Properties of ideal gases / liquids / solids

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Properties of ideal gases / liquids / solids

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

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special cases

• As an example, consider the ideal gas law, PvRT.
  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.

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The problem with special cases

• Because PvRT 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)

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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 PvRT 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, thats why it
  doesnt want other properties besides temperature
  to be input

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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.

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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

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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?

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Ideal gas formulas (1)
(approximate)
(approximate)
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Three ways of calculating Du
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Ideal gas formulas (2)
(approximate)
(approximate)
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Property relations for isentropic processes
involving ideal gases
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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

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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.