Unformatted text preview: it if the vapor feed rate, the outlet temperature of the partial condensate, and the
cooling water outlet temperature were specified. Exercise 4.3
Subject: Degrees of freedom analysis for an adiabatic, two-phase flash.
Given: Continuous, adiabatic flash of one feed into vapor and liquid products
Assumptions: Exiting streams are in equilibrium
Analysis: Number of variables.
All equations relating variables.
Number of equations.
Number of degrees of freedom
(a) Variables are those appearing in Figure 4.36
N V = 3C + 9
(b) C Component material balances
1 Energy balance
1 Pressure identity for two exiting streams
1 Temperature identity for two exiting streams
3 Mole fraction sums for three streams
C Vapor-liquid equilibrium equations
(c) NE = 2C + 6
(d) ND = NV - NE = (3C + 9) - (2C + 6) = C + 3
(e) Specify the feed completely ( feed rate, temperature, pressure and C - 1 mole
fractions) plus exiting pressure. Exercise 4.4
Subject: Degrees of freedom analysis for a non-adiabatic three-phase flash.
Given: Continuous, non-adiabatic flash of a liquid feed to produce a vapor and two liquid
phases as shown in Figure 4.33.
Assumptions: The three exiting phases are in equilibrium.
Find: Number of degrees of freedom.
Analysis: The variables are the heat transfer rate and four each of stream flow rates,
temperatures, pressures, and C mole fractions. Thus, NV = 4C + 13.
The equations are:
C Component material balances
1 Energy balance
2 Pressure identities for three exiting streams
2 Temperature identities for three exiting streams
4 Mole fraction sums for four streams
2C Phase equilibrium relations: KiI = yi / xiI and KiII = yi / xiII
Therefore, NE = 3C + 9
Number of degrees of freedom = ND = NV - ND = (4C + 13) - (3C + 9) = C + 4 Exercise 4.5
Subject: Application of Gibbs phase rule to seven-phase system of Figure 4.31.
Given: One gas and six liquid phases in equilibrium.
Assumptions: Gas phase includes N2 , O2 , and argon.
Find: Number of degrees of freedom by Gibbs phase rule.
Possible set of specifications to fix system.
Analysis: From Eq. (4-1), Number of degrees of freedom = C - number phases + 2
Number of components = 9 (N2 , O2 , argon, n-hexane, aniline, water, phosphorus,
gallium, and mercury.
Number of phases = 7
Number of degrees of freedom = 9 - 7 + 2 = 4
Specify T, P, and mole fractions of argon and oxygen in the air. Exercise 4.6
Subject: Partial vaporization of a mixture of benzene and ethyl alcohol.
Given: Vapor-liquid equilibrium data (T-x-y) for benzene-ethyl alcohol at 1 atm and vapor
pressure data for benzene and ethyl alcohol. Initial mixture contains 25 mol% benzene.
Assumptions: Phase equilibrium
Find: (a) Bubble point.
(b) Composition of vapor at bubble point.
(c) Composition of liquid at 25 mol% vaporization.
(d) Composition of liquid at 90 mol% vaporization.
(e) Same as part (c), except vapor is removed and then additional 35 mol% is vaporized.
(f) Plot of temperature vs. mol% vaporized for parts (c) and (e).
(g) Repeat of parts (a) to (f) assuming ideal solutions
Analysis: See plot of T-x-y data on next page, as drawn with a s...
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