Concept explainers
(a)
The volume flow rate of the mixture using the ideal gas mixture.
The mass flow rate of the mixture using the ideal gas mixture.
(a)
Answer to Problem 45P
The volume flow rate of the mixture using the ideal gas mixture is
The mass flow rate of the mixture using the ideal gas mixture is
Explanation of Solution
Refer to Table A-1E, Obtain the molar masses of
Consider 100 lbmol of the mixture. Since the volume fractions are equal to the mole fractions, calculate the mass of each component.
Here, the mole numbers of
Write the equation of total mass of the mixture.
Here, the mass of
Write the equation to calculate the apparent molecular weight of the mixture.
Write the equation to calculate the apparent gas constant of the mixture.
Here, the universal gas constant is
Write the equation of specific volume of the mixture.
Here, temperature of the mixture is T and atmospheric pressure is P.
Calculate the volume flow rate of the mixture.
Here, cross-sectional area of the pipe is A.
Calculate the mass flow rate of the mixture.
Conclusion:
Apply spreadsheet and substitute the given values of mole numbers and molar masses of
S.No | masses | Mole number (N), lbmol | Molar masses (M), lbm/lbmol | |
1 | 30 | 32 | 960 | |
2 | 40 | 28 | 1120 | |
3 | 10 | 44 | 440 | |
4 | 20 | 16 | 320 |
Substitute 960 lbm for
Substitute 2840 lbm for
Substitute
Substitute
Substitute
Thus, the volume flow rate of the mixture using the ideal gas mixture is
Substitute
Thus, the mass flow rate of the mixture using the ideal gas mixture is
(b)
The volume flow rate of the mixture using the compressibility factor based on Amagat’s law of additive volumes.
The mass flow rate of the mixture using the compressibility factor based on Amagat’s law of additive volumes.
(b)
Answer to Problem 45P
The volume flow rate of the mixture using the compressibility factor based on Amagat’s law of additive volumes is
The mass flow rate of the mixture using the compressibility factor based on Amagat’s law of additive volumes is
Explanation of Solution
Write the equation of reduced temperatures and pressures of
Here, the critical temperature of
Write the equation of compressibility factor of the mixture.
Here, the mole fraction of
Calculate the specific volume of the mixture.
Calculate the mass flow rate of the mixture using the compressibility factor based on Amagat’s law of additive volumes.
Here, the volume flow rate of mixture using the compressibility factor based on Amagat’s law of additive volumes is
Conclusion:
Refer to Table A-1E, obtain the critical temperatures and pressures of
Substitute 530 R for
Refer to Figure A-15, obtain the compressibility factor for
Substitute 0.30 for
Substitute 1500 psia for P, 0.869 for
Refer to part (a), the value calculated for volume flow rate is
Substitute
Thus, the mass flow rate of the mixture using the compressibility factor based on Amagat’s law of additive volumes is
(c)
The volume flow rate of the mixture using Kay’s pseudocritical pressure and temperature.
The mass flow rate of the mixture using Kay’s pseudocritical pressure and temperature.
(c)
Answer to Problem 45P
The volume flow rate of the mixture using Kay’s pseudocritical pressure and temperature is
The mass flow rate of the mixture using Kay’s pseudocritical pressure and temperature.
is
Explanation of Solution
Write the critical temperature of a gas mixture.
Write the critical pressure of a gas mixture.
Write the equation of reduced temperature and pressure.
Conclusion:
Substitute 0.30 for
Substitute 0.30 for
Substitute 530 R for
Refer to Figure A-15, obtain the compressibility factor for gas mixture by reading the values of
Substitute 1500 psia for P, 0.915 for
Refer to part (a), the value calculated for volume flow rate is
Substitute
Thus, the mass flow rate of the mixture using the compressibility factor based on Amagat’s law of additive volumes is
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Chapter 13 Solutions
Thermodynamics: An Engineering Approach
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