Explanation Write the expression to obtain the mole number of CH 4 ( N CH 4 ) . N CH 4 = m CH 4 M CH 4 (I) Here, molar mass of CH 4 is M CH 4 and mass of CH 4 is m CH 4 . Write the expression to obtain the mole number of C 3 H 8 ( N C 3 H 8 ) . N C 3 H 8 = m C 3 H 8 M C 3 H 8 (II) Here, molar mass of C 3 H 8 is M C 3 H 8 and mass of C 3 H 8 is m C 3 H 8 . Write the expression to obtain the mole number of C 4 H 10 ( N C 4 H 10 ) . N C 4 H 10 = m C 4 H 10 M C 4 H 10 (III) Here, molar mass of C 4 H 10 is M C 4 H 10 and mass of C 4 H 10 is m C 4 H 10 . Write the expression to obtain the total number of moles ( N m ) . N m = N CH 4 + N C 3 H 8 + N C 4 H 10 (IV) Write the expression to obtain the apparent molecular weight of the mixture ( M m ) . M m = m m N m (V) Write the expression to obtain the apparent gas constant of the mixture ( R ) . R = R u M m (VI) Here, universal gas constant is R u . Write the expression to calculate the work input during isothermal compression process ( w in ) . w i n = R T ln ( P 2 P 1 ) (VII) Here, temperature is T , gas constant is R and pressure is P . Write the expression of energy balance equation for closed system. E ˙ i n − E ˙ o u t = Δ E ˙ s y s t e m (VIII) Here, rate of energy transfer into the control volume is E ˙ i n , rate of energy transfer exit from the control volume is E ˙ o u t and rate of change in internal energy of system is Δ E ˙ s y s t e m Conclusion: Refer Table A-1, “Molar mass, gas constant, and critical point properties”, obtain the molar masses of CH 4 , C 3 H 8 and C 4 H 10 as 16.0 kg / kmol , 44.0 kg / kmol and 58.0 kg / kmol . Substitute 60 kg for m CH 4 and 16.0 kg / kmol for M CH 4 in Equation (I). N CH 4 = 60 kg 16.0 kg / kmol = 3.75 kmol Substitute 25 kg for m C 3 H 8 and 44.0 kg / kmol for M C 3 H 8 in Equation (II). N C 3 H 8 = 25 kg 44.0 kg / kmol = 0.5682 kmol Substitute 15 kg for m C 4 H 10 and 58.0 kg / kmol for M C 4 H 10 in Equation (III)

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ISBN: 9780073398174

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 13.3, Problem 59P

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Thermodynamics: An Engineering Approach

Ch. 13.3 - Consider a mixture of several gases of identical...Ch. 13.3 - Somebody claims that the mass and mole fractions...Ch. 13.3 - The sum of the mole fractions for an ideal-gas...Ch. 13.3 - Consider a mixture of two gases. Can the apparent...Ch. 13.3 - What is the apparent molar mass for a gas mixture?...Ch. 13.3 - Prob. 6P Ch. 13.3 - Consider a mixture of two gases A and B. Show that...Ch. 13.3 - The composition of moist air is given on a molar...Ch. 13.3 - Prob. 9P Ch. 13.3 - Prob. 10P

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