1 Lec 6: Psychrometrics and Engineering Equation Solver (EES)

2 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

3 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.

4 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. or

5 Psychrometrics The total number of moles is Thus the total pressure exerted by a mixture of ideal gases is

6 Psychrometrics The mole fraction y from chemistry is often used It can easily be shown that y i is also equal to

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

8 Psychrometrics One can show that Where M i is the molecular weight of the ith component of the mixture and M is the molecular weight of the mixture, given by

9 TEAMPLAY What are the mole fractions of the two constituents if 1 lb m of argon is mixed with 1 lb m of helium? What is the molecular weight of the resulting mixture?

10 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.)

11 Psychrometrics However, an additional complication introduced by the water vapor is the fact that it will condense if its partial pressure p i in the mixture reaches the saturation pressure. Consider the atmosphere at pressure p to be mixture of dry air “a” and water vapor “v”.

12 Psychrometrics Atmospheric cooling may be regarded as a constant pressure process from 1 to 2 in the figure below. p i, psia vivi T 2 = 60 °F T 1 = 90 °F

13 Psychrometrics Relative humidity  is a useful parameter in discussing human comfort. It is defined as p i, psia vivi T 2 = 60 °F T 1 = 90 °F

14 TEAMPLAY Work problem 3-58

15 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.

16 EES Allows parametric studies too tedious to assign as homework by hand. –Parametric tables work much like spreadsheets. Allows plotting quickly and easily.

17 TEAMPLAY 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.”

18 TEAMPLAY--EES Consider a simple problem: y 1 = mx 2 + 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)

19 TEAMPLAY-- EES After you have entered the sample equation, select “Windows”, “Formatted Equations” to see how it looks. Notice that the y_1 is now y 1, etc. Return to equations window and enter y 1 =10.

20 TEAMPLAY--EES Go to “Calculate” and select “Solve”.

21 TEAMPLAY Parametric studies In the previous TEAMPLAY problem, let us vary y 1 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, y 1 and maybe others.

22 TEAMPLAY See that y 1 is not specified in the problem statement in the “Equations Window”. Enter y 1 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.”

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

24 Obtaining a copy of EES for your computer Available from SELL (Software Evaluation Licensing Lab) in Teague 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.