Advanced Thermodynamics Note 11 Solution Thermodynamics: Applications

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Advanced ThermodynamicsNote 11Solution
Thermodynamics Applications

• Lecturer ???

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Liquid-phase properties from VLE data

• Fugacity
• For species i in the vapor mixture
• Vapor/liquid equilibrium
• The vapor phase is assumed an ideal gas
• Therefore
• The fugacity of species i (in both the liquid and
  vapor phases) is equal to the partial pressure of
  species i in the vapor phase.
• Its value increases from zero to Pisat for pure
  species i

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Fig. 12.1
Table 12.1
The first three columns are P-x1-y1 data. Columns
4 and 5 are Column 6 is
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Fig 12.3
Fig 12.2
Henrys constant, the limiting slope of the curve
at xi 0. Henrys law expresses
, it is approximate valid for small
values of xi
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Henrys law
Lewis/Randall rule
Gibbs/Duhem equation
x2 ? 1
x1 ? 0
Gibbs/Duhem equation for binary mixture at const.
T and P
The Lewis/Randall rule,
Division by dx1
when x1 1,
limit
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Excess Gibbs energy

• Table 12.2
• Column 6

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Fig. 12.5
Positive deviation from Raoults law behavior
The dimensionless excess Gibbs energy The value
of GE/RT is zero at both x1 0 and x1 1
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From Fig 12.5(b), linear relation
Similarly,
The Margules equations
Limiting conditions
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VLE data for diethyl ketone (1) / n-hexane (2) at
65C are given in the first three columns of
Table 12.4. Reduce the data.
Table 12.4
Fig 12.7
The solid lines. Not consistency! Omit Barkers
method
Fig 12.7(b) for (GE/x1x2RT) fitting
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Models for the excess Gibbs energy
weak

• GE/RT f (T, P, composition)
• At constant T

Data fitting, convenient, but only for binary
system
The Redlich/Kister expansion
The Margules equation
The van Laar equation
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Local composition models

• Can be applied to multi-component systems
• The Wilson equation
• The NRTL(Non-Random-Two-Liquid) equation
• The UNIQUAC equation and the UNIFAC method
• App. H.

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Property changes of mixing

• Excess properties

The M change of mixing
Because of their direct measurability, ?V and ?H
are the property changes of mixing of major
interest.
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Fig 12.10
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The excess enthalpy (heat of mixing) for liquid
mixture of species 1 and 2 at fixed T and P is
represented by the equation Determine
expressions for and as functions
of xi.
The partial properties
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Fig 12.13
1. Each ?M is zero for a pure species. 2. The
Gibbs energy change of mixing ?G is always
positive. 3. The entropy change of mixing ?S is
positive.
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Heat effects of mixing processes

• Heat of mixing
• For binary systems
• When a mixture is formed, a similar energy change
  occurs because interactions between the force
  fields of like and unlike molecules are
  different.
• Heat of solution
• based on 1 mol of solute dissolve in liquids

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Calculate the heat of formation of LiCl in 12 mol
of H2O at 25C.
Fig 12.14
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A single-effect evaporator operating at
atmospheric pressure concentrates a 15 (by
weight) LiCl solution to 40. The feed enters the
evaporator at the rate of 2 kg/s at 25C. The
normal boiling point of a 40 LiCl solution is
about 132C, and its specific heat is estimated
as 2.72 kJ/kg C. What is the heat transfer rate
in the evaporator?
Feed at 25C 2 kg/s 15 LiCl
1.25 kg superheated steam at 132C and 1 atm
0.75 kg 40 LiCl at 132C
Q
The energy balance
the total enthalpy of the product streams minus
the total enthalpy of the feed stream
liquid water is vaporized and heated to 132C
0.75 kg of 40 LiCl solution is heated to 132C
mixing of 0.45 kg of water with 0.30 kg of
LiCl(s) to form a 40 solution at 25C
separation of 2 kg of a 15 LiCl solution into
its pure constituents at 25C
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Enthalpy/concentration diagrams

• The enthalpy/concentration (Hx) diagram

Fig 12.17
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Solid NaOH at 70F is mixed with H2O at 70F to
produce a solution containing 45 NaOH at 70F.
How much heat must be transferred per pound mass
of solution formed?
Energy balance
45 NaOH on the basis of 1 (lbm) 0.45(lbm) of
solid NaOH dissolved in 0.55 (lbm) of H2O.
Fig 12.19, x1 0
Fig 12.19, x1 45