A piston–cylinder device initially contains 0.35 kg of steam at 3.5 MPa, superheated by 7.4°C. Now the steam loses heat to the surroundings and the piston moves down, hitting a set of stops at which point the cylinder contains saturated liquid water. The cooling continues until the cylinder contains water at 200°C. Determine (a) the final pressure and the quality (if mixture), (b) the boundary work, (c) the amount of heat transfer when the piston first hits the stops, and (d) the total heat transfer.
FIGURE P4–141
(a)
The final pressure of the piston-cylinder device.
The quality at the final state of the piston-cylinder device.
Answer to Problem 139RP
The final pressure of the piston-cylinder device is
The quality at the final state of the piston-cylinder device is
Explanation of Solution
Write the expression for the energy balance equation.
Here, the total energy entering the system is
Simplify Equation (I) and write energy balance relation of piston-cylinder device.
Here, the work to be done into the system is
Simplify the Equation (III), write energy balance relation when the piston first hits the stops state(1-2).
Here, the mass of the piston-cylinder device is
Similarly the Equation (IV), when the piston first hits and the final state(1-3).
Here, the mass of the piston-cylinder device is
Determine the state 1 temperature of the piston-cylinder device.
Here, the saturated temperature at 3500 kPa is
Conclusion:
Write the unit conversion pressure from MPa to kPa for piston-cylinder device.
From the Table A-5 “Saturated water-Pressure table”, obtain the value of saturated temperature at 3500 kPa pressure as
Substitute
From the Table A-4 through A-6 “Saturated water”, obtain the value of steam at various states for piston-cylinder device.
At state 1 pressure and temperature of steam as
At state 1-2 pressure and quality of state of steam as
At state 2-3 specific volume and temperature of steam as
Thus, the final pressure of the piston-cylinder device is
(b)
The boundary work done of the piston-cylinder device.
Answer to Problem 139RP
The boundary work done of the piston-cylinder device is
Explanation of Solution
Substitute 0 for
Here, the mass of piston-cylinder device is
Conclusion:
Substitute
Thus, the boundary work done of the piston-cylinder device is
(c)
The amount of heat transfer when the piston first hits the stops.
Answer to Problem 139RP
The amount of heat transfer when the piston first hits the stops is
Explanation of Solution
Conclusion:
Substitute
Thus, the amount of heat transfer when the piston first hits the stops is
(d)
The total amount heat transfer in the piston-cylinder device.
Answer to Problem 139RP
The total amount heat transfer in the piston-cylinder device is
Explanation of Solution
Conclusion:
Substitute
Thus, the total amount heat transfer in the piston-cylinder device is
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Chapter 4 Solutions
Thermodynamics: An Engineering Approach
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