Concept explainers
A mass of 3 kg of saturated liquid–vapor mixture of water is contained in a piston–cylinder device at 160 kPa. Initially, 1 kg of the water is in the liquid phase and the rest is in the vapor phase. Heat is now transferred to the water, and the piston, which is resting on a set of stops, starts moving when the pressure inside reaches 500 kPa. Heat transfer continues until the total volume increases by 20 percent. Determine (a) the initial and final temperatures, (b) the mass of liquid water when the piston first starts moving, and (c) the work done during this process. Also, show the process on a P-v diagram.
FIGURE P4–120
(a)
The initial temperature of the piston cylinder device.
The final temperature of the piston cylinder device.
Answer to Problem 120RP
The initial temperature of the piston cylinder device is
The final temperature of the piston cylinder device is
Explanation of Solution
Determine the total initial volume of piston cylinder device.
Here, the mass of the liquid phase is
Determine the total volume of the piston cylinder device at final state.
Determine the specific volume of the piston cylinder device at final state.
Here, the mass of the saturated liquid vapour mixture of water is contained in a piston cylinder device is
Conclusion:
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y is saturated pressure and saturated temperature.
For initial temperature of the piston cylinder device.
Show the temperature at pressure of 150 kPa, 160 kPa, and 175 kPa as in Table (1).
Pressure, kPa |
Temperature, C |
150 kPa | 111.35 |
160 kPa | |
175 kPa | 116.04 |
Substitute the value of x and y from Table (1) in Equation (IV) to calculate the value of initial temperature
Thus, the initial temperature of the piston cylinder device is
For specific volume of saturated liquid of the piston cylinder device.
Show the specific volume of saturated liquid at pressure of 150 kPa, 160 kPa, and 175 kPa as in Table (2).
Pressure, kPa |
Specific volume of saturated liquid, |
150 kPa | 0.001053 |
160 kPa | |
175 kPa | 0.001057 |
Substitute the value of x and y from Table (2) in Equation (IV) to calculate the value of specific volume of saturated liquid
For specific volume of saturated vapour of the piston cylinder device.
Show the specific volume of saturated vapour at pressure of 150 kPa, 160 kPa, and 175 kPa as in Table (3).
Pressure, kPa |
Specific volume of saturated vapour, |
150 kPa | 1.1594 |
160 kPa | |
175 kPa | 1.0037 |
Substitute the value of x and y from Table (3) in Equation (IV) to calculate the value of specific volume of saturated vapour
Substitute
Substitute
Substitute
The unit conversion of pressure from kPa to MPa.
For temperature of the piston cylinder device at final state.
Show the temperature at specific volume of the piston cylinder device at final state at
specific volume of the piston cylinder device at final state, |
Temperature, |
600 | |
700 |
Substitute the value of x and y from Table (4) in Equation (IV) to calculate the value of temperature of the piston cylinder device at final state
Thus, the final temperature of the piston cylinder device is
(b)
The mass of liquid water when the piston first starts moving.
Answer to Problem 120RP
The mass of liquid water when the piston first starts moving is
Explanation of Solution
Determine the specific volume of the piston cylinder device at this state.
Here, the mass of the saturated liquid vapour mixture of water is contained in a piston cylinder device is
Conclusion:
Since,
Substitute
Therefore, the value of specific volume of the piston cylinder device at this state is greater than
Thus, the mass of liquid water when the piston first starts moving is
(c)
The work done during the process state 2 and 3.
Answer to Problem 120RP
The work done during the process state 2 and 3 is
Explanation of Solution
Determine the work done in constant pressure process.
Conclusion:
Substitute
Thus, the work done during the process state 2 and 3 is
Show the P-v diagram of this process.
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Chapter 4 Solutions
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