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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
3
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.
total
vapor
liquidvapor
vapor
m
m
m m
mx
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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, pvu
m
Vp
m
Uh
m
H
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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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P
v
Superheated Region - 100% Vapor
Two-Phase or Saturation Region - gas and liquid
coexist
Subcooled or Compressed Liquid Region
Sat. Vapor Line
Sat. Liquid Line
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p
v
Table Page
A-4 936/7
A-5 938/9
A-4E 982/3
A-5E 983/4
saturation region
P=Psat and T=Tsat
Table Page
A-6 940/43
A-6E 986/88
If T=Tsat, P Psat
If P=Psat, T >Tsat
superheated region
Table Page
A-7 944
A-7E 989
If T=Tsat PPsat.
If P=Psat, TTsat.
subcooled or compressed liquid region
For water
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TEAMPLAYTEAMPLAY
Complete the table below as a team. The substance is water. Make sure everybody understands how to do it!
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TEAMPLAYTEAMPLAY
A container holds 1 kg of liquid water and 1 kg of steam in equilibrium at 0.7 MPa.
1. What is the temperature of the mixture in C?
2. If we hold the pressure constant and increase the temperature to 320 C, what is the change in volume?
3. 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 100C with the values of specific volume at of water at saturated liquid conditions and 100C and the following pressures:
5, 20, and 30 MPa.
What conclusions can be drawn from the comparison?
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What can we learn?
• Specific volume is approximately constant over large changes in pressure if T=C
• Liquid does not change specific volume significantly as pressure is changed…it can’t 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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P
v
Table Page
A-11 (T) 948
A-11E(T) 993
A-12 (P) 949
A-12E(P) 994
saturation region
P=Psat and T=Tsat
Table Page
A-13 950/1
A-13E 995/6
If T=Tsat, PPsat
If P=Psat, T>Tsat
superheated region
For R-134a
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TEAMPLAYTEAMPLAY
• What is the specific volume of saturated liquid R-134a @ 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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TEAMPLAYTEAMPLAY
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
RTPv
M
RR u
Ru = universal gas constant
= 8.3144 kPa•m3/kmol•K
= 1.545 ft • lbf/lbmol•R
mRTPV
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Molar mass or molecular weight is sometimes confusing
Take air as an example:
units SIin kmol
kg97.28Mair
units USCSin lbmol
lb97.28M m
air
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m
u
lb 28.97
lbmolx
Rlbmol
Btu 1.986 =
MR = R
Rlb
Btu0686.0R
m
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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IN GENERALIN GENERAL
STEAM should not beSTEAM should not betreated as AN IDEALtreated as AN IDEAL
GAS!GAS!
An exception is waterAn exception is watervapor in the atmospherevapor in the atmosphere
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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
cR
cR T
TT and
P
PP
PR and TR are reduced values.
Pc and Tc are critical properties.
Where:
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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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Compressibility factor
• It is shown in Figure 3-56 (p. 100) in terms of actual experimental data