a) Explanation Draw the T-s diagram of the ideal reheat-regenerative Rankine cycle as shown in Figure (1). Draw the layout of steam power plant as shown in Figure (2). Write the expression for the specific work input of pump I to the system. w p I ,in = v 1 ( P 2 − P 1 ) (I) Here, specific volume at state 1 is v 1 , pressure at state 1 is P 1 , and pressure at state 2 is P 2 . Write the Write the expression for the enthalpy of steam at state 2. h 2 = h 1 + w p I , in (II) Here, enthalpy at state 1 is h 1 . Write the Write the expression for the specific work input of pump II to the system. w p I I ,in = v 3 ( P 4 − P 3 ) (III) Here, specific volume at state 3 is v 3 , pressure at state 4 is P 4 , and pressure at state 3 is P 3 . Write the Write the expression for the enthalpy of steam at state 4. h 4 = h 3 + w p I I , in (IV) Here, enthalpy at state 3 is h 3 . Write the Write the expression for the quality of steam at state 8. x 8 = s 8 − s f s f g (V) Here, specific entropy at state 8 is s 8 , specific entropy of wet steam at 10 kPa is s f , and specific entropy of vaporization at 10 kPa is s f g . Write the Write the expression for the specific enthalpy of steam at state 8. h 8 = h f + x 8 h f g (VI) Here, specific enthalpy of wet steam at 10 kPa is h f , and specific enthalpy of vaporization at 10 kPa is h f g . Write the Write the expression for the energy balance equation for the system. E ˙ in − E ˙ out = 0 (VII) Here, energy flow at the inlet is E ˙ in , and energy flow at the outlet is E ˙ out . Rewrite equation (7) with mass and enthalpy terms. m ˙ 6 h 6 + m ˙ 2 h 2 = m ˙ 3 h 3 y h 6 + ( 1 − y ) h 2 = h 3 y = h 3 − h 2 h 6 − h 2 (VIII) Here, the fraction of steam extracted from the turbine is y . Write the expression for the heat transfer during reheat process. q reheat = h 7 − h 6 (IX) Here, enthalpy at state 7 is h 7 and enthalpy at state 6 is h 6 . Write the Write the expression for the exergy destruction for the reheat process. x destroyed,reheat = T 0 ( s 7 − s 6 + q R , 67 T R ) (X) Here, heat transferred during the process is q R , 67 , temperature of the heat source is T R , and ambient temperature is T 0 . Conclusion: Refer to Table A-5, “Saturated water-Pressure table”, obtain the following properties at the pressure of 10 kPa . h 1 = 191 .81 kJ / kg v 1 = 0.00101 m 3 / kg Substitute 0.00101 m 3 / kg for v 1 , 10 kPa for P 1 , and 800 kPa for P 2 in Equation (I). w p I ,in = 0.00101 m 3 / kg ( 800 − 10 ) kPa ( 1 kJ 1 kPa ⋅ m 3 ) = 0.79 kJ / kg Substitute 191 .81 kJ / kg for h 1 , and 0.79 kJ / kg for w p I ,in in Equation (II). h 2 = 191.81 kJ / kg + 0.79 kJ / kg = 192.6 kJ / kg Refer to Table A-5, “Saturated water-Pressure table”, obtain the following properties at the pressure of 0.8 MPa . h 3 = 720 .87 kJ / kg v 3 = 0.001115 m 3 / kg Substitute 0.001115 m 3 / kg for v 3 , 800 kPa for P 3 , and 10 , 00 kPa for P 4 in Equation (III). w p I I ,in = 0.00115 m 3 / kg ( 10 , 000 − 800 ) kPa ( 1 kJ 1 kPa ⋅ m 3 ) = 10 b) To determine The exergy destruction during reheat process

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Chapter 10.9, Problem 64P

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