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Assignment__4 - Assignment#4 PROBLEM 4.1 PROBLEM STATEMENT...

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Assignment #4 9/20/04 PROBLEM 4.1 PROBLEM STATEMENT: Water (2 kg) is contained in the vertical frictionless piston/ cylinder device shown below. The mass of the piston is such that the H 2 O exists as a saturated liquid at 10.0 MPa. There is a heat transfer to the cylinder until the piston reaches some stops, at which point the total volume is 0.02 m 3 . There is an additional heat is transfer to the water until the H 2 O exists as a saturated vapor. Determine the total work and the total heat transfer, and show the process on a T-v diagram. DIAGRAM DEFINING SYSTEM AND PROCESS: Q IN,1-3 GIVEN: Water, m=2 kg, frictionless piston State 1: Saturated liquid (x 1 = 0), P 1 =10.0 MPa State 2: V 2 =0.02 m 3 , P 2 =P 1 =10.0 MPa State 3: Saturated vapor (x 3 = 1), V 3 =V 2 =0.02 m 3 FIND: Total work and total heat transfer (kJ) ASSUMPTIONS: 1. The water in the container is a closed system. 2. States 1, 2, & 3 are equilibrium states. 3. No net change in kinetic or potential energy. GOVERNING RELATIONS: First Law, QUANTITATIVE SOLUTION: Once the piston reaches the stops, there is no change in volume, so From Table 11s, v 1 = v L (10 MPa) = 0.001452 m 3 /kg and u 1 =1392.8 kJ/kg. Thus,
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Since state 3 is a saturated vapor, u 3 =u V , which from Table 11s, corresponds to v 3 =v V =0.01 m 3 /kg. This value falls between 15 MPa and 16 MPa on Table 11s. By interpolation we find the value of u 3 where v 3 =v V =0.01 m 3 /kg. Hence, the total heat transfer is P-v Diagram 0.01 m 3 /kg v T 1 3 2 P 3 P 1 = P 2 =10.0 MPa DISCUSSION OF RESULTS: In applying the energy balance principle (First Law), it is good practice to show Q and W terms and thin eliminate terms for a given process as appropriate. In this case, for example, because the voume stays constant. By explicitly showing this in the equation, it is clear that this has been accounted for.
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PROBLEM 4.4 PROBLEM STATEMENT: Water (3 kg) in the frictionless piston-cylinder device shown is initially at a pressure of 1 MPa and a quality of 75%. There is a heat transfer until the temperature is 500°C. It takes a pressure of 2 MPa to lift the piston. What is the total heat transferred in the process? DIAGRAM DEFINING SYSTEM AND PROCESS: T 2 MPa P 2 = P 3 =2 MPa 3 W OUT,2-3 2 P 1 =1 MPa 1 Q IN,1-3 v 0.1461 m 3 /kg GIVEN: Water, mass=3 kg Pressure due to frictionless piston=2 MPa State 1: P 1 =1 MPa, x=75% State 2: P 2 =2 MPa State 3: T 3 =500°C, P 3 =P 2 =2 MPa FIND: Total heat transferred (kJ) ASSUMPTIONS: 1. The water in the container is a closed system.
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