Explanation Draw the T − s diagram for the simple Brayton cycle as shown in Figure (1). Write the relation for the temperature and pressure relation for the process 1-2. T 2 = T 1 ( P 2 P 1 ) ( k − 1 ) / k (I) Here, pressure at state 1 is P 1 , pressure at state 2 is P 2 , temperature at state 1 is T 1 , temperature at state 2 is T 2 and Specific heat ratio is k . Write the relation for the temperature and pressure relation for the process 3-4. T 4 = T 3 ( P 4 P 3 ) ( k − 1 ) / k (II) Here, pressure at state 4 is P 4 , pressure at state 3 is P 3 , temperature at state 4 is T 4 and temperature at state 3 is T 3 . Write the expression for the heat addition during the process 2-3 ( q i n ) . q i n = h 3 − h 2 = c p ( T 3 − T 2 ) (III) Here, enthalpy at state 3 is h 3 , enthalpy at state 2 is h 2 and specific heat of constant pressure is c p . Write the expression for the heat rejected during the process 1-4 ( q o u t ) . q o u t = h 4 − h 1 = c p ( T 4 − T 1 ) (IV) Here, specific enthalpy of air at the exit of the turbine is h 4 and specific enthalpy of air at the inlet to the compressor is h 1 . Write the expression for net work done ( w n e t ) per unit mass when the pressure ratio is 6. w n e t = q i n − q o u t (V) Write the expression for the thermal efficiency ( η t h ) of the system when the pressure ratio is 6. η t h = w n e t q i n (VI) Conclusion: From the Table A-2, “Ideal-gas specific heats of various common gases” obtain the following properties for air. c p = 1.005 kJ / kg ⋅ K k = 1.4 Substitute 2000 kPa for P 2 , 100 kPa for P 1 , 27 ° C for T 1 and 1.4 for k in Equation (I). T 2 = ( 27 ° C ) ( 2000 kPa 100 kPa ) 1.4 − 1 / 1.4 = ( 27 + 273 ) K ( 2000 kPa 100 kPa ) 0.4 / 1.4 = 706.1 K Substitute 100 kPa for P 4 , 2000 kPa for P 3 , 727 ° C for T 3 and 1

9th Edition

ISBN: 8220106796979

Author: CENGEL

Publisher: YUZU

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Chapter 9.12, Problem 88P

To determine

The net work produced per unit mass of air and the thermal efficiency of the cycle.

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Chapter 9 Solutions

EBK THERMODYNAMICS: AN ENGINEERING APPR

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The net work produced per unit mass of air and the thermal efficiency of the cycle.

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The net work produced per unit mass of air and the thermal efficiency of the cycle.

Chapter 9 Solutions