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L t 3 Ph b h i f b tLecture 3: Phase behavior of pure substance

Review• State Postulate, Equilibrium surface, Process

• Thermal contact, thermal equilibrium, Zeroth law, and

temperature

• Equation of state, Thermometry

• Scales of temperature• Scales of temperature

• Pressure

• Phase behaviour of pure substance

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Pure Substance Phase Behavior

• Experiment with water at Constant Pressure: T-v behavior• Saturation Temperature – temperature at which liquid and vapor coexist at given P, ie., the boiling temperature• Saturation Pressure – pressure at which liquid and vapor coexist at i Y i thgiven Y, ie., the vapor pressure

• The saturation T of water at 0.1 MPa is 99.6º C, and vice versa• At fixed pressure, the temperature does not change as long as the two phases coexist If heat is added the relative amount of vapor increases

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phases coexist. If heat is added, the relative amount of vapor increases

Vapor Pressure

• The vapor pressure of a pure liquid increases with increasing temperature• The vapor pressure has a unique value at a givenThe vapor pressure has a unique value at a given temperature• The vapor pressure curve terminates at a critical point beyond which there is no distinction between liquid and

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beyond which there is no distinction between liquid and vapor

T-v diagram for water

Horizontal line segment (tie-line) at each pressure connects a pair of saturated liquid and saturated vapor phases in equilibrium.Length of this line segment decreases with increasing pressure (and

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g g g p (temperature), and is of vanishing length at the critical point beyond which there is no distinction between liquid and vapor

T-v liquid-vapor equilibrium - water

As one moves from left to right in the saturation region at a given T and P, the relative amount of vapor grows at the expense of the liquid., p g p qQuality x = mg/m, fraction of total mass present as vapor, varies from 0 to 1 along tie lineAt any point on the line, v = (1-x)vf + xvg = vf + xvfg where vf and vg are

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g g gthe specific volumes of the liquid and vapor phases respectively, and vfg= vg - vf

Solid-Liquid Equilibrium• If container has ice at 0.1 MPa and -20ºC, and heat is

ftransferred, system remains homogeneous, with small

change in v, till the temperature reaches 0ºC, at which

temperature the ice begins to melt. As further heat is added,

the temperature remains constant till all the ice melts.

• This is the melting temperature, and this depends on the

pressure When solid and liquid are in equilibrium the solidpressure. When solid and liquid are in equilibrium, the solid

is said to be saturated.

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Sublimation, the Triple Point• If we begin with ice at 0.260 kPa and -20ºC, and add heat,

ºCthe temperature rises till -10ºC, at which point, the solid

directly converts to vapour (sublimation). The temperature

remains constant till all the ice has sublimed

• If finally we start with ice at 0.6115 kPa and -20ºC, and add y ,

heat, the system remains homogeneous till the temperature

reaches 0 01ºC at which point both liquid and vapourreaches 0.01 C, at which point both liquid and vapour

appear. This is the triple point, the unique T and p at which

h h f b i ilib ithree phases of a pure substance can coexist at equilibrium

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P-T Phase Diagram (Water)

Substance that expands upon freezing

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Substance that expands upon freezing

P-T Phase Diagram – CO2

Substance that expands upon melting

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Substance that expands upon melting

P-T Phase Diagram - Water

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PvT Surfaces

What determines which phase is stable at a given P and T?

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What determines which phase is stable at a given P and T?

T-v diagram for water

What about P-v diagram?

Superheated vapourCompressed (sub-cooled) liquid

Horizontal line segment (tie-line) at each pressure connects a pair of saturated liquid and saturated vapor phases in equilibrium.Length of this line segment decreases with increasing pressure (and

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g g g p (temperature), and is of vanishing length at the critical point beyond which there is no distinction between liquid and vapor

T-v liquid-vapor equilibrium - water

x = mg/mV = V + V = m v + m vV = Vf + Vg = mfvf + mgvgv = (1 – x)vf + xvg

= vf + xvfg

As one moves from left to right in the saturation region at a given T and P, the relative amount of vapor grows at the expense of the liquid., p g p qQuality x = mg/m, fraction of total mass present as vapor, varies from 0 to 1 along tie lineAt any point on the line, v = (1-x)vf + xvg = vf + xvfg where vf and vg are

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g g gthe specific volumes of the liquid and vapor phases respectively, and vfg= vg - vf

Some terms• Fusion (melting), Vaporization, and Sublimation, Triple

Point

• Liquid-Vapour Equilibrium -Saturated liquid and vapour,

Compressed (Sub-cooled) Liquid, Superheated Vapour,

Critical Point, Supercritical region, p g

• Solid – Liquid Equilibrium - Saturated solid and liquid

• Solid – Vapour Equilibrium - Saturated solid and vapour

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Thermodynamic tablesEngineering applications require the knowledge of the values of various properties of commonly used substances in different states. While figures are useful data are much more precisely presented in tables Some ofare useful, data are much more precisely presented in tables. Some of the tables include:• Critical constants – table A2

P ti f l t d lid (A3) d li id (A4) d id l (A5)• Properties of selected solids (A3) and liquids (A4), and ideal gases (A5)• Properties of water - saturated liquid and vapour, organized according to the temperature (B1.1), and pressure (B1.2). In these tables, apart f th t ti t t d th l f ififrom the saturation temperature and pressure, the values of specific volume (v), internal energy (u), enthalpy (h), and entropy (s) of coexisting liquid and vapour phases are given.

S h t d t (B1 3) Th t bl i i d di t• Superheated water vapour (B1.3). The table is organized according to the pressure. For each pressure, the values of v, u, h, and s are listed for various temperatures starting from the saturation temperature.

C d ( b l d) li id (B1 4) i d b b t f• Compressed (sub-cooled) liquid (B1.4), organized as above, but for various temperature values at and below saturation for various pressures

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Thermodynamic tables• Properties of water – saturated solid and vapour (B1.5) organized by temperature, as Table B1.1

T bl i il h f b h l i i i• Tables similar to those for water, but rather less extensive, are given in B2 to B7 for other substances

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