Sphw3 - HOMEWORK SET 3 4.35 A piston cylinder contains 1 kg of liquid water at 20oC and 300 kPa There is a linear spring mounted on the piston such

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HOMEWORK SET 3 4.35 A piston cylinder contains 1 kg of liquid water at 20 o C and 300 kPa. There is a linear spring mounted on the piston such that when the water is heated the pressure reaches 3 MPa with a volume of 0.1 m 3 . a) Find the final temperature b) Plot the process in a P-v diagram. c) Find the work in the process. Solution: Take CV as the water. This is a constant mass: m 2 = m 1 = m ; State 1: Compressed liquid, take saturated liquid at same temperature. B.1.1: v 1 = v f (20) = 0.001002 m 3 /kg, State 2: v 2 = V 2 /m = 0.1/1 = 0.1 m 3 /kg and P = 3000 kPa from B.1.3 => Superheated vapor close to T = 400 o C Interpolate: T 2 = 404 o C Work is done while piston moves at linearly varying pressure, so we get: 1 W 2 = P dV = area = P avg (V 2 V 1 ) = 1 2 (P 1 + P 2 )(V 2 - V 1 ) = 0.5 (300 + 3000)(0.1 0.001) = 163.35 kJ T C.P. v 2 1 300 kPa P C.P. v T 300 20 2 1 4.47 Consider a piston cylinder with 0.5 kg of R-134a as saturated vapor at -10 ° C. It is now compressed to a pressure of 500 kPa in a polytropic process with n = 1.5. Find the final volume and temperature, and determine the work done during the process. Solution: Take CV as the R-134a which is a control mass. m 2 = m 1 = m
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Process: Pv 1.5 = constant until P = 500 kPa 1: (T, x) v 1 = 0.09921 m 3 /kg, P = P sat = 201.7 kPa from Table B.5.1 2: (P, process) v 2 = v 1 (P 1 /P 2 ) (1 /1.5) = 0.09921 × (201.7/500) 2/3 = 0.05416 Given (P, v) at state 2 from B.5.2 it is superheated vapor at T 2 = 79 ° C Process gives P = C v -1.5 , which is integrated for the work term, Eq.(4.4) 1 W 2 = P dV = m 1 - 1.5 (P 2 v 2 - P 1 v 1 ) = 2 - 0.5 × (500 × 0.05416 - 201.7 × 0.09921) = -7.07 kJ 4.56 The refrigerant R-22 is contained in a piston/cylinder as shown in Fig. P4.56, where the volume is 11 L when the piston hits the stops. The initial state is 30 ° C, 150 kPa with a volume of 10 L. This system is brought indoors and warms up to 15 ° C. a. Is the piston at the stops in the final state? b . Find the work done by the R-22 during this process. Solution:
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This homework help was uploaded on 04/10/2008 for the course ME 235 taught by Professor Borgnakke during the Spring '07 term at University of Michigan.

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Sphw3 - HOMEWORK SET 3 4.35 A piston cylinder contains 1 kg of liquid water at 20oC and 300 kPa There is a linear spring mounted on the piston such

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