9-80E A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air enters the compressor at 520 R and the turbine at 2000 R. Accounting for the v tion of specific heats with temperature, determine (a) the ait temperature at the compressor exit, (b) the back work rati and (c) the thermal efficiency. 9-80E_ A simple ideal Brayton eycle with air as the working fluid has a pressure ratio of 10. The air temperature at the compressor exit, the back work ratio, and the thermal efficiency are to be determined. Assumptions 1 Steady operating conditions exist. 2 The air-standard assumptions are applicable. 3 Kinetic and potential cenergy changes are negligible. 4 Air isan ideal gas with variable specific heats. Properties The properties of air are given in Table A-17E, Analysis (a) Noting that provess 1-2 is isentropic, r fy =12427 Buulbm : H=s0R —> py inna 2000 ¥ 1, ~£ p, = (oxi 2147)=12.147 —9 2 “968 i is Fh, oh 217) 1h 240.11 Bat 4 (6) Process 3-4 isentropic, and thus, diy = 304,71 Beuitbm T,=200R —> ping + \i740 10 We jy Hy hy = 240.11-124.27=115.84 Buw'lbm. = hy = $04,71~265 83 = 238.88 Bru/lbm ‘Then the back-work ratio becomes yg = ee = S84 Bulb _ 4g Wrou 238.88 Bwlom (©) dy = hy hs = 504.71-240.11 = 264,60 Bew/lbm Waaout = "rout "in = 238.88—115,84 =123.04 Btw Wruaout _ 123.04 Btw/lbm Jin 264.60 Btw/Ibm uns9-81 A gas-turbine power plant operates on the simple Bray- ton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in the cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the value at the compressor inlet, Assuming aan isentropic efficiency of 80 percent for the compressor and 86 percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature. 9-81 A 32-MWW gas-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The mass flow rate of ar through the cycle is to be determined. Assumptions 1 Steady operating conditions exist. 2 The ait-standard assumptions are applicable. 3 Kinetic and potential energy changes are negligible. 4 Air isan ideal gas with variable specific heats Properties The properties of ar ae given in Table A-17. Analysis Using variable specific heats, 10.24 kike 5546 hy u 1, =310K —> Fir, ={Plrsa9)=9411 shy =s1932bhg hp Pe Wretout = Moa Mein = Mts ~~ (Bay Py te (0.86)932.93-519.32)-(562.26-310.24)/(0.80) = 40.68 kg9-43 Gy A simple Brayton cycle using sr asthe working © fluid has a pressure ratio of 10, The minimum and maximum temperatures in the cycle are 295 and 1240 K. ‘Assuming an isentropic efficiency of 83 percent for the com- pressor and 87 percent for the turbine, determine (a) the air temperature at the turbine exit, (b) the net work output, and (6) the thermal efficiency. 9.83 “7 4 simple Brayton cycle with air as the working fluid has a pressure ratio of 10. The air temperature at the turbine ‘exit, the net work output, and the thermal efficiency are to be determined Assumptions 1 Steady operating conditions exis, 2 The at-standard assumptions are applicable. 3 Kinetic and potential energy cl negligible. 4 Air isan ideal gas with variable specific heats. Properties Ve properties of air are given in Table A-17. Analysis (a) Noting that process 1-2s is isentropic, =570.26 kW/ky and 7 64.9K 3295.17 + 57026= 295.17 _ 66. 6oKIky On3 hy B, 1324.93 kg T=2M0K—> 7) yay pte, -(Flona-273— a, = 702.07 kiky and T,, =689.6K ny ak sls ha.) Pee 324.93 —(0.87{1324.93 - 702.07) = 783,04 kk Ths, 1 = T644K (6) y= hy ~hy =132493~626.60 = 698 3k ohhh = 783. 04~295.17 = 487 ORV Kw Maza“ in ~ou = 83-4879 = 210.4 Tg © ny Tse OSS 9 3013-301% Yn OOBIKTKE9-85 Repeat Prob. 9-83 using constant specific heats at room temperature. 9.85. simple Brayton cycle with air as the working fuid has pressure ratio of 10, The air temperature atthe turbine exit, the net work output, and the thermal efficiency are to be determined Assumptions 1 Steady operating conditions exist. 2 The ait-standard assumptions are applicable. 3 Kinetie and potential, ‘energy changes are negligible, 4 Airis an ideal gas with constant specific heats. Properties The properties of air at room temperature are cy = 1.005 kl/kg-K and Analysis (a) Using the compressor and turbine efficiency relations, 4 (Table A-2) 295 k \l0)"* "= 569.6K J -towe( 2) ax ell i) 1 <(nany Bt 295K =295 625.8K 083, xls =P So renonttiot) SAB =Tay ayo (os7h280- 6823) ~720K ” (1.005 karky -K\I240—625,9)K =617.3 Kky 1.005 kirkg- K)720—295)K = 427. 11k Waa in “out =6173-427.1= 190.24 (ny = Mase = OAKS 9 398) = 30.8% 617 3kiike. io9-86 Consider a simple Brayton cycle using air as the work- ing fluid; has a pressure ratio of 12: has a maximum cycle temperature of 600°C; and operates the compressor inlet at 100 kPa and 15°C. Which will have the greatest impact on the back-work ratio; a compressor isentropic efficiency of 80 percent or a turbine isentropic elficiency of 80 percent? Use constant specific heats at room temperature. FIGURE P9-869-86 A simple Brayton cycle with air as the working fluid operates between the specified temperature and pressure limits. ‘The effects of non-isentropic compressor and turbine on the back-work ratio is to be compared. Assumptions 1 Steady operating conditions exist. 2 The ait-standard assumptions are applicable. 3 Kinetic and potential cnergy changes are negligible. 4 Air isan ideal gas with constant specific heats 00S Ki/kg’K and k= 1.4 (Table A-2a), Properties The properties of air at room temperature are ¢ Analysis: For the compression process, 7 ana ann b) =k > 120m Tu) = 873 —(0.80)(873 — 429.2) =5180K The isentropic and actul work of compressor and turbine are Weamps =€p(Tin Ti) =(1.008KU kg: K A S85,8~288)K = 299.3 kk (1.005 kiVkg-K)(660.2 ~ 288)K =374.1k/kg Wroiy =€ p(T, ~Ty)= (L005 kl/kg- KY(873 ~518.0)K =356.8kI/kg ‘The back work ratio for 90% efficient compressor and isentropic turbine ease is a ‘comp _ 374.1 kg jus MO.0KIKg Tow 8387 ‘The back work ratio for 90% efficient turbine and isentropic compressor case is Tg = Stee. = DOSS _ 9.9387, Wr 356.80 Kg ‘The two results are identical9-87 Air is used as the working fluid in a simple ideal Brayton cycle that has a pressure ratio of 12, a compressor inlet temperature of 300 K, and a turbine inlet temperature of 1000 K. Determine the required mass flow rate of air for a net power output of 70 MW, assuming both the compres- sor and the turbine have an isentropic efficiency of (a) 100 percent and (b) 85 percent. Assume constant specific heats at room temperature. Answers: (2) 352 kes, (6) 1037 ke's 9-87 A gas turbine power plant that operates on the simple Brayton cycle with air as the working fluid has a specified pressure ratio. The required mass flow rate of ar is to be determined for two cases. Assumptions 1 Steady operating conditions exist, 2 The air-standard assumptions are applicable, 3 Kinetic and potential ‘energy changes are negligible. 4 Air isan ideal gas with constant specific heats Properties The properties of air at room temperature are r Gy = LODS Kiikg:K and = 1.4 (Table A-2) Analysis (a) Using the isentropic relations, 1000 K. ys (ethee Z ) = (300 Ky12)"*"*¥=610.2K g iB) (sy ea a 4 ~bomx{L)-a91.7K j -plTs, ~T,)= (1.005 kirkg-KY{610.2—300)K = 311.75 Kke = ep (U3 ~ Ta, )= (1.005 kd/kg-K X1000 - 491.7)K. ~ Wein = 51084—311.75 = 199.1 kik 10.84 kirk 70,000 ksis neon, DOO 3s canon 199.1 Kkg 2 MS (6) The net work output is determined to be Wasaout = Waz.ont Wain =r Meron Wain Me = (0.85{510.84)-311.75/0.85=67 5 ki/kg _ Wasiour _ 70,000 V/s Waraor 675k = 1037 ky/s9-88 An aircraft engine operates on a simple ideal Brayton ceycle with a pressure ratio of 10. Heat is added to the cycle at a rate of 500 kW; air passes through the engine at a rate of 1 kg/s; and the air at the beginning of the compression is at 70 kPa and 0°C. Determine the power produced by this ‘engine and its thermal efficiency. Use constant specific heats, at room temperature, 9-88 An aircraft engine operates as a simple ideal Brayton cycle with air as the working fluid, The pressure ratio and the rate of heat input are given, The net power and the thermal efficieney are to be determined Assumptions 1 Steady operating conditions exist. 2 The air-standard assumptions are applicable. 3 Kinetic and potential ‘energy changes are negligible. 4 Air isan ideal gas with constant specific heats. Properties The properties of air at room temperature are ¢y ~ 1.005 ki/kyK and k= 1.4 (Table A-2a). Analysis For the isentropic compression process, Ty = 1, * = 73K KIO) = 527.1K r “The heat akiton is . at tLe -HO8W ee i Z a an} AN; 1) > Sook sor. k + SOOKE 995 1.005 kI/kg-K ae “The temperature atthe exit of the turbine is your yen ="orsk{— | =530.9K 0 Applying the first law to the adiabatic turbine and the compressor produce sy =e p(T, —T,) = (1.005 kiikg: K 1025 ~$30.9)K = 496.6 kk, We =€p(Ty I) = (.005 kivkg: KXS27.1-273)K = 255.4 ks The net power produced by the engine is then Wing, =i, —We) = (1 ke/S496.6~285.4)klkg = 241.2KW Finally the thermal efficiency is Bigg _ 241.2KW ‘SOOKW on 4829-90 A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 KPa. ‘The working fluid is air, which enters the compressor at 40°C at a rate of $50 m'/min and leaves the turbine at 650°C. Using variable specific heats for air and assuming a compressor isentropic efficiency of 85 percent and a turbine isentropic efficiency of 88 percent, determine (a) the net power output, (b) the back work ratio, and (c) the thermal efficiency, Answers: (a) 6081 KW, (6) 0.536, (c) 37.4 percent 4c FIGURE P9-909.90 A gas-turbine plant operates onthe simple Brayton efficiency are to be determined, le. The net power output, the back work ratio, and the thermal Assumptions 1 The ar-standard assumptions are applicable. 2 Kinetic and potential energy changes are negli ‘an ideal gas with variable specific heats. ‘Combustion chamber ible. 3 Airis Properties The gas constant of air is R = 0.287 kirkg-K (Table A-1), Analysis (a) For this problem, we use the properties from EES software, Remember that for an ideal gas, enthalpy isa Function of temperature ‘only whereas entropy is functions ofboth temperature and pressure, Process 1-2: Compression 1, =40°C_—>h =313.6KUky 2 1 =40°C F, =100 kPa Js. -s740nane K P; =1600kPa 2, hy =50471 Buu/thm 2000 R y 1-108 —> hy YY g TS sor | b, oy = tilts )—> hy ‘* +r, 1474 A, % Weg = ila, Yc Wig “15 hy Wau “Wau -Weiy = 8536~$339 = 3197 Bais = 3379 kW r, (8{1.474)=11.79 —s hs, = 238,07 Buullbm 40 llnn/s(238.07-131 30}(0.80)= 5339 B's 0 Tom/s)(304.71 -291.30}BtuTon 536 Btu/s 9-93 A gascturbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 800 kPa. Air enters the compressor at 30°C and Ieaves at 330°C at a mass flow rate of 200 kg/s. The maximum cycle temperature is 1400 K. During operation of the eycle, the net power output is measured experimentally to be 60 MW. Assume constant properties for air at 300 K with ¢, = 0.718 KIKEK, c, 1,005 kitkg-K, R = 0.287 kitkg-K, k = 14. (a) Sketch the T-s diagram for the cycle () Determine the isentropic efficiency of the turbine for these operating conditions (©) Determine the cycle thermal efficiency.9-93 A simple Brayton eycle with ai as the working fluid operates between the specified temperature and pressure limits. The eycle is to be sketched on the 7-5 cycle and the isentropic efficiency of the turbine and the eyele thermal efficiency are to be determined Assumptions 1 Steady operating conditions exist. 2 The air-standard assumptions are applicable. 3 Kinetic and potential ‘energy changes are negligible. 4 Air isan ideal xas with constant specific heats, Properties The properties of ait are given as éy= 0.718 KIKE'K, y= 1.005 Klike-K, R= 0.287 ki/kgK, = 14. Analysis (b) For the compression process, Woo = tie p Ts Ti) 00 kes 005 kW/kg-KX330—30)K = 60,300kW For the turbine during the isentropic process, = (1400K OKA) a72.9K S00KPa (200 kg/s\I.005kI/kg:K(1400—772.9)K = 126,050 kW ‘The actual power output ftom the turbine is Woo = Wr —Weomp Weuiy = Wye +1 4upp = 60,000 + 60,300 = 120,300 KW ‘The isentropic efficiency ofthe turbine is then Wryyy _ 120,300 Wags 126,050kW Thais = =0.954=95.4% (©) The rate of heat input is Oa = gts “13 (200 kes) 1,005 ki/kg- K (1400 —(330 + 273)]K =160,200 kW, ‘The thermal efficiency is then Wye, 60,000 kW. Op 160.2000 Th 7.5%9-94 A gas-turbine power plant operates on a modified Brayton cycle shown in the figure with an overall pressure ratio of 8. Air enters the compressor at 0°C and 100 kPa. ‘The maximum eycle temperature is 1500 K. The compres- sor and the turbines are isentropic. The high pressure turbine develops just enough power to run the compressor. Assume fant properties for air at 300 K with c, = 0.718 ki/kg-K, 6, = 1.005 klk K, R = 0.287 Kkg-K, k= 14. (a) Sketch the Ts states. (b) Determine the temperature and pressure at state 4, the exit of the high pressure turbine. (If the net power output is 200 MW, determine mass flow rate of the air into the compressor, in kw/s. ‘Answers: (b) 1279 K, 457 KPo, (c) 442 kes jagram for the cycle, Label the data FIGURE P9-949-94 A modified Brayton cycle with at as the working fluid operates ata specified pressure ratio, The 7-s diagram is to be sketched and the temperature and pressure atthe exit ofthe high-pressure turbine and the mass flow rate oF air are to be determined. Assumptions 1 Steady operating conditions exist. 2 The air-standard assumptions are applicable. 3 Kinetic and potential ‘energy changes are negligible. 4 Air is an ideal gas with constant specific heats. Properties The properties of air are given as c= 0.718 KUKEK, ¢, = 1.005 kIkwK, R= 0.287 KIkyK, k= 14 Analysis (b) For the compression process, (2) ~annve" F, TThe power input to the compressor is equal to the power output, from the high-pressure turbine. Then, Warp tie 1s, 23K -suonar 2834) 150K 1004) oe 457.3KPa snl “The net power is that generated by the low-pressure turbine since the power output from the high-pressure turbine is equal to the power input to the compressor. Then, Wepre = tite p(T ~Ts) Wepre 200,000 kW Ty Fe) C005 RNikg:K\I278.5—828.K = 441.8kg/s