1. Equation of sate for Liquids & vapours Essential Information for development of casting systems….. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi

2. 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 Cu Configuration of atoms of Cu after melting.

3. P-T Diagrams to Represent a Substance

4. Pressure – Temperature Diagram of a Pure Substance SubstanceTriple point K & kPa Oxygen54 & 0.15 Nitrogen63 & 12.53 Water273.17 & 0.6113 Mercury234 & 0.2×10 -6 Copper1376 & 0.000079 Silver1234 & 0.01

5. P-T Diagrams to Represent Iron

6. Simons’s Equation for Melting Curve a & c are parameters depend on substance

7. Effect of Pressure on Melting Point

8. Metal Melting Point Metal Melting Point ( o C) Admiralty Brass900 - 940Incoloy1390 - 1425 Aluminum660Iridium2450 Aluminum Alloy 463 - 671Iron, Wrought1482 - 1593 Aluminum Bronze 600 - 655Iron, Gray Cast1127 - 1204 Antimony630Iron, Ductile1149 Brass, Red1000Lead327.5 Brass, Yellow930Magnesium650 Cadmium321 Magnesium Alloy 349 - 649 Chromium1860Manganese1244 Cobalt1495 Manganese bronze 865 - 890 Copper1084Mercury-38.86

9. Metal Melting Point Metal Melting Point ( o C) Inconel1390 - 1425Silver, Coin879 Monel1300 - 1350Silver, Pure961 Nickel1453Silver, Sterling893 Niobium (Columbium) 2470Sodium97.83 Osmium3025Steel, Carbon1425 - 1540 Palladium1555Steel, Stainless1510 Phosphorus44Tantalum2980 Platinum1770Thorium1750 Plutonium640Tin232 Potassium63.3Titanium1670 Red Brass990 - 1025Tungsten3400 Rhenium3186Uranium1132 Rhodium1965Vanadium1900 Ruthenium2482Yellow Brass905 - 932 Selenium217Zinc419.5 Silicon1411Zirconium1854

10. Properties of Liquids The equation of state created by Peng and Robinson has been found to be useful for liquids p = pressure a = empirical constant V m = molar volume R = ideal gas constant b = empirical constant T = temperature

12. Critical Points of Substances SubstanceT cr, Kp cr, MPaV cr, m 3 /kg Iron9250875 water647.322.120.00317

13. 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: A = 44.5380, χ = 0.25, λ = 0.00065, V 00 = 0.12515, n = 1.66608, and ν = 5.21887.