Explanation Draw the T − s diagram for the simple Brayton cycle as shown in Figure (1). Write the expression of temperature and pressure relation for the process 1-2. T 2 s = T 1 ( P 2 P 1 ) ( k − 1 k ) (I) Here, temperature at state point 2s is T 2 s . Pressure at state point 2 is P 2 , temperature at state point 1 is T 1 , Pressure at state point 2 is P 2 , and the specific heat ratio is k . Write the expression of temperature and pressure relation for the process 3-4. T 4 s = T 3 ( P 4 P 3 ) ( k − 1 k ) (II) Here, temperature at state point 4 s is T 4 s . Pressure at state point 3 is P 3 , temperature at state point 3 is T 3 , and Pressure at state point 4 is P 4 . Write the expression of power given to the compressor ( w C,in ) . w C,in = c P ( T 2 s − T 1 ) η C (III) Here, specific heat capacity of air is c P , the efficiency of the compressor is η C , temperature at state point 1 is T 1 and temperature at state point 2 s is T 2 s . Write the expression of power developed by the turbine ( w T,out ) . w T,out = η T c P ( T 3 − T 4 s ) (IV) Here, the efficiency of the turbine is η T and temperature at state point 3 is T 3 Write the expression of net power output of the power plant ( w net,out ) . w net,out = w T,out − w C,in (V) Write the expression mass flow rate of air ( m ˙ ) . m ˙ = W ˙ n e t , o u t w n e t , o u t (VI) Conclusion: From Table A-2, “Ideal2gas specific heats of various common gases”, obtain the following properties for air at room temperature. c p = 1.005 kJ / kg k = 1.4 Substitute 310 K for T 1 , 8 for ( P 2 P 1 ) , and 1.4 for k in equation (I). T 2 s = ( 310 K ) ( 8 ) 1.4 − 1 1.4 = 561.5 K Substitute 900 K for T 3 , 1 8 for ( P 4 P 3 ) , and 1

9th Edition

ISBN: 9781260048766

Author: CENGEL

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Chapter 9.12, Problem 87P

To determine

The mass flow rate of air through the cycle

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The mass flow rate of air through the cycle

Solution Summary: The author explains the mass flow rate of air through the cycle and the expression of temperature and pressure relation for the process 1-2.

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The mass flow rate of air through the cycle

Chapter 9 Solutions