FINAL EXAM Date: Thursday, December 21, 2006, 9 am 12 am Examiner: Prof. E. Timofeev Associate Examiner: Prof. D. Frost READ CAREFULLY BEFORE YOU PROCEED: Course: MECH-341 Thermodynamics II Semester: Fall 2006 Closed books, closed notes, no crib sheets. Standard calculators only. Thermodynamic tables are provided. Use interpolation when extracting data from the tables. Answer all (i.e. five) problems (the total number of points is 20 5100). The problems are printed on four pages. The fifth page is a formula sheet for your reference. PROBLEM 1. 20 points (2 points for each question). Write your answers on the multiple choice questions in the exam book, not here! The questions below, except for the multiple choice ones, call for a brief explanation. In some cases it may be greatly assisted by a sketch/diagram and/or an equation. 1. Consider a simple ideal Rankine cycle. If the condenser pressure is lowered while keeping turbine inlet state the same, then (c) the cycle efficiency will decrease; (e) the pump work input will decrease. 2. Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the steam is superheated to a higher temperature, then (c) the cycle efficiency will decrease; (e) the amount of heat input will decrease. 3. Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the cycle is modified with reheating, then (c) the pump work input will decrease; (e) the amount of heat input will decrease. 1
4. Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the cycle is modified with regeneration that involves one open feedwater heater, then (b) the amount of heat rejected will increase; (c) the cycle thermal efficiency will decrease; (d) the quality of steam at turbine exit will decrease; (e) the amount of heat input will increase. Select the correct statement per unit mass of steam flowing through the boiler. 5. What four processes make up the ideal Otto cycle? 6. The ideal Brayton and Rankine cycles are composed of the same four processes, yet look different when represented on a T -s diagram. Why?Explain. 7. In an ideal gas-turbine cycle with intercooling, reheating and regeneration, as the number of compression and expansion stages is increased, the cycle thermal efficiency approaches: (a) 100 percent; (b) the Otto cycle efficiency; (c) the Carnot cycle efficiency. 8. Can the dry-bulb and wet-bulb temperatures be equal? If no why? If yes in which case? 9. The pressure of a fluid always decreases during an adiabatic throttling process. Is this also the case for the temperature? Explain. 10. In which case would the adiabatic flame temperature be higher, complete combustion of methane (CH 4 ) (a) with the theoretical amount of oxygen, or (b) with the theoretical amount of air (all initially at 298 K, 1 atm)? Explain. PROBLEM 2. 20 points. A gas-turbine-powered Plymouth car built in 1960 had a turbine inlet temperature of 927 C, a pressure ratio of 4 and a regenerator effectiveness of 0.9. Using isentropic efficiencies of 80 percent both for the compressor and the turbine, assuming the ambient air to be at 300 K and 101.325 kpa and performing cold air standard analysis (constant specific heats at the ambient temperature: C p 1.005 kj/(kg K); k 1.4), determine: (a) the thermal efficiency of this car; (b) the mass flow rate of air for a net power output of 100 kw; Show the cycle on T -s and p-v diagrams and label all processes and states (please denote the state of ambient air as state 1 ). PROBLEM 3. 20 points. For a gas whose p-v-t behavior is described by Z 1 + B/v + C/v 2, where B B(T ) and C C(T ) are functions of temperature only and Z is the compressibility factor, derive an expression for the specific entropy change s(v 2, T ) s(v 1, T ) in an isothermal process. 2
PROBLEM 4. 20 points. Figure 1 shows a compressor followed by an aftercooler. Atmospheric air at 1 bar, 32 C, and 75% relative humidity enters the compressor with a volumetric rate of 2.83 m 3 /min. The compressor power input is 11.2 kw. The moist air exiting the compressor at 6.8 bar, 204 C flows through the aftercooler, where it is cooled at constant pressure, exiting saturated at 38 C. Condensate also exits the aftercooler at 38 C. There is no stray heat transfer between the aftercooler and its surroundings. For steady-state operation and negligible kinetic and potential energy effects, determine (using T ables): (a) the rate of heat transfer from the compressor to its surroundings, in kj/min; (b) the relative humidity after the compressor; (c) the mass flow rate of the condensate, in kg/min; (d) the rate of heat transfer from the moist air to the refrigerant circulating in the cooling coil, in tons of refrigeration. Please use the same state numbers as in Figure 1. Figure 1: Schematics for Problem 4 3
PROBLEM 5. 20 points. Figure 2 (see below) provides data for a boiler and air preheater operating at steady state. Methane (CH 4 ) entering the boiler at 25 C, 1 atm is burned completely (to CO 2 and H 2 O) with 170% of theoretical air. Ignoring stray heat transfer and kinetic and potential energy effects, determine: (a) The temperature, in C, of the air entering the boiler from the preheater; (b) The temperature, in C, to which the combustion products should be further cooled down at 1 atm (1.01235 bar) for condensation to occur. When solving, please use the same state numbers as in Figure 2. Assume that all gases can be treated as ideal ones. Figure 2: Schematics for Problem 5 4
Some reference information for all problems: R 8.314 kj/(kmol K) 1 ton 211 kj/min molecular weight of air 28.97 kg/kmol 1 bar 10 5 Pa T 2 T 1 T 2 T 1 p 2 p 1 ( p2 ) k 1 k p 1 ( ) v1 k 1 v 2 ( ) v1 k du T ds pdv dh T ds + vdp dψ pdv sdt dg vdp sdt v 2 ω 0.622p v p p v Q W P Q ṅ F n( h f + h) R Ẇ ṅ F P n( h f + h) RT P n + RT R n n e ( h f + h) e R P n i ( h f + h) i R 5