a) Explanation Draw the T − s diagram for the regenerative Brayton cycle as shown in Figure (1). Assuming constant specific heats Write the expression to calculate the pressure ratio of the cycle ( r p ) . r p = P 2 P 1 (I) Write the temperature and pressure relation for the isentropic process 1-2. T 2 = T 1 ( P 2 P 1 ) ( k − 1 ) / k = T 1 ( r p ) ( k − 1 ) / k (II) Here, temperature at state 1 is T 1 , temperature at state 2 is T 2 , pressure at state 1 is P 1 , pressure at state 2 is P 2 , the pressure ratio is r p , and the specific heat ratio is k . Write the temperature and pressure relation for the isentropic process 3-4. T 4 = T 3 ( P 4 P 3 ) ( k − 1 ) / k = T 3 ( 1 r p ) ( k − 1 ) / k (III) Here, temperature at state 4 is T 4 , temperature at state 3 is T 3 , pressure at state 4 is P 4 , and pressure at state 3 is P 3 Write expression to calculate the thermal efficiency of the cycle ( η th ) . η th = 1 − q out q in = 1 − c p ( T 6 − T 1 ) c p ( T 3 − T 5 ) = 1 − ( T 6 − T 1 ) ( T 3 − T 5 ) (IV) Here, the heat input to the cycle is q in , heat rejected by the cycle is q out , the specific heat at constant pressure is c p , temperature at state 5 is T 5 and temperature at state 6 is T 6 . Write the expression to calculate the power delivered by the gas-turbine power plant ( W ˙ net ) b) To determine The power delivered by the gas-turbine power plant assuming variable specific heats.

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Chapter 9.12, Problem 108P

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The power delivered by the gas-turbine power plant assuming constant specific heats.

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The power delivered by the gas-turbine power plant assuming variable specific heats.

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Chapter 9.12, Problem 107P

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