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Unformatted text preview: ”INDIAN INSTITUE OF TECHNOLOGY Date: ............... FN/AN Time: 3 hours Full Marks: 100 No. of Students:' 215 Spring End-Semester Examination, 2008 Mechanical Engineering Subject No.: ME22002 . 2"d Year B.Tech (H) ‘ Subject Name: Thermodynamics Answer all the questions. Marks for the questions are shown on the margin. Use steam tables (supplied with the Question Paper) as and when necessary. For air, use cp=1.004 kJ/kgK and cv=0.717 kJ/kg/K. For water, use c=4.2 kJ/kgK. 1. The net power output of the turbine in an ideal reheat-regenerative Rankine cycle is 100 MW. Steam enters the high-pressure (HP) turbine at 90 bar, 550°C. After expansion to 7 bar, some of the steam goes to an open heater and the balance is reheated to 400°C, after which it expands to 0.07 bar. a. What is the steam flow rate to the HP turbine ignoring KE and PE effects? b. What is the total pump work? c. Calculate the cycle efficiency. d. if there is a 10°C rise in the temperature of the cooling water, what is the rate of flow of the cooling water in the condenser? e. If the velocity of the steam flowing from the turbine to the condenser is limited to a maximum of 130 m/s, find the minimum diameter of the connecting tube. f. Draw a schematic component layout and the T-s diagram of the cycle. [5+3+7+4+4+5]:28 2. a) Liquid octane enters a steady—flow combustion chamber at 25°C and 8 bar at a rate of 0.8 kg/min. It is burned with 200% excess air that is compressed and preheated to 500 K and 8 bar before it enters the combustion chamber. After combustion, the products enter an adiabatic turbine at 1300 K and 8 bar and leave at 900 K and 2 bar. Assume all gases to be ideal gas. Considering complete combustion and an ambient temperature of 25°C, determine: i. The heat transfer rate (kW) from the combustion chamber ii. Power output (kW) of the turbine - [8+6] b) In a typical gas turbine plant reheater (which is a second combustion chamber), only fuel is added while in the primary combustion chamber, both fuel and air is supplied. Explain this precisely. [4] c) Cite one reason (using suitable cycle diagram) for not using Carnot cycle as a vapour power cycle. [4] 3. Consider a gas-turbine cycle with two stages of compression and two stages of expansion. The overall pressure ratio is 9. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. The pressure at the entrance to the first compressor is 100 kPa. The pressure ME22002 Thermodynamics, Spring End-Sem 2008 1 ratio for each stage of compression or expansion is 3 in order to attain minimum compression work; _~ and maximum expansion work. The turbine expansion is isentropic and the isentropic efficiencyof _ the compressor is 80%. Determine the ratio of turbine work to compressor work and-the thermal efficiency of the cycle, assuming (a) no regeneration and (b) ideal regeneratibn. Explain why the ratio of turbine to compressor work is less for a gas-turbine cycle than the ratio of turbine to pump work in a steam power cycle. Assume specific heats of air to be constant. Draw a labelled equipment layout and the corresponding T-s diagram of the regenerative cycle. [6+12+3+4] 4. (a) Compressed air enters a well insulated counterflow heat exchanger, operating at steady state, at 610 K, 10 bar and exits at 860 K, 9.7 bar. Hot combustion gas enters as a separate stream at 1020 K, 1.1 bar J and exits at 1 bar. Each stream has a mass flow rate of 90 kg/s. Heat , _ transfer between the outer surface of ' 231’“ the heat exchnager and the x ,. . 2‘35 surroundings can be ignored. Kinetic ~ ' : 2 ' . 2 XML“; ‘2 , , towing»: and potential energy effects are . g . .. _ M,” g negligible. Take To = 300 K and p.,=1 x 23%;” 2330; l i bar. Assuming the combustion gas 3 ’ ' , stream to have properties of air, and M assuming both streams to behave as . , , , _ ideal gas, determine for the heat jfempmws . I Tmmw exchanger: - stir ’ V I V I ‘/ i. the exit temperature of the combustion gas, in K. ii. the net change in the flow exergy rate from inlet to exit of each stream, in MW. iii. The rate of exergy destruction, in MW. ' [5+10+4] (b) The Joule-Kelvin coefficient #J is a measure of the temperature change during a throttling process. A similar measure of the temperature change produced by an isentropic change of pressure 6T V is provided by the coefficient #3 , where #3 = [5;] . Prove that #3 _Il'lJ = F . [6] s P ME22002 Thermodynamics. Spring End-Sem 2008 2 GIVEN DATA Ideal—gas properties of various substances NITRQGEN Dmmwc (N2) =0 kJ/kmol hM-' - 28.013 OXYGEN, DIATOMIC (0,) ‘ 11° 1' 0 kJ/kmol M = 31.999 (5 ~ 7:: kJ/kmol ~8670 “5753 173.308 ‘ 193.483 179.985 220.693 225.450 231.314 ‘ 234.227 250.01 1 252.878 WATER (H20) CARBON DIOXIDE (C0,) hf”; = ~24! 826 kJ/k'r‘nol ‘h° == —393 522 kJ/kmol = 18 015 T (E — 733,.) 3 i3 , K kJ/kmol kJ/kmol K 0 .“9904 0 100 —6617 152.386 179.010 200 -3282 . 175.488 199.976 . V 500 8 6922 8‘ 206 532 600 10499 . 213.051 ‘700 14190 3 , 218.739 274. 528 279.390 283. 931 ME22002 Thermodynamics, Spring E-nd 8em 2008 Enthalpy of formatiOn & Absolute entrogy at 25 °CI 1 bar . ’4 Substance Formula M State kJ/k‘mol Water H20 18.615 gas ~24: 826 Water : H30 18.015 liq 1 “285 830 Hydrogen peroxide H302 34.015 gas - 136 106 ‘L>j>‘,\..\k (" ‘ Carbon dioxide . ~393 522 213.795 Methane ‘ ~74 873 186.251 Acetylene as +226 731 Kl 7%. wimp _ a .m “M a i”: N < ’ 1 3587‘: mg :- 16133667" 269.917 306.647 348.945 255324? 387.979 , 114,232 -208 600 466.514 114.232 ‘ «250 105 360.575 Maxwell relations End of Paper ME22002 Thermodynamics, Spring End-Sem 2008 ...
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