Explanation Two-stage gas turbine Draw the T − s diagram for the two-stage gas-turbine with regeneration as shown in Figure (1). Write the expression to calculate the pressure ratio across each stage for two-stage gas turbine ( r p ) . r p = r (I) Here, the overall pressure ratio of the two-stage gas turbine is r . Write the expression to calculate the temperature at the end of the compression process for the two-stage gas turbine ( T c ) . T c = T min r p ( k − 1 ) / k (II) Here, the specific heat ratio of air is k , the minimum temperature of air in the two-stage gas turbine cycle is T min . Write the expression to calculate the temperature at the end of the expansion process for the two-stage gas turbine ( T c ) . T e = T max ( 1 r p ) ( k − 1 ) / k (III) Here, the maximum temperature of air in the two-stage gas turbine cycle is T max . Write the expression to calculate the heat input for the two-stage gas turbine ( q in ) . q in = 2 c p ( T max − T e ) (IV) Here, the specific heat of air at constant pressure is c p . Write the expression to calculate the heat output for the two-stage gas turbine ( q out ) . q out = 2 c p ( T c − T min ) (V) Write the expression to calculate the thermal efficiency of the given two-stage gas turbine ( η th ) . η th = 1 − q out q in (VI) Three-stage gas-turbine Draw the T − s diagram for three-stage gas-turbine with regeneration as shown in Figure (2). Write the expression to calculate the pressure ratio across each stage for three-stage gas turbine ( r p ) . r p = r 3 (VII) Here, the overall pressure ratio of the three-stage gas turbine is r . Write the expression to calculate the temperature at the end of the compression process for the three-stage gas-turbine ( T c ) . T c = T min r p ( k − 1 ) / k (VIII) Here, the minimum temperature of air in the three-stage gas turbine cycle is T min . Write the expression to calculate the temperature at the end of the expansion process for the three-stage gas turbine ( T c ) . T e = T max ( 1 r p ) ( k − 1 ) / k (IX) Here, the maximum temperature of air in the three-stage gas turbine cycle is T max . Write the expression to calculate the heat input for the three-stage gas turbine ( q in ) . q in = 3 c p ( T max − T e ) (X) Write the expression to calculate the heat output for the three-stage gas turbine ( q out ) . q out = 3 c p ( T c − T min ) (XI) Write the expression to calculate the thermal efficiency of the given three-stage gas turbine ( η th ) . η th = 1 − q out q in (XII) Conclusion: From Table A-2a, “Ideal-gas specific heats of various common gases”, obtain the following values of air at room temperature. c p = 1.005 kJ / kg ⋅ K c v = 0.718 kJ / kg ⋅ K R = 0.287 kJ / kg ⋅ K k = 1.4 Substitute 16 for r to find r p in Equation (I). r p = 16 = 4 Substitute 4 for r p , 293 K for T min , and 1.4 for k in Equation (II). T c = ( 293 K ) ( 4 ) 0.4 / 1.4 = 435.4 K Substitute 4 for r p , 1073 K for T max , and 1

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Chapter 9.12, Problem 176RP

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The thermal efficiency of the two-stage gas-turbine and the three-stage gas-turbine and compare the results.

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Chapter 9.12, Problem 174RP

Chapter 9.12, Problem 177RP

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The thermal efficiency of the two-stage gas-turbine and the three-stage gas-turbine and compare the results.

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