Phase Diagrams. Department of Mechanical Engineering Indian Institute of Technology Kanpur Kanpur India

Transcription

1 Phase Diagrams 1

2 Increasing the temperature isobarically T-v diagram of constant-pressure phase-change processes of a pure substance at various pressures numerical values are for water. 2

3 Temperature - Volume diagram 3

4 Pressure Volume diagram The pressure is gradually reduced by removing the weights 4

5 Remembering: P-v-T surfaces (i) The State Postulate: The state of a simple compressible substance is fixed by any two independent, intensive properties and (ii) Any equation with two independent variables in the form z = z (x, y) represents a surface 5

6 P-v-T Surface of a substance that expands on freezing. Orthogonal projection of P-v-T surface 6

7 P-v-T Surface of a substance that contracts on freezing. Orthogonal projection of P-v-T surface 7

8 solid Solid +liquid liquid solid Solid +liquid liquid P-v diagrams Critical point Critical point vapor vapor liquid + vapor liquid + vapor Triple line Triple line solid + vapor Substances that contract on freezing solid + vapor Substances that expand on freezing 8

9 PVT surface for ideal gases 9

10 Phase transformations Sublimation line: Solid and Vapor phase is in equilibrium Fusion line: Solid and Liquid phase is in equilibrium Vaporization line: Liquid and Vapor phase is in equilibrium Triple point: All the three phases are in equilibrium For water, T tp = 0.01 C P tp = kpa Above critical point: No sharp distinction in the liquid and vapor phases 10

11 Phase diagrams Along AB line: rate at which solid sublimes to form a gas=rate at which gas condenses to form a solid Along BC line: rate at which liquid boils to form a gas=rate at which gas condenses to form a liquid Along BD line: rate at which solid melts to form a liquid=rate at which liquid freezes to form a solid The triple point is the temperature and pressure at which all three phases can exist in equilibrium. Above the critical point, molecules are unable to liquify. The heat of fusion is the amount of energy given off when a substance freezes (or the amount of energy the substances requires to liquefy). The heat of vaporization is the amount of energy given off when a gas liquefies (or the amount of energy needed to vaporize the liquid). (Note the difference between the two figures) 11

12 Phase diagram of water Allotropic forms of solid phases: Pure substances can exist in a number of different solid phases Pure substances can have multiple triple points but there exists only one triple point where all the three phases can exist together. The other triple points can have two solid phases and one liquid phase or three solid phases 12

13 Regelation These two examples, usually cited, as NOT due to regelation Regelation is the phenomenon of melting under pressure and freezing again when the pressure is reduced. Regelation occurs only for substances, such as ice, that have the property of expanding upon freezing, for the melting points of those substances decrease with increasing external pressure. The melting point of ice falls by C for each additional atm of pressure applied. For example, a pressure of 500 atmospheres is needed for ice to melt at 4 C. 13

14 Phase diagram of Carbon-dioxide The triple-point pressure is greater than normal atmospheric pressure which is very unusual. At one atmosphere, we see CO 2 either as a gas or as a solid. Therefore, the commonly observed phase- transition under conditions of atmospheric pressure of about 100 kpa is a sublimation from solid directly to vapor, without passing through a liquid phase, which is why solid carbon dioxide is commonly referred to as dry ice. 14

15 Supercritical fluids Supercritical N 2 Supercritical CO 2 15

16 Property tables For most substances, the relationships among thermodynamic properties are too complex to be expressed by simple equations. Therefore, properties are frequently presented in the form of tables. Some thermodynamic properties can be measured easily, but others cannot and are calculated by using the relations between them and measurable properties. The results of these measurements and calculations are presented in tables in a convenient format. In your text book, Please see Tables A-4 and A-5 Table A-4: Saturation properties of water temperature basis Table A-5: Saturation properties of water pressure basis 16

17 Enthalpy: A new property It s a Combination Property The product pressure volume has energy units. (N/m 2 )*(m 3 ) The combination (u + Pv) is frequently encountered in the analysis of control volumes. 17

18 A quick look at the property tables Table A4/A5 18

19 Table A-4 19

20 Table A-5 20

21 Table A-6 and A-7 Superheated water vapor Compressed liquid water 21

22 Van der Waals equation of state 22

23 Percentage error: Equations of State For Nitrogen 23

24 Percentage error with ideal gas law For Water 24

25 Compressibility chart 25

26 Compressibility chart 26

27 Compressibility chart 27

28 End of Lecture 28