(a) Explanation Show the T-s diagram as in Figure (1). Express Prandtl number at state 8. P r 8 = P 8 P 7 P r 7 (I) Here, pressure at state 8 is P 8 , pressure at state 7 is P 7 and Prandtl number at state 7 is P r 7 . Express Prandtl number at state 10. P r 10 = P 10 P 9 P r 9 (II) Here, pressure at state 10 is P 10 , pressure at state 9 is P 9 and Prandtl number at state 9 is P r 9 . Express enthalpy at state 1. h 1 = h f @10 kPa (III) Here, enthalpy of saturation liquid at pressure of 10 kPa is h f @10 kPa . Express specific volume at state 1. v 1 = v f @10 kPa (IV) Here, specific volume of saturation liquid at pressure of 10 kPa is v f @10 kPa . Express initial work input. w pI,in = v 1 ( P 2 − P 1 ) (V) Here, pressure at state 2 and 1 is P 2 and P 1 respectively. Express enthalpy at state 2. h 2 = h 1 + w pI,in (VI) Express quality at state 6. x 6 = s 6 − s f @10 kPa s f g @10 kPa (VII) Here, entropy at state 6 is s 6 , entropy at saturation liquid and evaporation at pressure of 10 kPa is s f @10 kPa and s f g @10 kPa respectively. Express enthalpy at state 6. h 6 = h f @10 kPa + x 6 h f g @10 kPa (VIII) Here, enthalpy at saturation liquid and evaporation at pressure of 10 kPa is h f @10 kPa and h f g @10 kPa respectively. Express the mass flow rate of air in the gas-turbine cycle from energy balance equation. m ˙ air = h 3 − h 2 h 10 − h 11 m ˙ s (IX) Here, enthalpy at state 10 is h 10 , enthalpy at state 11 is h 11 , enthalpy at state 3 and 2 is h 3 and h 2 respectively, and mass flow rate of steam is m ˙ s . Conclusion: Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 7 and Prandtl number at state 7 corresponding to temperature at state 7 of 310 K . h 7 = 310.24 kJ / kg P r 7 = 1.5546 Substitute 12 for P 8 P 7 and 1.5546 for P r 7 in Equation (I). P r 8 = 12 ( 1.5546 ) = 18.66 Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 8 corresponding to Prandtl number at state 8 of 18.66 using an interpolation method. Write the formula of interpolation method of two variables. y 2 = ( x 2 − x 1 ) ( y 3 − y 1 ) ( x 3 − x 1 ) + y 1 (X) Here, the variables denote by x and y is Prandtl number at state8 and enthalpy at state 8 respectively. Show the enthalpy at state 8 corresponding to Prandtl number as in Table (1). Prandtl number at state 8 P r 8 Enthalpy at state 8 h 8 ( kJ / kg ) 18.36 ( x 1 ) 628.07 ( y 1 ) 18.66 ( x 2 ) ( y 2 = ? ) 19.84 ( x 3 ) 638.63 ( y 3 ) Substitute 18 .36, 18 .66 and 19 .84 for x 1 , x 2 and x 3 respectively, 628 .07 kJ / kg for y 1 and 638 .63 kJ / kg for y 3 in Equation (X). y 2 = ( 18 .66 − 18 .36 ) ( 638 .63 kJ / kg − 628 .07 kJ / kg ) ( 19 .84 − 18 .36 ) + 628 .07 kJ / kg = 630 .18 kJ / kg = h 8 Thus, enthalpy at state corresponding to Prandtl number at state 8 of 18.66 is, h 8 = 630 .18 kJ / kg Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 9 and Prandtl number at state 9 corresponding to temperature at state 9 of 1400 K . h 9 = 1515.42 kJ / kg P r 9 = 450.5 Here, enthalpy at state 9 is h 9 and Prandtl number at state 9 is P r 9 . Substitute 1 12 for P 10 P 9 and 450.5 for P r 9 in Equation (II). P r 10 = 1 12 ( 450.5 ) = 37.54 Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 10 s corresponding to Prandtl number at state 10 of 37.54 using an interpolation method. Show the enthalpy at state 10 corresponding to Prandtl number as in Table (2). Prandtl number at state 10 P r 10 Enthalpy at state 10 h 10 ( kJ / kg ) 37.35 ( x 1 ) 767.29 ( y 1 ) 37.54 ( x 2 ) ( y 2 = ? ) 39.27 ( x 3 ) 778.18 ( y 3 ) Use excels and substitutes the values from Table (II) in Equation (X) to get, h 10 = 768.38 kJ / kg Here, enthalpy at state 10 is h 10 . Refer Table A-5, “saturated water-pressure table”, and write the properties at pressure of 10 kPa . h f @10 kPa = 191.81 kJ / kg v f @10 kPa = 0 (b) To determine The rate of total heat input. (c) To determine The thermal efficiency of the combined cycle.

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Chapter 10.9, Problem 108RP

(a)

To determine

The mass flow rate of air in the gas-turbine cycle.

(b)

To determine

The rate of total heat input.

(c)

To determine

The thermal efficiency of the combined cycle.

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Chapter 10.9, Problem 107RP

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EBK THERMODYNAMICS: AN ENGINEERING APPR

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The mass flow rate of air in the gas-turbine cycle.

The rate of total heat input.

The thermal efficiency of the combined cycle.

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