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722 Isobutane expands adiabatically in a turbine from 5000 kPa and 52315 K (250 C) to 500 kPa at the rate of 07 kmol s-' If the turbine efficiency is 080, what is the power output of the turbine and what is the temperature of the isobutane leaving the turbine 723 The steam rate to a turbine for variable output is controlled by a throttle valve in the inlet line Steam is supplied to the throttle valve at 1700 kPa and 49815 K (225 C) During a test run, the pressure at the turbine inlet is 1000 kPa, the exhaust steam at 10 kPa has a quality of 095, the steam flow rate is 05 kg s-', and the power output of thc turbine is 180 kW (a) What are the heat losses from the turbine (6) What would be the power output if the steam supplied to the throttle valve were expanded isentropically to the final pressure 724 Carbon dioxide gas enters an adiabatic expander at 8 bar and 67315 K (400 C) and discharges at 1 bar If the turbine efficiency is 075, what is the discharge temperature and what is the work output per mole of C02 Assume COz to be an ideal gas at these conditions 725 Tests on an adiabatic gas turbine (expander) yield values for inlet conditions (TI, PI) and outlet conditions (Tz, P2) Assuming ideal gases with constant heat capacities, determine the turbine efficiency for one of the following: (a) TI = 500 K, P1 = 6 bar, Tz = 371 K, P2 = 12 bar, Cp/R = 712 (b) TI = 450 K, Pl = 5 bar, T2 = 376 K, P2 = 2 bar, Cp/R = 4 (c) Tl = 525 K, PI = 10 bar, T2 = 458 K, P2 = 3 bar, Cp/R = 11/2 (d) Tl = 475 K, Pl = 7 bar, T2 = 372 K, P2 = 15 bar, Cp/R = 912 (e) Tl = 550 K, PI = 4 bar, T2 = 403 K, P2 = 12 bar, Cp/R = 512 726 The efficiency of a particular series of adiabatic gas turbines (expanders) correlates with power output according to the empirical expression:
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Here, I w 1 is the absolute value of the actual power output in kW Nitrogen gas is to be expanded from inlet conditions of 550 K and 6 bar to an outlet pressure of 12 bar For a molar flowrate of 175 mol s-I, what is the delivered power in kW What is the efficiency of the turbine What is the rate of entropy generation & Assume nitrogen to be an ideal gas with Cp = (7/2)R
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727 A turbine operates adiabatically with superheated steam entering at 45 bar and 67315 K (400 C) If the exhaust steam must be "dry," what is the minimum allowable exhaust pressure for a turbine efficiency, 7 = 075 Suppose the efficiency were 080 Would the minimum exhaust pressure be lower or higher Why 728 Turbines can be used to recover energy from high-pressure liquid streams However, they are not used when the high-pressure stream is a saturated liquid Why Illustrate by determining the downstream state for isentropic expansion of saturated liquid water at 5 bar to a final pressure of 1 bar 729 Liquid water enters an adiabatic hydroturbine at 5 atm and 28815 K (15"C), and exhausts at 1 atm Estimate the power output of the turbine in J kg-' of water if its
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CHAPTER 7 Applications o Thermodynamics to Flow Processes f efficiency is q = 055 What is the outlet temperature of the water Assume water to be an incompressible liquid
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730 An expander operates adiabatically with nitrogen entering at Tl and PI with a molar flow rate A The exhaust pressure is P2, and the expander efficiency is q Estimate the power output of the expander and the temperature of the exhaust stream for one of the following sets of operating conditions (a) TI = 75315 K(480 C), P1= 6 bar, A = 02 kmol s-' , P2= 1 bar, q = 080 (b) TI = 67315 K(400 C), PI = 5 bar, A = 015 kmol s-', P2= 1 bar, q = 075 (c) Tl =77315 K(500 C), P1 =7bar, A =0175kmol s-', P2= I bar, q =078 (d) Tl = 72315 K(450 C), P1= 8 bar, i z = 01 kmol sf', P2= 2 bar, q = 085 (e) Tl = 75515 K(482"C), PI= 655 bar, A = 023 kmol s-', P2= 103 bar, q = 080 731 What is the ideal-work rate for the expansion process of Ex 76 What is the thermodynamic efficiency of the process What is the rate of entropy generation sG What is wLOs, Take T = 300 K , 732 Exhaust gas at 67315 K (400 C) and 1 bar from internal-combustion engines flows at the rate of 125 mol s-' into a waste-heat boiler where saturated steam is generated at a pressure of 1200 kPa Water enters the boiler at 29315 K (20 C) (T,), and the exhaust gases are cooled to within 10 K (10 C) of the steam temperature The heat capacity of the exhaust gases is Cp/ R = 334 112 x lop3TIK The steam flows into an adiabatic turbine and exhausts at a pressure of 25 kPa If the turbine efficiency q is 72%, (a) What is w,, the power output of the turbine (b) What is the thermodynamic efficiency of the boilerlturbine combination (c) Determine sG the boiler and for the turbine for (d) Express wl0,,(boiler) and %ost(turbine) as fractions of ( ~ i d , , lI, the ideal work of the process
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733 A small adiabatic air compressor is used to pump air into a 20-m3 insulated tank The tank initially contains air at 29815 K (25 C) and 10133 kPa, exactly the conditions at which air enters the compressor The pumping process continues until the pressure in the tank reaches 1000 kPa If the process is adiabatic and if compression is isentropic, what is the shaft work of the compressor Assume air to be an ideal gas for which C p = (7/2)R and Cv = (5/2)R 734 Saturated steam at 125 kPa is compressed adiabatically in a centrifugal compressor to 700 kPa at the rate of 25 kg s-' The compressor efficiency is 78% What is the power requirement of the compressor and what are the enthalpy and entropy of the steam in its final state 735 A compressor operates adiabatically with air entering at TI and P1 with a molar flow rate A The discharge pressure is P2 and the compressor efficiency is q Estimate the power requirement of the compressor and the temperature of the discharge stream for one of the following sets of operating conditions (a) Tl = 29815 K(25"C), PI = 10133kPa, ti ~ 0 kmol sC1, P2= 375kPa, q =075 1 (b) Tl = 35315 K(80 C), P1= 375kPa, A = 0 l kmol sf', P2= IOOOkPa, q =070 (c) Tl =30315K(30 C), P1= 100kPa, A =015 kmol s-', Pz =500kPa, q =080 (d) TI = 37315 K(lOO C), PI =5OOkPa, i z =005 kmol s-l, P2= 1300kPa, 77 = 075
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