i) Quality of steam at the end of expansion

ii) Power required to drive the pump

iii) Turbine power

iv) The Rankine efficiency

v) The heat flow in the condenser

Given:

P1 = 20 bar; X1= 1;

P2=0.3 bar

Solution:

i) Finding quality

S1 = S2 (isentropic expansion)

.sg1 = sf2 + X2 × sfg

6.337 = 0.944 + X2 × 6.825

X2 = 0.79

ii) Pump power

Wp = ∆P/10 = (20 -0.3)/10 = 1.97 kJ/kg

Pp = mWp = 10 × 1.97 = 19.7 kW

Also, Wp = h4-h3 and h3 = hf2

.h4 = Wp + hf2 = 1.97 + 289 = 290.97 kJ/kg

iii) Turbine power

Wt = h1-h2 = hg1 – (hf2 + X2 × hfg2)

= 2797 – (289 + 0.79 × 2336) = 662 kJ/kg

Pt = mWt = 10 × 662 = 6620kW

Ws = Wt - Wp = 662-1.97 = 660.03 kJ/kg

iv) Finding efficiency

Q= h1 - h4 = 2797 – 290.97 = 2506.3 kJ/kg

.η = W/Q = 660.03/2506.3 = 0.26

v) Heat flow in condenser

Qc = h3 - h2 = 289 + 0.79 × 2336 -289 = 1845.4 kJ/kg