Assignment Set 6 8.27 Steam is the working fluid in the ideal reheat cycle shown in Fig. P8.27 together with operational data. If the mass flow rate is 1.3 kg/s, determine the power developed by the cycle, in kW, and the cycle thermal efficiency. KNOWN: An ideal reheat cycle operates with steam as the working fluid. Operational data are provided. FIND: Determine the power developed by the cycle, in kW, and the cycle thermal efficiency. SCHEMATIC AND GIVEN DATA: T 1 Ɣ State p (bar) T (oC) h (kJ/kg) 1 140 520.0 3377.8 2 15 201.2 2800.0 3 15 428.9 3318.5 4 1 99.63 2675.5 5 1 99.63 417.46 6 140 3 Ɣ p = 140 bar Ɣ p = 15 bar 6Ɣ 5Ɣ 2 p = 1 bar Ɣ 4 s 431.96 Fig. P8.27 p3 = p2 = 15 bar Reheat Section Q in 3 p2 = 15 bar Steam Generator 1 p1 = 140 bar 2 Turbine 1 Turbine 2 W t 4 Q out 6 p6 = p1 = 140 bar Condenser Pump 5 p5 = p4 = 1 bar x5 = 0 (saturated liquid) W p 1 p4 = 1 bar ENGINEERING MODEL: 1. Each component of the cycle is analyzed as a control volume at steady state. The control volumes are shown on the accompanying sketch by dashed lines. 2. All processes of the working fluid are internally reversible. 3. The turbine and pump operate adiabatically. 4. Kinetic and potential energy effects are negligible. 5. Condensate exits the condenser as saturated liquid. ANALYSIS: The net power developed by the cycle is Wcycle Wt1 Wt2 Wp Mass and energy rate balances for control volumes around the two turbine stages and the pump give, respectively, (h1 h2 ) Turbine 1: Wt1 m (h h ) Turbine 2: W m t2 Pump: Wp 3 4 (h6 h5 ) m where m is the mass flow rate of the steam. Solving for the net power developed by the cycle yields Wcycle Wcycle [(h1 h2 ) (h3 h4 ) (h6 h5 )] m kJ kJ kJ º 1 kW § kg ·ª (3318.5 2675.5) (431.96 417.46) » ¨1.3 ¸«(3377.8 2800.0) s kg kg kg © ¹¬ ¼ 1 kJ/s Wcycle = 1568.2 kW The thermal efficiency is K Wcycle Q in The total rate of heat transfer to the working fluid as it passes through the steam generator and reheater is determined using mass and energy rate balances as Qin >(h1 h6 ) (h3 h2 )@ m 2 Solving for rate of heat transfer gives Qin kJ 1 kW § kg · = 4503.6 kW ¨1.3 ¸>(3377.8 431.96) (3318.5 2800.0)@ s ¹ kg 1 kJ/s © The thermal efficiency is then K Wcycle Q in 1568.2 kW = 0.3482 (34.82%) 4503.6 kW 3