Mixtures and Solutions

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Mixtures and Solutions
Michigan State University College of
Engineering Fall 2007 - ME444

• Harold Schock

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Mixtures of Ideal Gases
The mole fraction yi of component i is defined
as   ni no. of moles of i n total
moles in mixture   Similarly mass
fraction   mi mass of component i m
total mass in mixture
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What Properties Can We Measure?
 
We could have tables to determine the properties
of the mixture, but we would prefer to be able to
derive properties from the pure substances that
comprise the mixture.
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One Exception Air tables which are based on
the following
composition   MoleBasis   Nitrogen
78.10 Oxygen 20.95 Argon
0.92 CO2trace 0.03
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In general, properties of mixtures are defined
as partial molal properties.   For example lets
examine the internal energy of the
gases A B shown above     where
denotes the partial molal internal
energy. Similar equations can be developed for
other properties.
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Two models are used in conjunction
with mixtures of gases, namely
the Dalton
Model and the Amagat Model. Dalton Model
Properties of each component
are considered as each component existed
separately at the volume and temperature
of the mixture.
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Dalton Model
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Ideal Gas Dalton Model 
Mixture nnAnB   Components Using
Ideal Gas nnAnB   or PPAPB  where
PA and PB are called partial pressures.
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Amagat Model The properties of each component
are evaluated as though each component existed
separately at the pressure and temperature of the
mixture as shown in the figure.
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Ideal Gas Amagat Model
Mixture nnAnB   Components   n
nAnB   or or VVAVB   and
are called volume fractions.
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One can shown based on above
that     Using the Dalton model we can
continue, (each component occupies entire
volume)   Since for ideal gases u,h?u(T) and
h(T) only      
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are given in per mole pure A,B. The entropy
of an ideal gas is a function of T and
P   entropy/mole at T and PA  
entropy/mole at T and PB
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H2O-Air Mixtures
Assumptions 1. Solid or liquid phase has no
dissolved gases. 2. Gaseous phase can be treated
as a mixture of ideal gases. 3. When the
mixture and the condensed phase are at a given
T, the equilibrium between the condensed phase
and its vapor do not influence each other.

?
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Dew Point The dew point of a gas-vapor
mixture is the temperature at which the vapor
condenses when it is cooled at constant
pressure.   If the vapor is at the saturation
pressure and temperature, the mixture is called a
saturated mixture or saturated air.
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T-s Diagram for H2O
T
s
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Relative Humidity ?
In terms of the previous diagram
Since we are considering vapor to be an ideal
gas
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Humidity ratio (w) of an air-water vapor mixture
Since both the water vapor, air and mixture to
be ideal gases
and
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The Adiabatic Saturation Process
Saturated-Vapor Mixture
Air Vapor
Water
If 1 lt 100, H2O liquid will evaporate
and temperature of air-vap mixture will
decrease If a) Mixture leaving 2 is saturated
b) Process is adiabatic c) Pressure is
approximately constant
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Saturated-Vapor Mixture
Air Vapor
Water
Then, temperature on the mixture _at_ 2 is called
the adiabatic saturation temperature. In a SSSF
process, H2O liquid is added Neglectivity
changes in ICE and PE the first law for the SSSF
System is
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Wet-Bulb / Dry Bulb Temperature

• Humidity is usually found from
  dry bulb, wet bulb data
• Continuous-flow psychrometer
• Sling psychrometer

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Velocity air gt 3 m/s

• How does the wet bulb temperature change?
• If air-water vapor mixture is not saturated water
  on the wick starts to evaporated and this vapor
  diffuses into the air

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How does the wet bulb temperature change,
continued

• T of water in wick will drop because of the
  evaporation
• Heat is transferred from the thermometer and the
  air, and T therm. Drops
• Eventually, a steady rate will be reached

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Difference Between Wet Bulb and Adiabatic
Saturation Temperature (AST) Wet Bulb
influenced by heat and mass transfer AST
involves equilibrium between the entering
air-vapor mixture and water at the
AST However, for water-vapor mixtures at
atmospheric T, P the AST WBT
Not necessarily true at
Ts and Ps significantly different
from
ATMOSPHERIC CONDITIONS
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Summary

• Dalton Model Volume temperature constant,
  leads to the concept of partial pressures
• Amagat Model Pressure and temperature
  constant, leads to the concept of volume fractions

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Summary, (cont.)

• Concepts of and Dew Point Have been
  introduced and their relationship formulated
• Adiabatic saturation process allows one to easily
  measure the humidity of an air-vapor mixture

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Example problem 3.1-1.Two insulated tanks A and
B are connected by a valve. Tank A initially
contains oxygen at 400kPa and 100C. and has a
volume pf 10m3. Tank B initially contains
nitrogen at 200kPa and 500C and has a volume of
10m3. The valve is opened and remains open until
the mixture comes to a uniform state. Determine
the final temperature and pressure and the
entropy change for the system.
2m3
10m3
2m3
10m3
T
PB1 200kPa
PA1 200kPa
A
TB1 500C
B
TA1 100C
B Nitrogen
A Oxygen
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System Tank boundariesWhat is known? Tanks are
insulated ,and no work has been done
EP 3.1.2
First Law U2 U1 0
or
02
02
A1
N2
2
2
VN2
B1
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