Concept explainers
Carbon dioxide gas enters a pipe at 3 MPa and 500 K at a rate of 2 kg/s. CO2 is cooled at constant pressure as it flows in the pipe, and the temperature of the CO2 drops to 450 K at the exit. Determine the volume flow rate and the density of carbon dioxide at the inlet and the volume flow rate at the exit of the pipe using (a) the ideal-gas equation and (b) the generalized compressibility chart. Also, determine (c) the error involved in the first case.
FIGURE P3–89
(a)
The volume flow rate, density of carbon dioxide at the inlet, and the volume flow rate at the exit of the pipe using the ideal gas equation of state.
Answer to Problem 91P
The volume flow rate, density of carbon dioxide at the inlet, and the volume flow rate at the exit of the pipe using the ideal gas equation of state are
Explanation of Solution
Refer to Table A-1, obtain the gas constant, critical pressure, and the critical temperature of carbon dioxide.
Write the equation of volume flow rate at the inlet of the pipe.
Here, inlet temperature and inlet pressure are
Calculate the density at the inlet of pipe.
Calculate the equation of volume flow rate at the outlet of the pipe.
Here, outlet temperature and outlet pressure are
Conclusion:
Substitute
Substitute
Substitute
Thus, the volume flow rate, density of carbon dioxide at the inlet, and the volume flow rate at the exit of the pipe using the ideal gas equation of state are
(b)
The volume flow rate, density of carbon dioxide at the inlet, and the volume flow rate at the exit of the pipe using the generalized compressibility chart.
Answer to Problem 91P
The volume flow rate, density of carbon dioxide at the inlet, and the volume flow rate at the exit of the pipe using the generalized compressibility chart are
Explanation of Solution
Calculate the equation of reduced pressure at the inlet of the pipe.
Here, the critical pressure is
Calculate the equation of reduced temperature at the inlet of the pipe.
Here, the critical temperature is
Calculate the equation of reduced pressure at the outlet of the pipe.
Calculate the equation of reduced temperature at the outlet of the pipe.
Write the equation of volume flow rate at the inlet of the pipe.
Here, compressibility factor at the inlet of pipe is
Calculate the density at the inlet of pipe.
Calculate the equation of volume flow rate at the outlet of the pipe.
Here, compressibility factor at the outlet of pipe is
Conclusion:
Substitute 3 MPa for
Substitute 500 K for
Substitute 3 MPa for
Substitute 450 K for
Refer to Figure 3-48, obtain the compressibility factor at inlet state
Refer to Figure 3-48, obtain the compressibility factor at outlet state
Substitute 0.9791 for
Substitute 0.9791 for
Substitute 0.9656 for
Thus, the volume flow rate, density of carbon dioxide at the inlet, and the volume flow rate at the exit of the pipe using the generalized compressibility chart are
(c)
The error involved in the first case.
Answer to Problem 91P
The error involved in the first case are
Explanation of Solution
Calculate the percentage of error involved in the first case of volume flow rate at the inlet condition.
Here, calculated volume flow rate at inlet state from EOS is
Calculate the percentage of error involved in the first case of density at the inlet condition.
Here, calculated density at inlet state from EOS is
Calculate the percentage of error involved in the first case of volume flow rate at the outlet condition.
Here, calculated volume flow rate at outlet state from EOS is
Conclusion:
Substitute
Substitute
Substitute
Thus, the error involved in the first case are
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Chapter 3 Solutions
Thermodynamics: An Engineering Approach
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