Equation of sate for Liquids & vapours Essential Information for development of casting systems….....
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Transcript of Equation of sate for Liquids & vapours Essential Information for development of casting systems….....
![Page 1: Equation of sate for Liquids & vapours Essential Information for development of casting systems….. P M V Subbarao Professor Mechanical Engineering Department.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649ef15503460f94c01b4f/html5/thumbnails/1.jpg)
Equation of sate for Liquids & vapours
Essential Information for development of casting systems…..
P M V SubbaraoProfessor
Mechanical Engineering Department
I I T Delhi
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Theory of Melting• Melting is a vibrational instability released when the root mean
square amplitude of vibration reaches a critical fraction (10%) of the interatomic distance.
• Several investigators attempted to calculate the critical temperature for different planes when this instability will appear.
• The onset of melting of these particles is found to take place significantly below the bulk melting point.
• This is called as Debye temperature .
Initial FCC lattice structure for CuConfiguration of atoms of Cu
after melting.
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P-T Diagrams to Represent a Substance
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Pressure – Temperature Diagram of a Pure Substance
Substance Triple point
K & kPa
Oxygen 54 & 0.15
Nitrogen 63 & 12.53
Water 273.17 & 0.6113
Mercury 234 & 0.2×10-6
Copper 1376 & 0.000079
Silver 1234 & 0.01
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P-T Diagrams to Represent Iron
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Simons’s Equation for Melting Curve
1
c
triple
meltingtriplemelting
T
T
a
pp
a & c are parameters depend on substance
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Effect of Pressure on Melting Point
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MetalMelting Point
MetalMelting Point
(oC) (oC)Admiralty Brass 900 - 940 Incoloy 1390 - 1425
Aluminum 660 Iridium 2450Aluminum
Alloy463 - 671 Iron, Wrought 1482 - 1593
Aluminum Bronze
600 - 655 Iron, Gray Cast 1127 - 1204
Antimony 630 Iron, Ductile 1149Brass, Red 1000 Lead 327.5
Brass, Yellow 930 Magnesium 650
Cadmium 321Magnesium
Alloy349 - 649
Chromium 1860 Manganese 1244
Cobalt 1495Manganese
bronze865 - 890
Copper 1084 Mercury -38.86
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MetalMelting Point
MetalMelting Point
(oC) (oC)Inconel 1390 - 1425 Silver, Coin 879Monel 1300 - 1350 Silver, Pure 961Nickel 1453 Silver, Sterling 893
Niobium (Columbium)
2470 Sodium 97.83
Osmium 3025 Steel, Carbon 1425 - 1540Palladium 1555 Steel, Stainless 1510
Phosphorus 44 Tantalum 2980Platinum 1770 Thorium 1750
Plutonium 640 Tin 232Potassium 63.3 Titanium 1670Red Brass 990 - 1025 Tungsten 3400Rhenium 3186 Uranium 1132Rhodium 1965 Vanadium 1900
Ruthenium 2482 Yellow Brass 905 - 932Selenium 217 Zinc 419.5Silicon 1411 Zirconium 1854
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Properties of Liquids
The equation of state created by Peng and Robinson has been found to be useful for liquids
bVbbVV
Ta
bV
RTp
mmmm
p = pressure a = empirical constant Vm = molar volume R = ideal gas constant b = empirical constant T = temperature
Tp
TRTa
cr
cr 22
45724.0
cr
cr
p
RTb 0778.0
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010 T
NM
crT
TLMN
crT
TT
11
1,0 exp
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Critical Points of Substances
Substance Tcr, K pcr, MPa Vcr, m3/kg
Iron 9250 875
water 647.3 22.12 0.00317
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A MULTIPHASE EOS for Iron
• In the condensed state, we take into account the presence of four solid phases (α, γ, δ, and ε) and a liquid phase (l).
• The thermal EOS is expressed as:
TVppp attrep ,
repc
rep
pVV
RTp
nTatt
V
VeATVp
00
1
1,
A = 44.5380, χ = 0.25, λ = 0.00065, V00 = 0.12515, n = 1.66608, and ν = 5.21887.
Ap
VpV
rep
repc
ln100