2. Behavior of Substance During A Process P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Selection of Substance for A Happening…..

3. The substance contained by the system undergoes a thermodynamic process/cycle The potential of A Process/Cycle Depends on the substance used by (present in ) the system. How to begin the description of A Substance? Development of Equation of state… Is it possible to develop a single EOS model for any substance? Recapitulation

4. Pressure –Temperature Diagram of A Pure Substance

9. General Behaviour of Solids Incompressible Substance. Change in volume is infinitesimally small. Huge increase in temperature or pressure required for a finite change in volume/area/length. In an ideal (Hookean) solid, finite increase in pressure (stress) produces constant deformation (strain) at constant temperature. Thermal Expansion of Solids As the thermal energy in a solid increases, the mean separation of the atoms increases because the force curve is anharmonic. This causes the solid to expand. Linear, superficial and cubical Expansion coefficient.

10. EOS for Solids The volume of A solid: V = f (p,T) & p = g (V,T) Bulk modulus : Coefficient of volume or cubical expansion.

11. Universal Equation of State for Solids where and V 0 is the volume of solid and B 0 is bulk modulus at reference pressure.

12. Constants of EoS ParameterGoldNaclXenon B 0 (10 10 Pa)16.62.350.302  0 (10 -5 K -1 ) 4.2512.060.0 (  B/  p) 0 5.5 – 6.55.357.8 T R, K30029860

13. A common equation of state for Solid V m = molar volume T = temperature p = pressure C 1, C 2, C 3, C 4, C 5 = empirical constants The empirical constants are all positive and specific to each substance. For constant pressure processes, this equation is often shortened to V mo = molar volume at 0 0 C A, B = empirical constants

14. p-V-T Diagram of crystalline solid Phase Volume Pressure Temperature

15. Classification of Solids Crystal - Crystals are solids which are often very hard. The equations above are used for describing the physical properties of crystals. Glass - Glasses are generally very brittle. The equations above are useful for describing the physical behavior until the stress becomes too great and the material shatters. Elastomer - An elastomer is an amorphous solid which can be deformed with out breaking. The change in volume is generally negligible with deformation. However, the cross sectional area may change considerably. For changes in temperature and pressure, elastomers can be considered to be solids although much softer than other solids.

16. Special Solids Superplastic - The unique ability of superplastics to stretch is a mechanical property. Physically, superplastics are treated as solids. Bose-Einstein Condensate - A Bose-Einstein condensate have just been released. It might be a solid or a very supercooled gas or one very large single atom. Refractory - Refractory materials behave physically as solids.

17. Low Pressure Behavior of solids Direct vaporization of solids is known as sublimation Sublimation solid  vapor If the vapor pressure of the impurities in a solid are significantly lower than that of a solid sample, then sublimation can be used as a purification method.

18. Sublimation Curves Elemental solid Alloy Sublimation Point : temperature at which P vap = P sys. Vapor pressure or equilibrium vapor pressure is the pressure of a vapor in thermodynamic equilibrium with its condensed phases in a closed system.

19. Sublimation of water occurs below 61.13Pa 2856 kJ/kg 2520 kJ/kg 336 kJ/kg Sublimation of Ice p sublimation

20. Sublimation Curve for Water The triple point of water is 0.01 o C, 611.3 Pa Define

21. Triple Point The triple point of a substance is the temperature and pressure at which three phases of that substance coexist in thermodynamic equilibrium. For example, the triple point of mercury occurs at a temperature of 234.3156 K and a pressure of 0.2 mPa. The single combination of pressure and temperature at which liquid water, solid ice, and water vapour can coexist in a stable equilibrium occurs at exactly 273.16 K (0.01 °C) and a partial vapour pressure of 611.73 Pascals. Triple point of oxygen 54.3484K & 152 Pa. Triple point of Nitrogen 63.151K & 12520 Pa.

22. 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

23. Melting Curve

24. 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

26. Liquid – Vapour Equilibrium