Equation of sate for Liquids & vapours

Essential Information for development of casting systems…..

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

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.

P-T Diagrams to Represent a Substance

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

P-T Diagrams to Represent Iron

Simons’s Equation for Melting Curve

1

c

triple

meltingtriplemelting

T

T

a

pp

a & c are parameters depend on substance

Effect of Pressure on Melting Point

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

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

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

010 T

NM

crT

TLMN

crT

TT

11

1,0 exp

Critical Points of Substances

Substance Tcr, K pcr, MPa Vcr, m3/kg

Iron 9250 875

water 647.3 22.12 0.00317

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