Question

Need some help with this

1. (15pts) A power plant was assumed to described by an ideal Rankine cycle without any irreversibility. The boiler produces saturated steam at a pressure of 120 bar (I). The steam expands adiabatically thru a turbine exiting as a saturated vapor/liquid mixture at pressure of 0. Ibar (2). The mixture passes thru a condenser (P=0.1 bar) until it is all saturated liquid (3). It is then pumped adiabatically to the boiler pressure of 120bar (4) at which point heat is added in the boiler to produce saturated steam to begin the cycle again (1). The total flow rate of steam and/or water thru the plant is 2x10 kg/hr. a) Find the quality (mass fraction of vapor) of the vapor/liquid mixture exiting the turbine (2) b) Find the thermal efficiency and total power output of the turbine You may use hs h3t (p4-p3)vs, where v refers to specific volume c) Extra credit (5pts) If the turbine was still adiabatic but had internal irreversibilities such that the turbine efficiency was 85% find i. The new value for h2 ii. The new quality of the exiting vapor/liquid mixture iv. The entropy generated in the turbine

Answer 1

a) x_4 = 0.645 b) h = output/input = omega_T - omega_P/v_s = (h_3 - h_4) - (h_2 - h_1)/h_3 - h_2 h = 37.72% power = 520 times 10^3 kw c)now value = Q_5 = h_3 - h_4/h_3 - h_4 (1) h_4^' = 1279 kj/kg from property table at p = 0.1 bar h = 1275 kj/kg (2) x = 0.705 (3) x = 5.930 kj/kg energy generated = ds = 5.930 - 5.492 4) ds = 0.445 kj/kg