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ME40 HW6 Solutions

# ME40 HW6 Solutions - 7-39 An insulated rigid tank contains...

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7-39 An insulated rigid tank contains a saturated liquid-vapor mixture of water at a specified pressure. An electric heater inside is turned on and kept on until all the liquid vaporized. The entropy change of the water during this process is to be determined. Analysis From the steam tables (Tables A-4 through A-6) ( )( ) ( )( ) K kJ/kg 6.8649 vapor sat. K kJ/kg 2.8168 0562 . 6 25 . 0 3028 . 1 /kg m 0.4243 0.001 1.6941 0.25 0.001 25 . 0 kPa 100 2 1 2 1 1 3 1 1 1 1 = = = + = + = = - + = + = = = s s x s s x x P fg f fg f v v v v v Then the entropy change of the steam becomes ( ) kJ/K 8.10 = - = - = K kJ/kg ) 2.8168 6.8649 )( kg 2 ( 1 2 s s m S Δ 7-64 Steam expands in an adiabatic turbine. Steam leaves the turbine at two different pressures. The process is to be sketched on a T - s diagram and the work done by the steam per unit mass of the steam at the inlet are to be determined. Assumptions 1 The kinetic and potential energy changes are negligible. Analysis (b) From the steam tables (Tables A-4 through A-6), 831 . 0 kJ/kg 6 . 2179 kPa 10 kJ/kg 3 . 2921 MPa 1 K kJ/kg 8826 . 6 kJ/kg 1 . 3423 MPa 6 C 00 5 3 3 1 3 3 2 1 2 2 1 1 1 1 = = = = = = = = = = ° = s s s x h s s P h s s P s h P T A mass balance on the control volume gives 3 2 1 m m m & & & + = where 1 3 1 2 9 . 0 1 . 0 m m m m & & & & = = We take the turbine as the system, which is a control volume. The energy balance for this steady-flow system can be expressed in the rate form as 3 1 2 1 out , 1 1 3 3 2 2 out , 1 1 out in 9 . 0 1 . 0 h m h m W h m h m h m W h m E E s s & & & & & & & & & & + + = + + = = or kJ/kg 3 . 1169 ) 6 . 2179 )( 9 . 0 ( ) 3 . 2921 )( 1 . 0 ( 1 . 3423 9 . 0 1 . 0 9 . 0 1 . 0 3 2 1 out , 3 2 out , 1 = - - = - - = + + = h h h w h h w h s s The actual work output per unit mass of steam at the inlet is kJ/kg 993.9 = = = ) kJ/kg 3 . 1169 )( 85 . 0 ( out , out s T w w η W e H 2 O 2 kg 100 kPa Turbine P 1 = 6 MPa T 1 = 500 ° C P 3 = 10 kPa P 2 = 1 MPa 0.0 1.1 2.2 3.3 4.4 5.5 6.6 7.7 8.8 9.9 11.0 0 100 200 300 400 500 600 700 s [kJ/kg-K] T [°C] 6000 kPa 1000 kPa 10 kPa Steam IAPWS 1 2 3

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7-93 Air is compressed in a piston-cylinder device in a reversible and adiabatic manner. The final temperature and
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