8-106 8-114 Steam expands in a two-stage adiabatic turbine from a specified state to another specified state. Steam is reheated between the stages. For a given power output, the reversible power output and the rate of exergy destruction are to be determined. Assumptions 1 This is a steady-flow process since there is no change Heat with time. 2 Kinetic and potential energy changes are negligible. 3 The turbine is adiabatic and thus heat transfer is negligible. 4 The 2 MPa 2 MPa environment temperature is given to be T0 = 25C. 350C 500C Properties From the steam tables (Tables A-4 through 6) P1 8 MPa h1 3399.5 kJ / kg T1 500C s1 6.7266 kJ / kg K Stage I Stage II 5 MW P2 2 MPa h2 3137.7 kJ / kg T2 350C s 2 6.9583 kJ / kg K 8 MPa 500C P3 2 MPa h3 3468.3 kJ / kg T3 500C s 3 7.4337 kJ / kg K 30 kPa x = 97% P4 30 kPa h4 h f x 4 h fg 289.27 0.97 2335.3 2554.5 kJ/kg x 4 0.97 s 4 s f x 4 s fg 0.9441 0.97 6.8234 7.5628 kJ/kg K Analysis We take the entire turbine, excluding the reheat section, as the system, which is a control volume. The energy balance for this steady-flow system can be expressed in the rate form as E E E system 0 (steady) 0 inout Rate of net energy transfer by heat, work, and mass Rate of change in internal, kinetic, potential, etc. energies E in E out m h1 m h3 m h2 m h4 W out W out m [(h1 h2 ) (h3 h4 )] Substituting, the mass flow rate of the steam is determined from the steady-flow energy equation applied to the actual process, W out 5000 kJ/s m 4.253 kg/s h1 h2 h3 h4 (3399.5 3137.7 3468.3 2554.5)kJ/kg The reversible (or maximum) power output is determined from the rate form of the exergy balance applied on the turbine and setting the exergy destruction term equal to zero, X destroyed0 (reversible) X system0 (steady) 0 X X out in Rate of net exergy transfer by heat, work,and mass Rate of exergy destruction Rate of change of exergy X in X out m 1 m 3 m 2 m 4 Wrev,out Wrev,out m (1 2 ) m ( 3 4 ) m [(h1 h2 ) T0 (s2 s1) Δke0 Δpe0 ] m [(h3 h4 ) T0 (s4 s3 ) Δke0 Δpe0 ] Then the reversible power becomes W rev,out m h1 h2 h3 h4 T0 ( s 2 s1 s 4 s 3 ) (4.253 kg/s)[(3399.5 3137.7 3468.3 2554.5)kJ/kg (298 K)(6.9583 6.7266 7.5628 7.4337)kJ/kg K] 5457 kW Then the rate of exergy destruction is determined from its definition, X W W 5457 5000 457 kW destroyed rev,out out PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.