(a) To determine The net exergy carried in by the gas steam. Explanation The following figure shows the T - s diagram of the Rankine cycle. Figure-(1) In Figure-(1), the state 1 to 2 shows the actual expansion in the turbine, state 1 to 2s shows the isentropic expansion in the turbine, state 2 to state 3 shows the heat rejection in condenser, state 3 to state 4 shows the actual compression in pump, state 3 to state 4s shows the actual compression in pump and state 4 to 1 shows the heat addition in the boiler. The expression for net exergy carried in by the gas. ( Φ i − Φ e ) a i r = m ˙ a i r m ˙ [ ( h i − h e ) − T o ( s i − s e ) ] (I) Here, The temperature of surrounding is T o ,the mass flow rate of water is m ˙ , the mass flow rate of air is m ˙ a i r , specific entropy at point exit and inlet of heat exchanger is s i and s e and specific enthalpy at point exit and inlet of heat exchanger is h i and h e respectively. Write the expression for the entropy at point 2s. s 2 s = s f 2 s + x 2 s s f g 2 s (II) Here, the entropy at point 2s is s 2 s , the entropy of saturated liquid ( s f ) is s f 2 s , the quality of mixture at point 2s is x 2 s and the entropy of water-vapor mixture is s f g 2 s . Write the expression for enthalpy at point 2s. h 2 s = h f 2 s + x 2 s h f g 2 s (III) Here, the enthalpy of saturated liquid is h f 2 s , the dryness fraction at point 2s is x 2 s , the enthalpy of liquid vapor mixture is h f g 2 s . Write the expression for enthalpy at point 2. h 2 = h 1 − η t ( h 1 − h 2 s ) (IV) Here, the enthalpy at point 1 is h 1 , the enthalpy at point 2s is h 2 s and the isentropic efficiency of turbine is η t . Write the expression for enthalpy at point 2. h 2 = h f 2 s + x 2 h f g 2 s (V) Here, the enthalpy at point 2 is h 2 . Write the expression for pump work during process 3-4. W p 1 = − v 3 ( p 4 − p 3 ) (VII) Here, the pressure at point 4 is p 4 , the pressure at point 3 is p 3 , and the specific volume is v 3 . Write the expression for entropy at point 2. s 2 = s f 2 s + x 2 s f g 2 s (VI) Here, the entropy at point 2 is s 2 . Write the expression for enthalpy at point 4. h 4 = h 3 − ( − W p 1 η p 1 ) (VIII) Here, the specific enthalpy at point 3 is h 3 , and the isentropic efficiency of pump 1 is η p 1 . Write the expression for energy balance for heat exchanger. m ˙ ( h 1 − h 4 ) = m ˙ a i r ( h i − h e ) (IX) Here, the mass flow rate of water is m ˙ , the mass flow rate of air is m ˙ a i r and specific enthalpy at point exit and inlet of heat exchanger is h i and h e respectively Conclusion: Refer to Table A-4 “Properties of superheated water vapor” to obtain enthalpy ( h 1 ) as 3321.4 kJ/kg , specific entropy ( s 1 ) as 6.5282 kJ/kg ⋅ K corresponding to pressure 100 MP and temperature 480 ° C . Refer to Table A-3 “Properties of saturated water-pressure table” to obtain enthalpy of saturated liquid ( h 3 ) as 151.53 kJ/kg , enthalpy of water-vapor mixture ( h f g ) as 2415.9 kJ/kg , entropy of saturated liquid ( s 3 ) as 0.521 kJ/kg ⋅ K , entropy of water-vapor mixture ( s f g ) as 7.8094 kJ/kg ⋅ K , and specific volume ( v f ) as 1.0064 × 10 − 3 m 3 / kg corresponding to pressure 6 kPa . The enthalpy h 3 and h f are equal, and the entropy s 3 and s f are equal. Process 1-2s is isentropic process, thus the entropies at states 1 and 2s are equal. s 1 = s 2 s = 6.5282 kJ/kg ⋅ K Substitute 6.5282 kJ/kg ⋅ K for s 2 s , 0.521 kJ/kg ⋅ K for s f 2 s , 7.8094 kJ/kg ⋅ K for s f g 2 s ,in Equation (II) ( 6.5282 kJ/kg ⋅ K ) = ( 0.521 kJ/kg ⋅ K ) + x 2 s ( 7.8094 kJ/kg ⋅ K ) ( 6.5282 kJ/kg ⋅ K ) − ( 0.521 kJ/kg ⋅ K ) = x 2 s ( 7.8094 kJ/kg ⋅ K ) ( 6.0072 kJ/kg ⋅ K ) = x 2 s ( 7.8094 kJ/kg ⋅ K ) x 2 s = 0.7692 Substitute 151.53 kJ/kg for h f 2 s , 0.7692 for x 2 s and 2415.9 kJ/kg for h f g 2 s in Equation (III). h 2 s = h f 2 s + x 2 s h f g 2 s = ( 151.53 kJ/kg ) + 0.7692 ( 2415.9 kJ/kg ) = ( 151.53 kJ/kg ) + ( 1851.31 kJ/kg ) = 2009.84 kJ/kg Thus, the specific enthalpy at point 2s is 2009.84 kJ/kg . Substitute 3321.4 kJ/kg for h 1 , 0.8 for η t and 2009.84 kJ/kg for h 2 s in Equation (IV). h 2 = ( 3321 (b) To determine The thermal efficiency of the cycle. (c) To determine The net exergy destruction. (d) To determine The exergetic efficiency.

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

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Chapter 8.6, Problem 84P

(a)

To determine

The net exergy carried in by the gas steam.

(b)

To determine

The thermal efficiency of the cycle.

(c)

To determine

The net exergy destruction.

(d)

To determine

The exergetic efficiency.

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Chapter 8.6, Problem 83P

Chapter 8.6, Problem 85P

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