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Thermo solution3 - Copy

# Thermo solution3 - Copy - 650:351 Thermodynamics Doyle...

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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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Homework Assignment No. 3 Problem 4.21 An escalator raises a 100 kg bucket of sand 10 m in 1 minute. Determine the total amount of work done during the process. Solution The work is 1 W 2 = i 2 1 F dx The force is the weight of the bucket. Thus, F = (100)(9 . 8) = 980 N Thus, 1 W 2 = (980)(10) = 9 . 8 kJ 650:351 Thermodynamics Page 1
Homework Assignment No. 3 Problem 4.33 A 400 L tank A contains argon gas at 250 kPa and 30 C. Cylinder B , having a frictionless piston of such mass that a pressure of 150 kPa will Foat it, is initially empty. The valve is opened and argon Fows into B and eventually reaches a uniform state of 150 kPa and 30 C throughout. What is the work done by the argon ? Solution The work done by the argon is 1 W 2 i 2 1 pdV The argon does no work on tank A as the gas es- capes because the volume of tank A remains con- stant. The argon does work on the piston is tank B because it raises the piston ( i.e. , changes the volume in tank B ). In this process, the pressure in tank B remains constant by balance of forces on the piston. Thus, 1 W 2 = (150)(10 3 )( V 2 V 1 ) where V 2 is the ±nal volume of tank B and V 1 = 0. 650:351 Thermodynamics Page 2

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Homework Assignment No. 3 Problem 4.33 The mass of the argon is m = pV RT = (250)(10 3 )(400)(0 . 001) (208 . 13)(303 . 15) = 1 . 5849 kg where R = 208 . 13 J/kg · K is the gas constant for argon. The Fnal volume of argon in tanks A and B com- bined is V = mRT p = (1 . 5849)(208 . 13)(303 . 15) (150)(10 3 ) = 0 . 6667 m 3 Thus, the volume of tank B is V 2 = 0 . 6667 (400)(0 . 001) = 0 . 26667 m 3 Thus, 1 W 2 = (150)(10 3 )(0 . 26667) = 40 kJ 650:351 Thermodynamics Page 3
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Thermo solution3 - Copy - 650:351 Thermodynamics Doyle...

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