(a) To determine The thermal efficiency of the cycle for pressure ratio 6 . The thermal efficiency of the cycle for pressure ratio 8 . The thermal efficiency of the cycle for pressure ratio 12 . Explanation Write the expression for the thermal efficiency of the cycle. η = 1 − ( h 4 − h 1 ) ( h 3 − h 2 ) (I) Here, specific enthalpy at state 1 is h 1 , specific enthalpy at state 2 is h 2 , specific enthalpy at state 3 is h 3 , and specific enthalpy at state 4 is h 4 . Write the expression for the relative pressure at state 2. P r 2 = r p P r 1 (II) Here, the pressure ratio is r p , relative pressure at state 1 is P r 1 . Write the expression for the relative pressure at state 4. P r 4 = P r 3 r p (III) Here, relative pressure at state 3 is P r 3 . Conclusion: Refer to table A-22, “Ideal Gas Properties of Air”, to obtain the specific enthalpy of the air at 300 K as 300.19 kJ / kg and relative pressure as 1.386 . Calculation for the compressor pressure ratio of 6 . Substitute 6 for r p , and 1.386 for P r 1 in Equation (II). P r 2 = ( 6 ) ( 1.386 ) = 8.316 Refer to table A-22, “Ideal Gas Properties of Air”, to obtain the specific enthalpy of the air at 8.316 relative pressure as 501.36 kJ / kg and temperature as 498.4 K . Refer to table A-22, “Ideal Gas Properties of Air”, to obtain the specific enthalpy of the air at 1400 K as 1515.42 kJ / kg and relative pressure as 450.5 . Substitute 6 for r p , and 450.5 for P r 3 in Equation (III). P r 4 = ( 450.5 ) 6 = 75.08 Refer to table A-22, “Ideal Gas Properties of Air”, to obtain the specific enthalpy of the air at 75.08 relative pressure as 932.20 kJ / kg and temperature as 899.3 K . Substitute 300.19 kJ / kg for h 1 , 501.36 kJ / kg for h 2 , 1515.42 kJ / kg for h 3 , and 932.20 kJ / kg for h 4 in Equation (I). η = 1 − 932.20 kJ / kg − 300.19 kJ / kg 1515.42 kJ / kg − 501.36 kJ / kg = 1 − 0.6232 = 0.3768 × 100 % = 37.68 % Thus, the thermal efficiency of the cycle for pressure ratio 6 is 37.68 % . For r p = 8 : Substitute 8 for r p , and 1.386 for P r 1 in Equation (II). P r 2 = ( 8 ) ( 1.386 ) = 11.088 Refer to table A-22, “Ideal Gas Properties of Air”, to obtain the specific enthalpy of the air at 11 (b) To determine The back work ratio of the cycle for pressure ratio 6 . The back work ratio of the cycle for pressure ratio 8 . The back work ratio of the cycle for pressure ratio 12 . (c) To determine The net power develop by the cycle for pressure ratio 6 . The net power developed by the cycle for pressure ratio 8 . The net power developed by the cycle for pressure ratio 12 .

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ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

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Chapter 9.14, Problem 50P

(a)

To determine

The thermal efficiency of the cycle for pressure ratio 6.

The thermal efficiency of the cycle for pressure ratio 8.

The thermal efficiency of the cycle for pressure ratio 12.

(b)

To determine

The back work ratio of the cycle for pressure ratio 6.

The back work ratio of the cycle for pressure ratio 8.

The back work ratio of the cycle for pressure ratio 12.

(c)

To determine

The net power develop by the cycle for pressure ratio 6.

The net power developed by the cycle for pressure ratio 8.

The net power developed by the cycle for pressure ratio 12.

Expert Solution & Answer

Chapter 9 Solutions

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The thermal efficiency of the cycle for pressure ratio 6 . The thermal efficiency of the cycle for pressure ratio 8 . The thermal efficiency of the cycle for pressure ratio 12 .

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The thermal efficiency of the cycle for pressure ratio 6. The thermal efficiency of the cycle for pressure ratio 8. The thermal efficiency of the cycle for pressure ratio 12.

The back work ratio of the cycle for pressure ratio 6. The back work ratio of the cycle for pressure ratio 8. The back work ratio of the cycle for pressure ratio 12.

The net power develop by the cycle for pressure ratio 6. The net power developed by the cycle for pressure ratio 8. The net power developed by the cycle for pressure ratio 12.

Chapter 9 Solutions

The thermal efficiency of the cycle for pressure ratio 6.

The thermal efficiency of the cycle for pressure ratio 8.

The thermal efficiency of the cycle for pressure ratio 12.

The back work ratio of the cycle for pressure ratio 6.

The back work ratio of the cycle for pressure ratio 8.

The back work ratio of the cycle for pressure ratio 12.

The net power develop by the cycle for pressure ratio 6.

The net power developed by the cycle for pressure ratio 8.

The net power developed by the cycle for pressure ratio 12.