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Lec 6: Psychrometrics and Engineering Equation Solver (EES)

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• For next time:– Read: § 3-6 to 3-7

• Outline:– Property diagrams– Psychrometrics and relative humidity– EES Example

• Important points:– How to use the property tables– How to plot a process in a property diagram– How to use relative humidity

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Psychrometrics

• Air may be dealt with as a mixture of non-reacting ideal gases.

• Dry air is air with no water vapor.• Moist air contains water vapor.• Dry air may be regarded as a mixture of

nitrogen, oxygen, argon, carbon dioxide, and trace amounts of other gases--for example, neon, helium and methane.

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Psychrometrics

• A useful model of a mixture of ideal gases is the Dalton model:– Each component “i” behaves as if it

were alone in the mixture at the temperature T of the mixture and volume V occupied by the mixture.

V

RTmp i

i V

TRnp ui

i or

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Psychrometrics

• The total number of moles is

• Thus the total pressure exerted by a mixture of ideal gases is

V

TnR

V

TRnpp...ppp uu

j

1ii

j

1iij21

j

1ii21 n...nnn

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Psychrometrics

• The mole fraction y from chemistry is often used

• It can easily be shown that yi is also equal to

n

ny i

i

p

p

n

ny ii

i

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Psychrometrics

• The mass fraction “mf” is also important in dealing with mixtures, and it is defined as

m

mmf i

i

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Psychrometrics

• One can show that

• Where Mi is the molecular weight of the ith component of the mixture and M is the molecular weight of the mixture, given by

iii M

Mmfy

j

1iiijj2211 MyMy...MyMyM

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TEAMPLAYTEAMPLAY

• What are the mole fractions of the two constituents if 1 lbm of argon is mixed with 1 lbm of helium?

• What is the molecular weight of the resulting mixture?

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Psychrometrics

• These relationships are good for mixtures of ideal gases in general.

• The components of air, even the water vapor, behave as ideal gases in general.

• (The water vapor behaves as an ideal gas because its pressure and temperature are relatively low.)

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Psychrometrics

• However, an additional complication introduced by the water vapor is the fact that it will condense if its partial pressure pi in the mixture reaches the saturation pressure.

• Consider the atmosphere at pressure p to be mixture of dry air “a” and water vapor “v”.

va ppp

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Psychrometrics

• Atmospheric cooling may be regarded as a constant pressure process from 1 to 2 in the figure below.

pi, psia

vi

T2 = 60 °FT1 = 90 °F

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0.26

0.70

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Psychrometrics

• Relative humidity is a useful parameter in discussing human comfort. It is defined as

pi, psia

vi

T2 = 60 °F

T1 = 90 °F1

20.26

0.70 3

3

1

Tat sat

v

p

p

p

p

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TEAMPLAYTEAMPLAY

• Work problem 3-58

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Engineering Equation Solver (EES)

• Solves non-linear algebraic equations faster than one can do by hand.– Unknown variable can appear anywhere

in the equation, even on either side of the equal sign.

• Provides a database of thermodynamic tables such as those in your book.

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EES

• Allows parametric studies too tedious to assign as homework by hand.– Parametric tables work much like

spreadsheets.

• Allows plotting quickly and easily.

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TEAMPLAYTEAMPLAY

• Minimize today’s lecture and get to the desktop.• Click on the desktop icon for EES 32, --no

password is required.• Click OK until you get a blank screen.• Click on “File” and then “New.”• The next screen should be an “Equations

Window.”

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TEAMPLAY--EESTEAMPLAY--EES

• Consider a simple problem:y1 = mx2 + ln x

• If you wanted to know x(y), this was a trial and error solution not too long ago, for most folks.

• Enter it into EES thusly:y_1=m*x**2 + ln (x)

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TEAMPLAY-- EESTEAMPLAY-- EES

• After you have entered the sample equation, select “Windows”, “Formatted Equations” to see how it looks. Notice that the y_1 is now y1, etc.

• Return to equations window and enter y1=10.

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TEAMPLAY--EESTEAMPLAY--EES

• Go to “Calculate” and select “Solve”.

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TEAMPLAYTEAMPLAY

• Parametric studies• In the previous TEAMPLAY problem, let

us vary y1 from 1 to 8 in increments of 1 (8 runs) and see how x varies.

• Under “Tables”, select “New Parametric Table”

• Click and drag the variables you want to see to the right--x, y1 and maybe others.

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TEAMPLAYTEAMPLAY

• See that y1 is not specified in the problem statement in the “Equations Window”.

• Enter y1 via “Alter Values” under “Tables”

• Click on the column headings to be able to enter units.

• You must solve the table before you can plot it.

• Under “Calculate” select “Solve Table.”

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TEAMPLAYTEAMPLAY

• Under “Plot” select “New Plot Window” and “X-Y Plot”.

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Obtaining a copy of EES for your computer

• Available from SELL (Software Evaluation Licensing Lab) in Teague 1105.

• Take a blank CD and they will burn one for you. May have to return to pick up.

• Alternatively, check out a CD there which you must return. Right now, waiting list.

• Everything you need should be on the CD, including a manual.

• The copy will expire August 31, 2004.