# TAMU CHEN 205 - extra-sol567 (8 pages)

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- School:
- Texas A&M University
- Course:
- Chen 205 - Chem Engr Thermo I

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ME 24 221 THERMODYNAMICS I Solutions to extra problem set from Chapters 5 6 and 7 Fall 2000 October 30 2000 J Y Murthy 5 61 Saturated x 1 water at 25 C is contained in a hollow spherical aluminum vessel with inside diameter of 0 5 m and a 1 cm thick wall The vessel is heated until the water inside is saturated vapor Considering the vessel and water together as a control mass calculate the heat transfer for the process C V Vessel and water This is a control mass of constant volume m m U U Q W Q State 1 v 0 001003 0 01 x 43 359 0 4346 m kg u 104 88 0 01 x 2304 9 127 9 kJ kg State 2 x 1 and constant volume so v v V m vg T2 v 0 4346 T 146 1 C V INSIDE V Al u uG2 2555 9 0 06545 0 5 0 06545 m mH O 0 1506 kg 0 4346 6 0 52 0 5 0 00817 m 6 mAl AlVAl 2700 x 0 00817 22 065 kg Q U U mH O u u H O mAlCV Al T T 0 1506 2555 9 127 9 22 065 x 0 9 146 1 25 2770 6 kJ 5 63 A rigid insulated tank is separated into two rooms by a stiff plate Room A of 0 5 m contains air at 250 kPa 300 K and room B of 1 m has air at 150 kPa 1000 K The plate is removed and the air comes to a uniform state without any heat transfer Find the final pressure and temperature C V Total tank Control mass of constant volume Mass and volume m m m V V V 1 5 m Energy Eq m u m uA m uB Q W 0 Ideal gas at 1 m P V RT 250 0 5 0 287 300 1 452 kg u 214 364 kJ kg from Table A 7 Ideal gas at 2 m P V RT 150 1 0 287 1000 0 523 kg u 759 189 kJ kg from Table A 7 m m m 1 975 kg u m uA m uB m 1 452 214 364 0 523 759 189 1 975 358 64 kJ kg Table A 7 T 498 4 K P m RT V 1 975 0 287 498 4 1 5 188 3 kPa 5 71 Two containers are filled with air one a rigid tank A and the other a piston cylinder B that is connected to A by a line and valve as shown in Fig P5 71 The initial conditions are mA 2 kg TA 600 K PA 500 kPa and VB 0 5 m3 TB 27 C PB 200 kPa The piston in B is loaded with the outside atmosphere and the piston mass in the standard gravitational field The valve is now opened and the air comes to a uniform condition in both volumes Assuming no heat transfer find the initial mass in B the volume of tank A the final pressure and temperature and the work W Cont m m mA1 mB1 Energy m u mA1uA1 mB1uB1 W System P const P B1 P W PB1 V V Substance PV mRT mB1 PB1VB1 RTB1 1 161 kg V mA1RTA1 PA1 0 6888 m3 P PB1 200 kPa A 7 uA1 434 8 uB1 214 09 kJ kg m u P V mA1uA1 mB1uB1 PB1V m h 1355 92 kJ h 428 95 kJ kg T 427 7 K V mtotRT P 1 94 m W 200 1 94 1 1888 150 25 kJ 5 83 Water at 150 C quality 50 is contained in a cylinder piston arrangement with initial volume 0 05 m3 The loading of the piston is such that the inside pressure is linear with the square root of volume as P 100 CV 0 5 kPa Now heat is transferred to the cylinder to a final pressure of 600 kPa Find the heat transfer in the process Continuty m2 m1 m u2 u1 1Q 2 1W2 Energy State 1 v 0 1969 u 1595 6 kJ kg m V v 0 254 kg Process equation P 100 CV 1 2 so V V 1 2 P 100 P 100 P 100 500 0 05 x 0 0885 V V x P 100 475 8 100 1 2 dV 100x V V C V 1 5 V 1 5 W PdV 100 CV 3 2 100 V V 1 2 3 2 3 P V P V W 100 0 0885 0 05 3 2 600 x 0 0885 475 8 x 0 05 3 20 82 kJ State 2 P v V m 0 3484 u 2631 9 kJ kg Q 0 254 x 2631 9 1595 6 20 82 284 kJ P P 100 C V 1 100 1 2 2 V T 196 C 5 85 A closed cylinder is divided into two rooms by a frictionless piston held in place by a pin as shown in Fig P5 85 Room A has 10 L air at 100 kPa 30 C and room B has 300 L saturated water vapor at 30 C The pin is pulled releasing the piston and both rooms come to equilibrium at 30 C and as the water is compressed it becomes twophase Considering a control mass of the air and water determine the work done by the system and the heat transfer to the cylinder P PG H O at 30 C PA2 PB2 4 246 kPa Air I G P A1VA1 m R T PA2VA2 PG H O at 30 CVA2 V A2 100 x 0 01 m 0 2355 m 4 246 V B2 VA1 VB1 V A2 0 30 0 01 0 2355 0 0745 m m V B1 vB1 0 3 9 121x10 3 kg 32 89 v B2 8 166 m kg 8 166 0 001004 x B2 x 32 89 0 001 xB2 0 2483 System A B W 0 U 0 IG T 0 uB2 125 78 0 2483 x 2290 8 694 5 uB1 2416 6 kJ kg Q 9 121x10 6 34 3 694 5 2416 6 15 7 kJ A large SSSF expansion engine has two low velocity flows of water entering High pressure steam enters at point 1 with 2 0 kg s at 2 MPa 500 C and 0 5 kg s cooling water at 120 kPa 30 C enters at point 2 A single flow exits at point 3 with 150 kPa 80 quality through a 0 15 m diameter exhaust pipe There is a heat loss of 300 kW Find the exhaust velocity and the power output of the engine C V Engine SSSF Constant rates of flow Qloss and W State 1 State 2 Table B 1 3 h1 3467 6 Table B 1 1 h2 125 77 W 1 Engine 2 3 Q loss h3 467 1 0 8 2226 5 2248 3 kJ kg v3 0 00105 0 8 1 15825 0 92765 m3 kg Continuity …

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