Phase rule


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Phase rule

  1. 1. PHASE RULE Prof. H. K. Khaira Professor in MSME Deptt. MANIT, Bhopal
  2. 2. The Phase Diagram • Phase diagram: shows the regions of pressure and temperature at which its various phases are thermodynamically stable. • Phase boundary: a boundary between regions, shows the values of P and T at which two phases coexist in equilibrium.
  3. 3. The Gibbs Phase Rule • The phase rule is f=c–p+2 Where f = degrees of freedom c = number of components p = number of phases at equilibrium for a system of any composition.
  4. 4. The Gibbs Phase Rule • Degree of freedom (f): It is the number of external variables that can be changed independently without disturbing the number of phases in equilibrium. These are pressure, temperature and composition. • Component: a chemically independent constituent of a system • number of components (c): the minimum number of independent species necessary to define the composition of all the phase present in the system • Phase: a state of matter that is uniform throughout in chemical composition and physical state.
  5. 5. The Phase Rule • Number of phase (p): – Gas or gaseous mixture – single phase – Liquid – one, two and three phases • two totally miscible liquids – single phase • a slurry of ice and water – two phases – Solid • a crystal is a single phase • an alloy of two metals – two phases (immiscible) • one phase (miscible)
  6. 6. Chapter 7 The Phase Rule (a) (b) The difference between (a) a single-phase solution, in which the composition is uniform on a microscopic scale, and (b) a dispersion containing two phases, in which regions of one component are embedded in a matrix of a second component. 7
  7. 7. Examples of Two Phases
  8. 8. H2O phase diagram: P — T D 218 atm C Y P / 10 5 Pa I solid liquid Line S Point 1 atm Region R 0.00611 gas A O 0.0024 0.01 T3 Tf 99.974 Tb 374.2 t/℃ 10
  9. 9. H2O phase diagram: P — T Region (s, l, g): D P / 10 5 Pa 218 atm C f=2, one phase Y I solid Line (OA, AD, AC): liquid S f=1, two phases in equilibrium 1 atm R 0.00611 gas A Point (A): O 0.0024 0.01 T3 Tf 99.974 Tb t/℃ 374.2 Tc f=0, three phases in equilibrium 11
  10. 10. Simple Example
  11. 11. Chapter 7 Physical Chemistry One-component phase equilibrium Hence, for a one-component system (pure water) f=1-p+2=3-p,(C=1) f ≥0, p ≥1, 3≥p≥1 p=1,f=2 p=2,f=1 p=3,f=0 13
  12. 12. Phase Rule in Metallurgical Systems • But in case of metallurgical systems, the pressure is kept constant. • Hence the Phase Rule gets modified to F=C–P+1