Properties of ideal gases / liquids / solids

• Ideal gases (and sometimes liquids / solids) are ‘special cases’ where properties behave in relatively simple ways

‘special cases’

• As an example, consider the ideal gas law, Pv=RT. This law is plotted in red. Note the behavior is simple compared to the true behavior in blue.

• Note also that the blue and the red curves converge far above and to the right of the vapor dome. In general, superheated vapors far from the vapor dome will behave as ideal gases, and will exhibit this simple behavior.

The problem with special cases

• Because Pv=RT is simple to compute, the book does not list specific volume, v, in tables for ideal gases. See for example table A-17.

• Then, although it is simple, it is still harder than if they just listed it in the table, because you have to do a computation (however, on the plus side, you do not have to interpolate)

EES and special cases• Since EES allows property lookups for special cases and non-

special cases alike, this is all behind the scenes. Therefore, these special cases are sort of transparent in EES. However, you will see special cases show up in EES, for example, like this:

• To remedy the above warning, you just drop the P specification in the parentheses. In the same way that Pv=RT is a simple relationship, h and u are both simpler than the general case for ideal gases: they are functions of temperature only. EES wants to remind you of that, that’s why it doesn’t want other properties besides temperature to be input

u = u(T) for an ideal gas

• You can see that u is independent of pressure in the ideal gas zone (far from the vapor dome) in the plot.

• Also note that there are actually 5 regions labeled in this plot rather than the usual 3 of compressed liquid, saturated mixture, and superheated vapor

• h = h(T) as well for an ideal gas since h = u + Pv and Pv = RT.

• You can see u = u(T), h = h (T) in table A-17.

How far from the vapor dome does a gas become an ideal gas?

• It depends upon how good you want the ideal gas approximation to be

• This Figure is 3-49. The numbers are:

• Biggest numbers here are near the critical point, but even bigger numbers would show up for liquid

Straight lines on property plots are a sign of a ‘special case’

• Each of the straight lines in the P-h diagram for water represents some kind of special case. There are 3 different straight lines here. What does each mean?

Ideal gas formulas (1)

(approximate)

(approximate)

Three ways of calculating u

Ideal gas formulas (2)

(approximate)

(approximate)

Property relations for isentropic processes involving ideal gases

Other special cases

• This presentation has focused on ideal gases but there are also formulas for special-case liquids and solids, see e.g. section 4-5 pg 189 and section 7-8 pg 357…

What should I study relative to property calculations on exams?

• I will generally give you tables (e.g., problems involving steam)

• If I gave you a problem that required you to use formulas to calculate properties, I would lead you through it.

• If you can do steam problems on paper and air problems in EES you should be fine.