Lec 7: Property tables, ideal and real gases

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Lec 7 Property tables, ideal and real gases
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• For next time
• Read 3-8 to 3-12
• HW4 due
• Outline
• EES
• Quality, internal energy, enthalpy
• Real gases
• Important points
• How to use the quality to find properties of
  mixtures
• How to evaluate a given process in a property
  diagram
• How to calculate and apply corrections to the IGL
  for real gases

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TEAMPLAY

• Find, for water, the following properties the
  saturation pressure at a saturation temperature
  of 100 ?F.
• and find the saturation temperature at a pressure
  of 6 MPa.
• Make sure everyone in your group understands how
  to do this.

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Quality

• We often represent the relative amount of vapor
  present by something called the quality x.

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Quality is related to the horizontal differences
of P-V and T-v diagrams
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What is the new v?
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So...
v (1-x)vf xvg vf x(vg - vf) or,
writing vfg ? vg vf v vf xvfg
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Obtaining u in the vapor dome

• What you do for v works for u (and for other
  things)

u (1-x)uf xug uf x(ug - uf) uf
xufg
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A new property enthalpy, H

• Enthalpy is simply the sum of the internal
  energy, U, and the pressure volume product, pV
• H ? U pV
• Now,

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Enthalpy--the bottom line

• H U pV
• h u pv

h (1-x)hf xhg hf x(hg - hf) hf
xhfg
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The P-V or P-v plane

• For the next few lectures we will often look at
  the two dimensions P and v, or P and V.
• The P is always on the ordinate and the v is
  always on the abcissa, just opposite to the
  familiar x-y plane.

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Sat. Liquid Line
Subcooled or Compressed Liquid Region
Sat. Vapor Line
Superheated Region - 100 Vapor
Two-Phase or Saturation Region - gas and liquid
coexist
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For water
p
Table Page A-6 940/43 A-6E
986/88 If TTsat, P ? Psat If PPsat, T
gtTsat superheated region
Table Page A-7 944 A-7E 989 If
TTsat P?Psat. If PPsat, T?Tsat. subcooled
or compressed liquid region
Table Page A-4 936/7 A-5
938/9 A-4E 982/3 A-5E
983/4 saturation region PPsat and TTsat
v
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Superheat tables--compressed liquid tables are
similar
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TEAMPLAY
Complete the table below as a team. The
substance is water. Make sure everybody
understands how to do it!
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TEAMPLAY

• A container holds 1 kg of liquid water and 1 kg
  of steam in equilibrium at 0.7 MPa.
• What is the temperature of the mixture in ?C?
• If we hold the pressure constant and increase the
  temperature to 320 ?C, what is the change in
  volume?
• Show the process on the Pv diagram.

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Sample Problem
Compare the values of the specific volume of
water at saturated liquid conditions and 100?C
with the values of specific volume at of water at
saturated liquid conditions and 100?C and the
following pressures 5, 20, and 30 MPa. What
conclusions can be drawn from the comparison?
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SOLUTION
From compressed liquid tables
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What can we learn?

• Specific volume is approximately constant over
  large changes in pressure if TC
• Liquid does not change specific volume
  significantly as pressure is changedit cant be
  compressed
• When compressed liquid tables are not available,
  estimate property data at sat. liquid conditions
  at the same temperature as the compressed liquid.

IMPORTANT!!
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Consider R-134a (Refrigerant 134a)

• We can make a diagram for this as we did for
  water but there is no data in the compressed or
  subcooled liquid region.

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For R-134a
Table Page A-13
950/1 A-13E 995/6 If TTsat,
P?Psat If PPsat, TgtTsat superheated region
P
Table Page A-11 (T) 948 A-11E(T)
993 A-12 (P) 949 A-12E(P) 994 saturation
region PPsat and TTsat
v
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R-134a IS NOT AN IDEAL GAS!
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TEAMPLAY

• What is the specific volume of saturated liquid
  R-134a _at_ 0 C?
• What is the internal energy at -10 C and 0.14
  MPa?
• What is the pressure at x 0.1 and 0 F?
• What is h at the same conditions?

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TEAMPLAY
Under what conditions is it appropriate to apply
the ideal gas equation of state?
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Ideal gas law is a simple equation of state
Ru universal gas constant 8.3144
kPam3/kmolK 1.545 ft lbf/lbmolR
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Molar mass or molecular weight is sometimes
confusing
Take air as an example
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Specific gas constant
Universal gas constant given inside back cover of
your textbook
Specific gas constant calculated by dividing
universal gas constant by molar mass
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Percent error for applying ideal gas equation of
state to steam
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(No Transcript)
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Real gases

• Pv ZRT, or
• Pv ZRuT, where v is volume per unit mole.

Z is known as the compressibility factor
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Principle of corresponding states
The compressibility factor Z is the same for
all gases at the same values of the reduced
temperature and reduced pressure.
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Compressibility factor

• What is it really doing?
• It accounts mainly for two things
• Molecular structure
• Intermolecular attractive forces

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Reduced properties
Where
PR and TR are reduced values.
Pc and Tc are critical properties.
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Where do you find critical properties?

• Look in the appendices of your text book.
• For the SI system they are on p. 930 in Table
  A-1, along with molar mass.
• For USCS system, they are on p. 976 in Table A-1E

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Reduced properties

• This works great if you are given a gas, a P and
  a T and asked to find the v.
• However, if you are given P and v and asked to
  find T (or T and v and asked to find P), you can
  use the pseudoreduced volume.

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Reduced properties

• In those cases use the pseudoreduced volume

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Compressibility factor

• It is shown in Figure 3-56 (p. 100) in terms of
  actual experimental data

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Compressibility factor for ten substances
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TEAMPLAY
Use the compressibility factor to determine the
error in treating oxygen gas at 160 K and 3 MPa
as an ideal gas.