Concept explainers
The spring-loaded piston–cylinder device shown in Fig. P3–63 is filled with 0.5 kg of water vapor that is initially at 4 MPa and 400°C. Initially, the spring exerts no force against the piston. The spring constant in the spring force relation F = kx is k = 0.9 kN/cm and the piston diameter is D = 20 cm. The water now undergoes a process until its volume is one-half of the original volume. Calculate the final temperature and the specific enthalpy of the water.
FIGURE P3–63
The final temperature of the spring-loaded piston-cylinder device.
The enthalpy of the spring-loaded piston-cylinder device.
Answer to Problem 63P
The final temperature of the spring-loaded piston-cylinder device is
The enthalpy of the spring-loaded piston-cylinder device is
Explanation of Solution
Write the final temperature of the spring-loaded piston-cylinder device using linear
Here, the spring constant is
Determine the final specific volume of the spring-loaded piston-cylinder device.
Determine the quality of final state for the spring-loaded piston-cylinder device.
Here, the specific volume of saturated liquid is
Determine the enthalpy at the final state of the spring-loaded piston-cylinder device.
Here, the specific enthalpy of saturated liquid is
Conclusion:
From the Table A-6, “Superheated water” to obtain the value of the specific volume of steam at 4 MPa of pressure and
Substitute
Substitute
Refer to Table A-6, “Saturated water”, obtain the below properties at the final pressure
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y are pressure and temperature.
Show the pressure at
S. No |
Pressure, kPa |
Temperature, |
1 | 218.41 | |
2 | ||
3 | 223.95 |
Calculate final temperature at the pressure
Substitute
From above calculation the final temperature at the pressure
Thus, the final temperature of the spring-loaded piston-cylinder device is
Repeat the above Equation (V), to obtain the value of specific volume of saturated liquid, the specific volume of saturated vapour, specific enthalpy of saturated liquid and the specific enthalpy of saturated vapour at the final pressure
Substitute
Substitute
Thus, the enthalpy of the spring-loaded piston-cylinder device is
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Chapter 3 Solutions
Thermodynamics: An Engineering Approach
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