# ES 202 Fluid and Thermal Systems Lecture 15: Properties in Two-Phase Region (1/16/2003)

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ES 202 Fluid and Thermal Systems Lecture 15: Properties in Two-Phase Region (1/16/2003)

Lecture 15ES 202 Fluid & Thermal Systems2 Assignments Homework: –3-28, 3-29 in Cengel & Turner Reading assignment –Tables A-4 to A-14 in Cengel & Turner

Lecture 15ES 202 Fluid & Thermal Systems3 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 15ES 202 Fluid & Thermal Systems4 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 15ES 202 Fluid & Thermal Systems5 Review of Lecture 14 What is the State Principle? Identify the regions on the P-v, T-v planes

Lecture 15ES 202 Fluid & Thermal Systems6 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?

Lecture 15ES 202 Fluid & Thermal Systems7 T-v Diagram Two-phase dome Superheated vapor Compressed liquid Critical Point Saturated vapor line Saturated liquid line increasing direction of pressure constant pressure line

Lecture 15ES 202 Fluid & Thermal Systems8 P-v Diagram Two-phase dome Superheated vapor Compressed liquid Critical Point Saturated vapor line Saturated liquid line increasing direction of temperature constant temperature line

Lecture 15ES 202 Fluid & Thermal Systems9 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 15ES 202 Fluid & Thermal Systems10 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

Lecture 15ES 202 Fluid & Thermal Systems11 Introducing Quality Definition: mass fraction of vapor in the mixture Geometric interpretation: Serves as another independent thermodynamic variable in the “Two-phase dome” d D f g

Lecture 15ES 202 Fluid & Thermal Systems12 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.

Lecture 15ES 202 Fluid & Thermal Systems13 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

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