a) Explanation Draw the T-s diagram for the ideal cogeneration power plant as shown in Figure (1). Draw the layout of cogeneration power plant as shown in Figure (2). Write the expression for the specific work input of pump I to the system. w pI,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 expression for the enthalpy of steam at state 2. h 2 = h 1 + w pI,in (II) Here, enthalpy at state 1 is h 1 . Write the expression for the energy balance equation for the system. E ˙ in = E ˙ out (III) Rewrite Equation (3) and rearrange the terms with mass and enthalpy terms. m ˙ 4 h 4 = m ˙ 2 h 2 + m ˙ 3 h 3 h 4 = m ˙ 2 h 2 + m ˙ 3 h 3 m ˙ 4 (IV) Here, enthalpy at state 3 is h 3 , mass flow rate at state points 2,3 and 4 are m ˙ 2 , m ˙ 3 , and m ˙ 4 respectively. Write the expression for the specific work input of pump II to the system. w pII,in = v 4 ( P 5 − P 4 ) (V) Here, specific volume at state 4 is v 4 , pressure at state 5 is P 5 , and pressure at state 4 is P 4 . Write the expression for the enthalpy of steam at state 4. h 5 = h 4 + w pII,in (VI) Write the expression for the quality of steam at state 8. x 8 = s 8 − s f s f g (VII) 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 expression for the specific enthalpy of steam at state 8. h 8 = h f + x 8 h f g (VIII) 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 expression for the power output from the turbine. W ˙ T,out = m ˙ 6 ( h 6 − h 7 ) + m ˙ 8 ( h 7 − h 8 ) (IX) Here, mass flow rate at point 6 and 8 are m ˙ 6 and m ˙ 8 . Write the expression for the total power input to the system. W ˙ p,in = m ˙ 1 w pI,in + m ˙ 4 w pII,in (X) Write the expression for the net power output of the cycle. W ˙ net = W ˙ T,out − W ˙ p,in (XI) Conclusion: Refer to saturated steam table, and interpret the values of h 1 , and v 1 for a pressure of 10 kPa as 191 .81 kJ / kg , and 0.00101 m 3 / kg . Substitute 0.00101 m 3 / kg for v 1 , 10 kPa for P 1 , and 1 , 200 kPa for P 2 in Equation (I). w pI,in = 0.00101 m 3 / kg ( 1 , 200 − 10 ) kPa ( 1 kJ 1 kPa ⋅ m 3 ) = 1.20 kJ / kg Substitute 191 .81 kJ / kg for h 1 , and 1.20 kJ / kg for w pI,in in Equation (II). h 2 = 191.81 kJ / kg + 1.20 kJ / kg = 193.01 kJ / kg Refer to steam table, and interpret the value of h 3 for a pressure of 1.2 MPa as 798.33 kJ / kg . Substitute 193.01 kJ / kg for h 2 , 798.33 kJ / kg for h 3 , 22.50 kg / s for m ˙ 2 , 7.50 kg / s for m ˙ 3 , and 30 kg / s for m ˙ 4 in Equation (IV). h 4 = ( 22.50 × 193.01 ) + ( 7.50 × 798.33 ) 30 = 344.34 kJ / kg Refer to saturated steam table, and interpret the value of v 4 for a enthalpy of 344.34 kJ / kg as 0.001031 m 3 / kg . Substitute 0.001031 m 3 / kg for v 3 , 4 , 000 kPa for P 5 , and 1 , 200 kPa for P 4 in Equation (V) b) To determine The utilization factor of the cogeneration plant

8th Edition

ISBN: 9780073398174

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 10.9, Problem 69P

To determine

The net power output of the cycle

To determine

The utilization factor of the cogeneration plant

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Chapter 10.9, Problem 68P

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