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2kg of water at 1 MPa and 420 degree C is cooled within piston cylinder in a con

ID: 1842713 • Letter: 2

Question

2kg of water at 1 MPa and 420 degree C is cooled within piston cylinder in a constant pressure process until it hits a set of stops. This set of stops prevents the water from being compressed to a volume below 0.2 m^3. Once the piston head hits the stops, the water continuous to be cooled to a final temperature of 170 degree C. Determine the following: a. The specific volume of the water at the initial state in [m^3/kg] The specific volume of the water when the piston head initially hits the stops in [m^3/kg] c. What is the quality of the water when the piston head initially hits the stops? If quality is not defined (i.e. is not applicable for this phase), please explain What is the final pressure of the water once the water is cooled to 170 degree C? d. Draw a T-v diagram showing the process from the initial state (the state described by part a) to the state at C which the piston heat initially hits the stops (the state described by parts 'b'). You will need to make sure that the following is included in this diagram for full credit. i. indicate location of state 1 (with its corresponding I_1, v_1 labeled on the axis) in relation to the vapor dome ii. Indicate location of state 2 (with its corresponding T_2, v_2 labeled on the axis) in relation to the vapor dome iii. A line drawn between the two along which the process occurs (i.e. indicate the process path)

Explanation / Answer

A. From steam table at 1 MPA and 420 Celsius, specific volume = 0.316 m3/kg

B. Specific volume when piston hits stop is volume/mass = 0.2/2= 0.1

C. At v= 0.1 m3/kg and pressure 1 MPA, by interpointerpolation usin steam table, we get x = dryness fraction= 0.5117

D. Now at 170 Celsius and 0.1 specific volume, pressure is 0.792 MPA and dryness fraction is 0.41.

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