
Concept explainers
a)
The volumetric flow rate and mass flow rate of the mixture treating it as an ideal gas mixture.
a)

Answer to Problem 42P
The volume flow rate is
The mass flow rate is
Explanation of Solution
Write the expression to obtain the mass of
Here, number of moles of
Write the expression to obtain the mass of
Here, number of moles of
Write the expression to obtain the mass of
Here, number of moles of
Write the expression to obtain the mass of
Here, number of moles of
Write the expression to obtain the total mass of each component
Write the expression to obtain the total number of moles
Write the expression to obtain the molar mass of the mixture
Write the expression to obtain the gas constant of the mixture
Here, universal gas constant is
Write the expression to obtain the specific volume of the mixture
Here, temperature and pressure is
Write the expression to obtain the volume flow rate
Here, velocity is V, area is A, and diameter is D.
Write the expression to obtain the mass flow rate
Conclusion:
Refer Table A-1, “Molar mass, gas constant, and critical point properties”, obtain the molar masses of
Substitute 30 kmol for
Substitute 40 kmol for
Substitute 10 kmol for
Substitute 20 kmol for
Substitute 960 kg for
Substitute
Substitute 2,840 kg for
Substitute
Substitute
Substitute
Thus, the volume flow rate is
Substitute
Thus, the mass flow rate is
b)
The volumetric flow rate and mass flow rate using a compressibility factor based on Amagad’s law of additive volume.
b)

Answer to Problem 42P
The volume flow rate is
The mass flow rate is
Explanation of Solution
Write the expression to obtain the reduced temperature of
Here, critical temperature of
Write the expression to obtain the reduced pressure of
Here, critical temperature of
Write the expression to obtain the reduced temperature of
Here, critical temperature of
Write the expression to obtain the reduced pressure of
Here, critical temperature of
Write the expression to obtain the reduced temperature of
Here, critical temperature of
Write the expression to obtain the reduced pressure of
Here, critical temperature of
Write the expression to obtain the reduced temperature of
Here, critical temperature of
Write the expression to obtain the reduced pressure of
Here, critical temperature of
Write the expression to obtain the compressibility factor of a mixture
Here, compressibility factor of
Write the expression to obtain the specific volume of the mixture
Write the expression to obtain the volume flow rate
Here, velocity is V, area is A, and diameter is D.
Write the expression to obtain the mass flow rate
Conclusion:
Substitute 288 K for
Substitute 8 MPa for
Refer Table A-15, “Nelson-Olbert generalized compressibility chart”, obtain compressibility factor, Z for
Substitute 288 K for
Substitute 8 MPa for
Refer Table A-15, “Nelson-Olbert generalized compressibility chart”, obtain compressibility factor, Z for
Substitute 288 K for
Substitute 8 MPa for
Refer Table A-15, “Nelson-Olbert generalized compressibility chart”, obtain compressibility factor, Z for
Substitute 288 K for
Substitute 8 MPa for
Refer Table A-15, “Nelson-Olbert generalized compressibility chart”, obtain compressibility factor, Z for
Substitute 0.30 for
Substitute 0.8709 for
Substitute
Thus, the volume flow rate is
Substitute
Thus, the mass flow rate is
c)
The volumetric flow rate and mass flow rate using Key’s pseudocritical pressure and temperature.
c)

Answer to Problem 42P
The volume flow rate is
The mass flow rate is
Explanation of Solution
Write the expression to obtain the pseudo-critical temperature of the mixture
Here, critical temperature of
Write the expression to obtain the pseudo-critical pressure of the mixture
Here, critical pressure of
Write the expression to obtain the reduced temperature
Write the expression to obtain the reduced pressure
Write the expression to obtain the specific volume of the mixture
Write the expression to obtain the volume flow rate
Write the expression to obtain the mass flow rate
Conclusion:
Substitute 0.30 for
Substitute 0.30 for
Substitute 288 K for
Substitute 8 MPa for
Refer Table A-15, “Nelson-Olbert generalized compressibility chart”, obtain compressibility factor,
Substitute 0.92 for
Substitute
Thus, the volume flow rate is
Substitute
Thus, the mass flow rate is
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Chapter 13 Solutions
Thermodynamics: An Engineering Approach
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