he=Xhg+(1-X)h,at T Substituting the values h=0.646×2538.1+0354×83.96kJ/kg =16694kJ/kg The turbine work/unit mass is the difference between the enthalpy at state b and state c, hb-he= curb=2749-16694=1079.6kJ/kg We can apply a similar process to find the conditions at state d: (T) ( (Ta)-s/(T)s2(T) We have given that T=Td. Also sd=Sa=s, at 300C. The quality at state d is x,=3253-029660353<x The enthalpy at state d is h2=Xb2+(-x =0.353x2538.1+0.647x83.96=950.8kJ/kg The work of compression(pump work)is Ahad =ha-hd. Substituting the numerical values Ma=1344-950.=3933kJ/kg The ratio of turbine work to compression work (pump work )is-nurbine=2.75 We can check the efficiency by computing the ratio of net work (Wnet =turbine -wcompression) to the heat input(Ts). Doing this gives, not surprisingly, the same value as the Carnot equation b)Efficiency and work ratio for a cycle with adiabatic efficiencies of pump and turbine both equal to 0.8(non-ideal components) We can find the turbine work using the definition of turbine and compressor adiabatic efficiencies The relation between the enthalpy changes is Wmurbine =h-he, =nrurbine(hb-h)=actual turbine work received Substituting the numerical values, the turbine work per unit mass is 863.7 kJ/kg 2B-112B-11 h Xh X h c cg c = +− ( ) f 1 at Tc . Substituting the values, hc =× +× 0. .. . 646 2538 1 0 354 83 96 kJ/kg =1669.4 kJ/kg. The turbine work/unit mass is the difference between the enthalpy at state b and state c, hhw b c −= = − = turbine 2749 1669 4 1079 6 . . kJ/kg. We can apply a similar process to find the conditions at state d: X s sT sT sT s sT s T d d fd g d fd c f d fg d = − ( ) ( ) − ( ) = − ( ) ( ) . We have given that T T c = d . Also sss d = = a f at 300 Co . The quality at state d is X X d = c − = 3 253 0 2966 8 3706 0 353 . . . . < The enthalpy at state d is h Xh X h d d = +− g ( ) d f 1 = 0.353 x 2538.1 + 0.647 x 83.96 = 950.8 kJ/kg. The work of compression (pump work) is ∆h hh ad = −a d . Substituting the numerical values, ∆had = 1344- 950.8 = 393.3 kJ/kg. The ratio of turbine work to compression work (pump work) is w w turbine compression = 2 75 . We can check the efficiency by computing the ratio of net work (ww w net turbine compression = − ) to the heat input ( T sa fg ). Doing this gives, not surprisingly, the same value as the Carnot equation. b) Efficiency and work ratio for a cycle with adiabatic efficiencies of pump and turbine both equal to 0.8 (non-ideal components). We can find the turbine work using the definition of turbine and compressor adiabatic efficiencies. The relation between the enthalpy changes is w hh hh turbine b =− = − c turbine b c ( ) ′ η = actual turbine work received. Substituting the numerical values, the turbine work per unit mass is 863.7 kJ/kg