Session-5

We will cover,

• Phase Diagrams • State Principle and Quality • Evaluating Properties

1 P-v Diagram

Critical Point

increasing direction of temperature Superheated constant temperature vapor line Compressed liquid

e

n i l

d S i Two-phase at u ur q a i dome t l e d d v e a t po a r r l u in t e a

S

2 T-v Diagram

Critical Point increasing direction of pressure

Compressed Superheated liquid constant pressure line vapor

S a e t n u i rat l ed d i u Two-phase v q a i p l o dome r d li e n t e a r

u t

a

S

3 State Principle

Two independent, intensive thermodynamic properties are sufficient to fully determine the thermodynamic state of a pure substance.

4 The “Two-Phase” Dome

• A mixture of liquid and vapor

• Temperature and pressure are NOT independent in the two-phase dome – One specifies the other – Example: boiling point of water at different altitudes

• need another independent property to completely specify the state: – concept of quality

5 Introducing Quality

• Define properties in the “Two-Phase” dome U = U +U • For example: f g – extensive property: internal energy mu = m f u f +mgug – using quality, its intensive counterpart m m can be expressed as a mass-weighted f g u = u f + ug average of the saturated liquid and m m saturated vapor values u = (1− x) u f + x ug

• Internal energy in the above example can be replaced by any other extensive property, e.g. volume, enthalpy, entropy, etc.

6 Introducing Quality (Cont’d)

• Definition: mass fraction of vapor in the mixture m x = g m + m f g • Geometric interpretation on phase diagram: a x = b

– saturated liquid: x = 0 f g – saturated vapor: x = 1 a

• Serves as another independent b thermodynamic variable in the “Two-phase” dome

7 Phase Determination (Case 1)

• Case 1: Given P and T – Look up saturation table – Compare given P and T against saturation values in the table ¾ In pressure table, ƒ Recall constant pressure line T > T (P) on T-v diagram sat

T = Tsat(P) ƒ If T < Tsat(P), T < T (P) compressed liquid. sat

ƒ If T = Tsat(P), saturated liquid-vapor mixture.

ƒ If T > Tsat(P), superheated vapor.

8 Phase Determination (Case 1 Cont’d)

• Case 1: Given P and T – Look up saturation table – Compare given P and T against saturation values in the table

¾ In temperature table, ƒ Recall constant temperature P > P (T) line on P-v diagram sat

P = Psat(T) ƒ If P > Psat(T), P < P (T) compressed liquid. sat

ƒ If P = Psat(T), saturated liquid-vapor mixture.

ƒ If P < Psat(T), superheated vapor.

9 Phase Determination (Case 2)

• Case 2: Given P (or T) and v (or u, h, s) – Look up saturation table

– Find saturated liquid and vapor values for v (or u, h, s) at Psat = P

1) If v < vf(Psat), compressed liquid. (1)

2) If v = vf(Psat), (2) (3) (4) P saturated liquid. sat

3) If vf(Psat)< v < vg(Psat), (5) saturated liquid-vapor mixture.

4) If v = vg(Psat), saturated vapor.

5) If v > vg(Psat), superheated vapor. vf(P) vg(P)

10 Summary

• Compressed liquid (quality is undefined, any two intensive thermodynamic properties suffice)

• Saturated liquid (x = 0)

• Saturated liquid-vapor mixture (0 < x < 1)

• Saturated vapor (x = 1)

• Superheated vapor (quality is undefined, any two intensive thermodynamic properties suffice)

11 Flow Chart

Determine phase of substance

Compare with saturation table

Compressed Liquid Two-phase Mixture Superheated Vapor

Direct look up Determine quality Direct look up

Interpolate other properties

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