ES 202Fluid and Thermal Systems

Lecture 15:Properties in Two-Phase Region

(1/16/2003)

Lecture 15 ES 202 Fluid & Thermal Systems 2

Assignments

• Homework:– 3-28, 3-29 in Cengel & Turner

• Reading assignment– Tables A-4 to A-14 in Cengel & Turner

Lecture 15 ES 202 Fluid & Thermal Systems 3

Announcements

• More on Lab 2 write-up– due tomorrow– no length limit– Contents: water wall, Torricelli experiment, pipe friction– data interpretation

• Problem session today at 7 pm in O167– show outline

• Bring your text book to class next Monday

Lecture 15 ES 202 Fluid & Thermal Systems 4

Road Map of Lecture 15

• Review of Lecture 14

• Phase diagram– familiarity with terminology

– familiarity with various regions

• Focus on two-phase dome– dependency between temperature and pressure

– new property: quality

• Exercise on properties table

Lecture 15 ES 202 Fluid & Thermal Systems 5

Review of Lecture 14• What is the State Principle?

• Identify the regions on the P-v, T-v planes

Lecture 15 ES 202 Fluid & Thermal Systems 6

Working with P-v, T-v Diagrams

• Compressed liquid• Superheated vapor• The two-phase (vapor) dome• Saturated liquid line• Saturated vapor line• Critical point

• Trace a constant pressure curve on the T-v diagram– how it relates to the ideal gas model– in what direction is pressure increasing?

• Trace a constant temperature curve on the P-v diagram– how it relates to the ideal gas model– in what direction is temperature increasing?

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T-v Diagram

Two-phasedome

Superheatedvapor

Compressedliquid

Critical Point

Saturated vapor line

Satu

rate

d liq

uid

line

increasing direction of pressure

constant pressure line

Lecture 15 ES 202 Fluid & Thermal Systems 8

P-v Diagram

Two-phasedome

Superheatedvapor

Compressedliquid

Critical Point

Saturated vapor line

Satu

rate

d liq

uid

line

increasing direction of temperature

constant temperatureline

Lecture 15 ES 202 Fluid & Thermal Systems 9

Illustration of Two-Phase Mixture

• Imagine a heating process in a cylinder with a constant weight as a lid (closed system; control mass)

liquid

vapor

heating

}mixture of liquid and vapor

Lecture 15 ES 202 Fluid & Thermal Systems 10

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 (reference to P-v diagram, table)

– example: boiling point of water at different altitudes

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

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Introducing Quality

• Definition: mass fraction of vapor in the mixture

• Geometric interpretation:

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

gf

g

mm

mx

D

dx

d

D

f g

Lecture 15 ES 202 Fluid & Thermal Systems 12

Significance of Quality

• Define properties in the “Two-Phase dome”

• For example:– extensive property: internal energy

– using quality, its intensive counterpart can be expressed as a mass-weighted

average of the saturated liquid and

saturated vapor values

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

gf UUU

ggff umummu

gg

ff u

m

mu

m

mu

gf uxuxu )1(

Lecture 15 ES 202 Fluid & Thermal Systems 13

Saturated Temperature, Pressure Tables

• Show saturated water – temperature table (Table A-4)– indicate dependency between temperature and saturation

pressure– indicate saturated liquid and saturated vapor values for

various intensive properties

• Show saturated water – pressure table (Table A-5)– indicate dependency between pressure and saturation

temperature– indicate saturated liquid and saturated vapor values for

various intensive properties