quiz-solution3

quiz-solution3 - the pressure inside the cylinder remains...

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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. 3 A piston/cylinder initially contains helium at an ini- tial pressure p 1 = 200 kPa and initial temperature T 1 = 400 C. The piston area is 1 m 2 . The weight of the piston is constant and the pressure above the piston (i.e., the ambient pressure) remains con- stant. Note the conFguration of the piston-cylinder in the Fgure and the stops that prevent the piston from moving downwards more than 1 m. The cylin- der is cooled to T 2 = 100 C. Assume an ideal gas. What is the work done by the helium ? Initial conFguration Solution Since the piston weight is constant and the pressure above the piston remains constant, therefore
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Unformatted text preview: the pressure inside the cylinder remains the same provided that the piston doesn’t touch the stops . Let’s make the simplest assumption and then determine if it is correct. 650:351 Thermodynamics Page 1 Quiz No. 3 Assume that the piston does not touch the stops. Then trom the ideal gas equation, pV = mRT Since the mass m does not change, p 1 V 1 RT 1 = p 2 V 2 RT 2 Since we assumed that the piston does not touch the stops, p 2 = p 1 and thus V 2 V 1 = T 2 T 1 = (100 + 273 . 15) (400 + 273 . 15) = 0 . 5543 Thus, the piston is not resting on the stops and our assumption is correct, The work one is 1 W 2 = i pdV = p 1 i dV = p 1 ( V 2 − V 1 ) = p 200 · 10 3 P (0 . 5543 − 1)(2) = − 178 . 3 kJ where V 1 = (1)(1 + 1) = 2 m 3 . 650:351 Thermodynamics Page 2...
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  • Spring '08
  • DoyleNight
  • Knight Department of Mechanical and Aerospace Engineering Rutgers, State University of New Jersey New Brunswick

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quiz-solution3 - the pressure inside the cylinder remains...

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