 = 5.3800
hg2 = 2720.9 sg2 = 7.0207

For adiabatic and reversible expansion: s2* = s1

s2* = sf2 + ( x2* ) ( sg2 ) = sf1

x2* = ( s1 - sf2 ) / ( sfg2 )

x2* = ( 6.4502 - 1.6408 )/ ( 5.380 ) = 0.8939 = 89.39%

h2* = hf2 + ( x2* ) ( hg2 )

h2* = 548.86 + ( 0.8939 ) ( 2172.0 ) = 2490.5

w sub T* = h1 - h2*

w sub T* = 3159.2 - 2490.5 = 668.7 kJ per kg

w sub T = ( E sub T ) ( w sub T* )

w sub T = ( 0.85 ) ( 668.7 ) = 568.4 kJ per kg <--------.

h2 = h1 - w sub T

h2 = 3159.2 - 568.4 = 2590.8 kJ per kg

x2 = ( h2 - hf2 ) / ( hfg2 )

x2 = ( 2590.8 - 584.86 ) / ( 2172.0 ) = 0.9235 = 92.35 % <----------------------------------

I assumed the following:
Steady flow
Delta ke ~ 0.0
Delta pe ~ 0.0
q ~ 0.0
Two phases at turbine exit