Explanation Show the simple Brayton cycle with air as the working fluid on the T − s diagram. For the given Brayton cycle with air as the working fluid T i , h i , P r i and P i are the temperature at i t h state, specific enthalpy at i t h state, relative pressure at i t h state, and pressure at i t h state respectively. Write the expression of the pressure ratio for the Brayton cycle ( r p ) . r p = P 2 P 1 (I) Write the expression of heat rejected from the power plant ( Q ˙ out ) . Q ˙ out = m ˙ ( h 4 − h 1 ) (II)) Here, the mass flow rate of air is m ˙ . Write the expression of relation between the relative pressure and actual pressure for the process 1-2. P r 2 = P 2 P 1 P r 1 (III) For zero net work produced by the power plant, both the input and output work are equal. W ˙ C,in = W ˙ T,out m ˙ ( h 2 s − h 1 ) η C = m ˙ ( h 3 − h 4 ) (IV) Here, the power developed by the turbine is W ˙ T,out , and the power given to the compressor is W ˙ C,in . Conclusion: Substitute 120 psia for P 2 and 15 psia for P 1 in Equation (I). r p = 120 psia 15 psia = 8 Refer Table A-17E given in the textbook to find the properties of air at 2,000 R ( T 3 ) and 1,200 R ( T 4 ) , which gives 504.71 Btu / lbm for h 3 , and 291.30 Btu / lbm for h 4 . Rearrange Equation (I) and find h 1 .Substitute 40 lbm / s for m ˙ , 291

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Chapter 9.12, Problem 92P

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The efficiency of the compressor for which the power plant produces zero net work.

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