Concept explainers
Determine the specific volume of superheated water vapor at 15 MPa and 350°C using (a) the ideal-gas equation, (b) the generalized compressibility chart, and (c) the steam tables. Also determine the error involved in the first two cases.
(a)
The specific volume of superheated water vapour based on the ideal gas equation.
The error involved.
Answer to Problem 84P
The specific volume of superheated water vapour based on the ideal gas equation is
The error involved is
Explanation of Solution
Write the equation of specific volume of superheated water using ideal gas equation of state.
Here, gas constant is R, pressure and temperature of R-134a are P and T respectively.
Calculate the percentage of error involved.
Here, specific volume at pressure and temperature of 15 MPa and
Conclusion:
Refer to Table A-1, obtain the gas constant, R of water as
Substitute
Thus, the specific volume of superheated water vapour based on the ideal gas equation is
Refer to Table A-6, obtain the value of
Substitute
Thus, the error involved is
(b)
The specific volume of superheated water vapour based on the generalized compressibility chart.
The error involved.
Answer to Problem 84P
The specific volume of superheated water vapour based on the generalized compressibility chart is
The error involved is
Explanation of Solution
Calculate the reduced pressure.
Here, pressure of superheated water vapour is P and critical pressure is
Calculate the reduced temperature.
Here, temperature of superheated water vapor is T and critical temperature is
Calculate the specific volume of superheated water vapour based on the generalized compressibility chart.
Here, the specific volume at ideal condition is
Conclusion:
Refer to Table A-1, obtain the critical pressure and critical temperature of water.
Substitute 22.06 MPa for
Substitute 647.1 K for
Refer to figure A-15, “The compressibility chart”, obtain the compressibility factor, Z by reading the calculated reduced pressure and reduced temperature as 0.65.
Substitute 0.65 for Z and
Thus, the specific volume of superheated water vapour based on the generalized compressibility chart is
Substitute
Thus, the error involved is
(c)
The specific volume of superheated water vapour based on the data from tables.
Answer to Problem 84P
The specific volume of superheated water vapour based on the data from table is
Explanation of Solution
Refer to Table A-6, obtain the specific volume at pressure and temperature of 15 MPa and
Thus, the specific volume of superheated water vapour based on data from steam tables is
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