quiz-solution4

# Quiz-solution4 - 1 = 1500 kPa and V 2 = mRT 2 p 2 =(1(287(500 1 5 Â 10 6 = 0 09567 m 3 650:351 Thermodynamics Page 1 Quiz No 4 Thus the piston must

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650:351 Thermodynamics Doyle Knight Department of Mechanical and Aerospace Engineering Rutgers - The State University of New Jersey New Brunswick, NJ USA Tel: 732 445 4464 · Email: [email protected] OFce hours: Tuesday and ±riday, 9:00 am to 11:30 am and by appointment

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Quiz No. 4 A piston/cylinder has 1 kg of air at 1500 kPa and 1200 K. The cylinder has stops so that the min- imum volume is 0.15 m 3 . The air now cools to 500 K by heat transfer to the ambient. The air is the control mass. Find the ±nal volume, the ±nal pressure, the heat transfer 1 Q 2 and the work done 1 W 2 for the control mass. Assume an ideal gas with constant speci±c heats (Table A.5). Initial con±guration Solution The initial volume is found from the Ideal Gas Equation V 1 = mRT 1 p 1 = (1)(287)(1200) 1 . 5 · 10 6 = 0 . 2296 m 3 Assume that the piston doesn’t hit the stops. Then, p 2 = p
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Unformatted text preview: 1 = 1500 kPa and V 2 = mRT 2 p 2 = (1)(287)(500) 1 . 5 Â· 10 6 = 0 . 09567 m 3 650:351 Thermodynamics Page 1 Quiz No. 4 Thus, the piston must hit the stops. During the cooling, the pressure inside the cylinder equals p 1 = 1500 kPa. Thus, 1 W 2 = i 2 1 pdV = p 1 i 2 1 dV = p 1 ( V 2-V 1 ) = 1 . 5 Â· 10 6 (0 . 15-. 2296) =-1 . 194 Â· 10 5 J The fnal pressure is obtained From the Ideal Gas Law p 2 = mRT 2 V 2 = (1)(287)(500) . 15 = 9 . 5667 Â· 10 5 Pa The heat added is obtained From the Â±irst Law oF Thermodynamics 1 Q 2 = 1 W 2 + U 2-U 1 since Î”KE = Î”PE = 0. Using c v = 0 . 717 kJ/kg-K, U 2-U 1 = mc v ( T 2-T 1 ) = (1)(717 . )(500-1200) =-5 . 019 Â· 10 5 J Thus, 1 Q 2 =-1 . 194 Â· 10 5-5 . 019 Â· 10 5 =-6 . 213 Â· 10 5 J 650:351 Thermodynamics Page 2...
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## This note was uploaded on 04/04/2008 for the course 650 351 taught by Professor Doylenight during the Spring '08 term at Rutgers.

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Quiz-solution4 - 1 = 1500 kPa and V 2 = mRT 2 p 2 =(1(287(500 1 5 Â 10 6 = 0 09567 m 3 650:351 Thermodynamics Page 1 Quiz No 4 Thus the piston must

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