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Assignment__4

# 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.
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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