Gibbs phase rule and lever rule

ppt of Gibbs phase rule and lever rule

1. GIBBS PHASE RULE AND LEVER RULE Material Science and Metrology

2. Gibbs Phase Rule Consider a glass of water. This is a pure substance (H20) in a single phase. It can be described with a number of thermodynamic properties including temperature, pressure, volume, entropy, enthalpy and Gibbs energy. However not all of these properties are independent. In fact, for the glass of water, only two intensive thermodynamic properties are independent. Thus, if we specify temperature and pressure, all the other properties, in their intensive (i.e. their value per mole of substance) form, can be determined.

3. Temperature and pressure are often taken as independent intensive variables.(see P-T diagram) This is because it is usually easy to experimentally vary and measure these two properties directly. However, any intensive property can be choosen to be one of the independent variables. If the intensive enthalpy (J/ mol ) and intensive entropy (J/ mol K) of the water in the glass were specified, its temperature and pressure could then be found using the steam tables or a Mollier diagram.

4. The Gibbs phase rule tells how many independent intensive properties, F, can be chosen. This will depend on the number of chemical species, N, and number of phases, pi, present. In the absence of chemical reaction, the Gibbs phase rule is simply: single phase (pi=1) F=2+1-1=2 two phases (pi=2) F=2+1-2=1 three phase (pi=3) F=2+1-3=0 F=2+N-pi For a pure substance (N=1), the Gibbs phase rule can be applied as follows:

5. An example showing that for a single phase of a pure substance, F=2: For a glass of liquid water, specify one of the independent intensive variables to be pressure. Choose this pressure to be 1 atm. If liquid is in the glass, the temperature can take any value between 0 'C and 100 'C. Within this range, the temperature can be choosen independently of the pressure. Thus, both T and P are independent. After choosing a (T, P) pair, any other property, such as volume or entropy, can be found using the steam tables or a Mollier diagram. Therefore the remaining properties can not be independently choosen after T and P are specified.

6. Example showing that for two coexistant phases of a pure substance, F=1. For a glass of boiling water (also call saturated liquid water) in equilibrium with saturated steam, specify the one of the independent intensive variables to be pressure. Choose this pressure to be 1 atm. In order for the water to boil (or be saturated) at this pressure, the temperature must be 100 'C. Thus, the temperature can not be choosen independently of the pressure when both liquid and vapor water are present. Thus, only the P is independent. The temperature required at other pressures, as well as the values of all remaining thermodynamic properties, can be found in the tables for saturated steam or on a Mollier diagram.

7. Example showing that for three coexistant phases of a pure substance, F=0. At the triple point; vapor, liquid and solid all coexist. For any given substance, the triple point occurs only at one a specific pair of temperature and pressure. Once it is stated the substance at the triple point, the values of this temperature and pressure pair as well as the values of all other thermodynamic properties can be found in a table or graph. Thus, no thermodynamic property can be choosen independently.

8. Lever rule The lever rule is a tool used to determine mole fraction of each phase of a binary equilibrium phase diagram. It is used to determine the percent of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line. In an alloy with two phases, α and β, which themselves contain two elements, A and B, the lever rule states that the weight percentage of the α phase is where a is the weight percentage of element B in the α phase b is the weight percentage of element B in the β phase c is the weight percentage of element B in the entire alloy all at some fixed temperature.  

9. Binary phase diagrams Before any calculations can be made, a tie line is drawn on the phase diagram to determine the percent weight of each element; on the phase diagram to the right it is line segment LS. This tie line is drawn horizontally at the composition's temperature from one phase to another (here the liquid to the solids). The percent weight of element B at the liquidus is given by w l and the percent weight of element B at the solidus is given by w s . The percent weight of solid and liquid can then be calculated using the following lever rule equations: percent weight of solid phase : percent weight of liquid phase : where w o is the percent weight of element B for the given composition.  

10. The numerator of each equation is the original composition we are interested in +/- the Opposite lever arm . That is if you want the percent weight of solid then take the difference between the liquid composition and the original composition. And then the denominator is the overall length of the arm so the difference between the solid and liquid compositions.

11. THANK YOU