ES312 Energy Transfer Fundamentals

Unit C: Thermodynamic Analysis

ROAD MAP . . .

C-1: p-v-T Relations

C-2: Thermodynamic Property Tables

ES312 Energy Transfer Fundamentals

Unit C-1: List of Subjects

Phases of a Pure Substance

Thermodynamic State and Phase Change

T-v Diagram

p-v Diagram

p-T Diagram and p-v-T Surface

PURE SUBSTANCE

A substance that has a fixed chemical composition throughout is called a “pure substance.”

A pure substance does not have to be of a single chemical element or compound

A mixture of various chemical elements or compounds also qualifies as a pure substance, as long as

the mixture is homogeneous

Air: is a mixture of several gases, but can be treated as a pure substance

Mixture of oil and water: is not a pure substance

A mixture of two or more phases of pure substance is still a pure substance, as long as the chemical

composition of all phases is the same.

Mixture of ice and liquid water: is a pure substance (homogeneous)

Mixture of liquid air and gaseous air: is not a pure substance (the composition of liquid air and

gaseous air are different, thus not homogeneous)

PHASES OF A PURE SUBSTANCE

A pure substance may have several “phases.”

Solid: the molecules are arranged in a 3-D pattern (called, “lattice”) that is repeated throughout.

Liquid: the molecules are no longer at fixed positions

Gas: the molecules are far apart from each other

UNIT C-1PAGE 1 of 7

Phases of a Pure Substance

Nitrogen and gaseous air are pure substancesA mixture of liquid and gaseous water is a pure

substance, but a mixture of liquid and gaseous air is not

The arrangement of atoms in different phases: (a) molecules are at relatively fixed positions in a solid, (b) groups of

molecules move about each other in the liquid phase, and (c) molecules move about at random in the gas phase

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PHASE-CHANGE PROCESS OF PURE SUBSTANCES

As a familiar substance, water is used to demonstrate the basic principles of phase-change process (a

pure substances exhibit the similar general behavior). Main focus is the liquid and vapor phases and

their mixture, demonstrated by a piston-cylinder device.

STATE 1 (Compressed or subcooled Liquid)

Under the given condition of water (1 atm and 20 C), water exists in the liquid phase, called the

“compressed” or “subcooled” liquid; meaning that it is NOT about to vaporize.

STATE 2 (Saturated Liquid)

As more heat is transferred, the temperature keeps rising until it reaches 100 C. At this point, water

is still a liquid, but any heat addition will cause some of the liquid to vaporize: this is called the

“saturated” liquid; meaning that it is about to vaporize.

STATE 3 (Saturated Liquid-Vapor Mixture)

Once boiling starts, the temperature stops rising until the liquid is completely vaporized. Until all

liquid water is completely vaporized, liquid and gaseous water (vapor) can co-exist: this is called the

“saturated liquid-vapor mixture.”

STATE 4 (Saturated Vapor)

As more heat is transferred, the entire cylinder is filled with vapor that is on the borderline of the

liquid phase: this is called the “saturated” vapor; meaning that any loss of heat from this vapor will

cause some of the vapor to condense

STATE 5 (Superheated Vapor)

As more heat is transferred, the vapor in the cylinder begins to increase: this is called the

“superheated” vapor; meaning that it is NOT about to condense.

UNIT C-1PAGE 2 of 7

Thermodynamic State and Phase Change

At 1 atm and 20 C, water exists in

the liquid phase (compressed liquid)

At 1 atm and 100 C, water exists as a liquid

that is ready to vaporize (saturated liquid)

At 1 atm, the temperature remains

constant at 100 C until the last drop of

liquid is vaporized (saturated vapor)

As more heat is transferred, part of

the saturated liquid vaporizes

(saturated liquid-vapor mixture)

As more heat is transferred, the

temperature of the vapor starts to rise

(superheated vapor)

PRESSURE DEPENDENCE OF PHASE-CHANGE PROCESS

Water starts to boil at 100 C at 1 atm (101.325 kPa): this is strictly under the constant pressure

condition of 1 atm (101.325 kPa).

The temperature at which water starts boiling depends on the pressure; therefore, if the pressure is

fixed, so is the boiling temperature.

At a given pressure, the temperature at which a pure substance changes phase is called the

saturation temperature (satT ).

At a pressure of 101.325 kPa, satT = 99.97 C.

At a given temperature, the pressure at which a pure substance changes phase is called the saturation

pressure (satp ).

At a temperature of 99.97 C, satp = 101.325 kPa.

TEMPERATURE-VOLUME DIAGRAM (1)

The phase-change process under a constant pressure is called the T-v diagram.

T-v diagram of constant-pressure phase-change process is available for common substances used in

engineering applications.

UNIT C-1PAGE 3 of 7

T-v Diagram (1)

T-v diagram for the heating process of water at constant pressure

TEMPERATURE-VOLUME DIAGRAM (2)

T-v diagram of constant-pressure phase-change process can further be plotted on different pressure

values. As the pressure changes, one can observe the different values for saturation temperatures.

The horizontal line that connects the saturated liquid and saturated vapor states is called the

“saturation line”: meaning that the saturated two-phase mixture (liquid-vapor) exist along this line.

As the pressure increases, this saturation line continues to “shrink,” and it becomes a point when the

pressure reaches 22.06 MPa for the cases of water: this point is called the “critical point,” and it is

defined as the point at which the saturated liquid and saturated vapor states are identical.

CRITICAL POINT

One can define a boundary between compressed liquid and saturated two-phase mixture by

connecting the locations of STATE 2: this is called the “saturated liquid line”).

Also, similarly, one can define a boundary between saturated two-phase mixture and superheated

vapor by connecting the locations of STATE 4: this is called the “saturated vapor line”).

VAPOR DOME

Saturated liquid and vapor lines will meet at the critical point, completing the map of three different

regions in the diagram: this is called the “vapor dome.”

Above critical point (supercritical pressures), there is no distinct phase-change process.

UNIT C-1PAGE 4 of 7

T-v Diagram (2)

T-v diagram of constant-pressure phase-change

processes of a pure substance (water) at various

pressures

T-v diagram of a pure substance

At supercritical pressures (P > Pcr),

there is no distinct phase-change

(boiling) process)

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For water: Table A-1 (A-1E) p

cr = 22.06 MPa

Tcr

= 373.95 °C

vcr

= 0.003106 m3/kg

PRESSURE -VOLUME DIAGRAM

The general shape of the p-v diagram of a pure substance is very much like the T-v diagram.

For a given temperature, the phase change process (compressed liquid => saturated liquid-vapor =>

superheated vapor) is plotted, similar to the T-v diagram.

EXTENDED PRESSURE-VOLUME DIAGRAM (INCLUDING THE SOILD PHASE)

Most substances “contract” during a solidification (i.e., freezing) process. However, a few

substances (actually including water) “expand” as they freeze.

Water “expands” upon freezing: means that water ice is lighter than liquid water.

The p-v diagrams for both groups of substances are available.

TRIPLE LINE

Under certain conditions, all three phases (for water: solid-ice, liquid-water, and gas-vapor) can

coexist in equilibrium. These triple-phase states form a line, called the “triple line.”

At low pressures, solids evaporate without melting first: this is called “sublimation.”

UNIT C-1PAGE 5 of 7

p-v Diagram (1)

Triple Line:

Three-phases coexist

(solid, liquid, and vapor)

P-v diagram of a substance that contracts on freezing

At low pressures (below the triple-point

value), solids evaporate without melting

first (sublimation)

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TRIPLE POINT

The triple line often appears as a point on a diagram, and it is called “triple point.”

For water,

Triple point temperature: tpT 0.01 C

Triple point pressure: tpp 0.6117 kPa

Below triple point pressure, no substance can exist in the liquid phase in stable equilibrium state.

However, substances at high pressures can exist in the liquid phase at below triple point temperature.

For water,

Water cannot exist in liquid form in equilibrium at atmospheric pressure at temperatures below 0 C,

but it can exist as liquid at 20 C at 200 MPa pressure. Also, ice exists at several different solid

phases at pressure above 100 MPa.

UNIT C-1PAGE 6 of 7

p-v Diagram (2)

Triple Point:

three-phases coexist

(solid, liquid, and vapor) P-v diagram of a substance that expands on freezing (i.e., water)

At triple point pressure and

temperature, a substance exists

in three phases in equilibrium

PRESSURE-TEMPERATURE DIAGRAM

The p-T diagram of a pure substance is often called the “phase” diagram, since all three phases are

separated from each other by three lines.

Sublimation line: separates the solid and vapor regions

Vaporization line: separates the liquid and vapor regions

Melting (or “fusion”) line: separates the solid and liquid regions

These three lines meet at the triple point, where all three phases coexist in equilibrium.

The vaporization line ends at the critical point, because no distinction can be made between liquid

and vapor phases above the critical point.

Substances that expand and contract on freezing differ only in the melting line on the diagram.

THE PRESSURE-VOLUME-TEMPERATURE SURFACE

The state of a simple compressible substance is fixed by any two independent, intensive properties.

Once the two appropriate properties are fixed, all the other properties become dependent properties. We

can represent the p-v-T behavior of a substance as a surface in space.

UNIT C-1PAGE 7 of 7

p-T Diagram and p-v-T Surface

P-T diagram of a pure substance

P-v-T surface of a pure substance

that contracts on freezing

P-v-T surface of a pure substance

that expands on freezing (i.e., water)