Chapter 12: Ideal Gas Mixtures and Psychrometric Applications

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Chapter 12 Ideal Gas Mixtures and Psychrometric
Applications
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Objectives

• Many systems of interest involve gas mixtures of
  two or more components. ???????????????????
• To apply the principles of thermodynamics
  introduced thus far to these systems requires
  that we evaluate properties of the mixtures.
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• Means are available for determining the
  properties of mixtures from the mixture
  composition and the properties of the individual
  pure components from which the mixtures are
  formed.???????????????????????

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• The objective of the present chapter is to study
  mixtures where the overall mixture and each of
  its components can be modeled as ideal gases.
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• General ideal gas mixture considerations are
  provided in the first part of the
  chapter.????????????????????
• Understanding the behavior of ideal gas mixtures
  of air and water vapor is prerequisite to
  considering air-conditioning processes in the
  second part of the chapter. In those processes,
  we sometimes must consider the presence of liquid
  water as well.????????????????,???????????????,???
  ????????
• We will also need to know how to handle ideal gas
  mixtures when we study the subjects of combustion
  and chemical equilibrium in Chapters 13 and 14,
  respectively.?????????????????????????

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Ideal gas mixtures General consideration
12.1 Describing Mixture Composition????????
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Example 12.1 Converting mole fractions to mass
fractions
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Example 12.2 Converting mass fractions to mole
fractions
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12.2 Relating p,v,T for ideal gas mixtures
F12-1
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Two models
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12.3 Evaluating U,H,S and Specific heats for the
mixture
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12.4 Analyzing systems involving mixtures12.4.1
Mixture Processes at cst. composition
Eq.12.35
F12-2
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Using ideal gas Tables

• Table A-22 (p.796) on a mass basis (for air)
• Table A-23 (p.798) on a molar basis (for selected
  gases)
• Eq.12.35 can be determined using eq.6.21b

eq.6.21b
p.228 eq.6.12 The 2nd Tds eq.
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Example 12.3 Compressing an ideal gas mixture
Find (a). the final Temperature, (b). the work
(c) the heat transfer (d) the change in entropy
of the mixture
(a)
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Example 12.3 (cont..)
(b)
P271, eq.6.55, polytropic process, n ?1
P271, eq.6.57, ideal gas case, n ?1
(c)
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Example 12.3 (cont..)
(d)
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Example 12.4 gas mixture expanding isentropically
through a nozzle
Find (a). the Temperature at the nozzle exit, in
K, (b). the entropy change of the CO2 and O2 from
inlet to exit, in kJ/kmol.K (c) the exit
velocity, in m/s.
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Derive 233.42 kJ/kmol.K At T510 K
0.2(221.206)0.8(235.7)232.8 At T520 K
0.2(221.812)0.8(236.575)233.62 Gives T2517.6 K
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Is stale(???) airplane air making us sick?

• About half the air we breath on some airplanes is
  fresh air, and the rest is recirculated.

B12-1
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12.4.2 Mixing of ideal gases

• Mixing gases that are initially separate
• Such mixing is irreversible because the mixture
  forms spontaneously
• In this section, irreversibility of mixing is
  demonstrated through calculations of the entropy
  production.
• Three factors contribute to the entropy
  production
• The gases are initially at different T
• The gases are initially at different P
• The gases are distinguishable from one another

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Example 12.5 Adiabatic mixing at constant total
volume
(a) Find the final temperature of the mixture, in
oR, (b) the final pressure of the mixture, in
atm, (c) the amount of entropy produced in the
mixing process, in Btu/oR
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Solution to (a)
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• (460540)/2500 oR 40 oF
• Select Cv from Table A20E, p.844 for 40 oF
• Convert from mass basis to molar basis

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Solution to (b)
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Solution to (c)
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Example 12.6 Adiabatic mixing of 2 streams
(a) Find the mass flow rate of the dry air and
O2, (b) the mole fraction of the dry air and O2
in the exiting mixture (c) the time rate of
entropy production
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Solution to (c)
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Psychrometric Applications
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12.5 Introducing Psychrometric principles
F12-3 Mixture of dry air and water vapor is
termed moist air
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T-v diagram for water vapor in an air-water
mixture
F12-4
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• Humidity ratio (???)
• Relative Humidity (????)

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pg614
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Evaluating H, U and S
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12.5.3 Modeling moist air in equilibrium with
liquid water

• Can be described with the following idealization
• The dry air and water vapor behave as independent
  ideal gases,
• The equilibrium between the liquid phase and the
  water vapor is not significantly disturbed by the
  present of the air
• The partial pressure of the water vapor equals
  the saturation pressure of water corresponding to
  the T of the mixture pvpg(T)

F12-5
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12.5.4 Evaluating the dew point Temperature
F12-6
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Example 12.7 Cooling moist air at cst. P
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Example 12.8 Cooling moist air at cst. V
(a)
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22 oC
(b)
(c)
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Example 12.9 Evaluating heat transfer for moist
air cooling at cst. V
State 1
Q
22 oC
State 2
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12.5.5 Evaluating humidity ratio using the
adiabatic-Saturation T (Tas)
F12-7
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B12-2 How cold is cold ?

• Wind chill effect

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12.6 Psychrometers measuring the wet-bulb and
dry-bulb Temperatures
F12-8
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12.7 Psychrometric chart
F12-9
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12.8 Analyzing Air-conditioning processes
12.8.1 Applying mass and energy balances to
air-conditioning systems
mass balance
F12-10
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energy balance
F12-10
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Example 12.10 Heating Moist air in a duct
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Alternative Psy.chart solution
E12.10b
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12.8.3 Dehumidification ??
F12-11
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Example 12.11 Dehumidifier
(a)
(b)
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(c)
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12.8.4 Humidification ??
F12-12
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Example 12.12 Steam-spray Humidifier
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12.8.5 Evaporative cooling????
F12-13
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Example 12.13 Evaporative Cooler
0.01069 if hf0
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12.8.6 Adiabatic mixing of 2 moist air streams
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F12-14
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Example 12.14 Adiabatic mixing of moist streams
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(b) Find T3
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12.9 Cooling Tower ???
F12-15
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Example 12.15 Power Plant Cooling Tower
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Summaries

• In this chapter we have applied the principles of
  thermodynamics to systems involving ideal gas
  mixtures, including the special case of
  psychrometric applications involving air-water
  vapor mixtures, possibly in the presence of
  liquid water. Both closed system and control
  volume applications are presented.

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• The first part of the chapter deals with general
  ideal gas mixture considerations and begins by
  describing mixture composition in terms of the
  mass fractions or mole fractions.
• Two models are then introduced for the p-v-T
  relation of ideal gas mixtures
• the Dalton model, which includes the partial
  pressure concept,
• the Amagat model.
• Means are also introduced for evaluating the
  enthalpy, internal energy, and entropy of a
  mixture by adding the contribution of each
  component at its condition in the mixture.
• Applications are considered where ideal gas
  mixtures undergo processes at constant
  composition as well as where ideal gas mixtures
  are formed from their component gases.

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• In the second part of the chapter, we study
  psychrometrics.
• Special terms commonly used in psychrometrics are
  introduced, including moist air, humidity ratio,
  relative humidity, mixture enthalpy, and the dew
  point, dry-bulb, and wet-bulb temperatures.
• The psychrometric chart, which gives a graphical
  representation of important moist air properties,
  is introduced.
• The principles of conservation of mass and energy
  are formulated in terms of psychrometric
  quantities, and typical air-conditioning
  applications are considered, including
  dehumidification and humidification, evaporative
  cooling, and mixing of moist air streams. A
  discussion of cooling towers is also provided.

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