Chapter 3

PROPERTIES OF PURESUBSTANCES

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Objectives

• Introduce the concept of a pure substance.

• Discuss the physics of phase-change processes.

• Illustrate the P-v, T-v, and P-T property diagrams and P-v-Tsurfaces of pure substances.

• Demonstrate the procedures for determining thermodynamicproperties of pure substances from tables of property data.

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PURE SUBSTANCE

• Pure substance: Any substance that has a fixed chemicalcomposition throughout.

• For example, air is a mixture of several gases, but it is considered tobe a pure substance.

• Nitrogen and gaseous air are both pure substances.

• A mixture of liquid and gaseous water is a pure substance.

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PHASES OF A PURE SUBSTANCE

The molecules in a solid are kept at their positions bythe large spring-like inter-molecular forces.

The positions of the molecules are essentially fixedover a period of time.

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PHASES OF A PURE SUBSTANCE

In a solid, the attractive and repulsive forces between the molecules tend tomaintain them at relatively constant distances from each other.

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 PROCESSES OF PURESUBSTANCES

• Compressed liquid (or subcooled liquid): Any liquid that it is notabout to vaporize. The addition of any heat only increases thetemperature of the liquid, but does not cause any liquid to changephase.

At 1 atm and 20°C, water exists in the liquidphase (compressed liquid).

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PHASE-CHANGE PROCESSES OF PURESUBSTANCES

• Saturated liquid: Only liquid is present. Any addition of heat willcause some liquid to vaporize leading to a mixture of saturated liquidand vapor.

At 1 atm pressure and 100°C, water existsas a liquid that is ready to vaporize(saturated liquid).

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• Saturated liquid-vapor mixture: Any further addition of heat,causes more liquid to evaporate to form more vapor.

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• Saturated vapor mixture: Exactly enough heat has been addedto convert all of the liquid to vapor.

At 1 atm pressure, the temperature still remainsat 100°C until the last drop of liquid is vaporizedto form pure saturated vapor.

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• Superheated vapor: All liquid has already been converted to vapor, andany further addition of heat will only lead to ‘hotter’ vapor.

As more heat is transferred, thetemperature of the vapor will now startto rise leading to a superheatedvapor.

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T-v diagram for theheating process ofwater at constantpressure.

If the entire process between these states is reversed by cooling thewater while maintaining the pressure at the same value, the water willgo back to state 1, retracing the same path. While doing so, theamount of heat released will exactly match the amount of heat addedduring the original heating process.

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PROPERTY DIAGRAMS FOR PHASE-CHANGE PROCESSES

• Variations of properties during phase-change are best studied andunderstood when graphed in the T-v, P-v, and P-T planes.

T-v diagram ofconstant-pressurephase-changeprocesses of a puresubstance at variouspressures(numerical valuesare for water).

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• saturated liquid line

• saturated vapor line

• compressed liquid region

• superheated vapor region

• saturated liquid–vapormixture region (wet region)

T-v diagram of a pure substance.

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Saturation Temperature and Saturation Pressure• The temperature at which water starts boiling depends on the

pressure. Thus, if the pressure is fixed, so is the boiling temperature.• Water boils at 100°C at 1 atm pressure.

• Saturation pressure Psat: The pressure at which a pure substancechanges phase at a given temperature.

Theliquid–vaporsaturationcurve of apuresubstance(in thiscase,water).

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Saturation Temperature and Saturation Pressure• The temperature at which water starts boiling depends on the

pressure. Thus, if the pressure is fixed, so is the boiling temperature.• Water boils at 100°C at 1 atm pressure.• Saturation temperature Tsat: The temperature at which a pure

substance changes phase at a given pressure.• The atmospheric pressure, and thus the boiling temperature of water,

decreases with elevation.

Theliquid–vaporsaturationcurve of apuresubstance(in thiscase,water).

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• Latent heat: The amount of energy absorbed or released during aphase-change process.

• Latent heat of fusion: The amount of energy absorbed during melting.It is equivalent to the amount of energy released during freezing.

• Latent heat of vaporization: The amount of energy absorbed duringvaporization. It is equivalent to the energy released duringcondensation.

• The magnitudes of the latent heats depend on the temperature orpressure at which the phase change occurs.

• At 1 atm pressure, the latent heat of fusion of water is 333.7 kJ/kg andthe latent heat of vaporization is 2256.5 kJ/kg.

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Some Consequences of Tsat and Psat

Dependence

The temperature of liquidnitrogen exposed to theatmosphere remainsconstant at 196°C, and thusit maintains the testchamber at 196°C.

The variation of thetemperature of fruits andvegetables with pressureduring vacuum cooling from25°C to 0°C.

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At supercritical pressures(P > Pcr), there is nodistinct phase-change(boiling) process.

T-v diagram of a pure substance.

Critical point: The pointat which the saturatedliquid and saturatedvapor states are identical.

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P-v diagram of a pure substance.The pressure in a piston–cylinder

device can be reduced byreducing the weight of the piston.

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Extending theDiagrams to Includethe Solid Phase

P-v diagram of a substance thatcontracts on freezing.

P-v diagram of a substance thatexpands on freezing (such as water).

At triple-point pressureand temperature, a

substance exists in threephases in equilibrium.

For water,Ttp = 0.01°C

Ptp = 0.6117 kPa

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Sublimation: Passing fromthe solid phase directly intothe vapor phase.

At low pressures (belowthe triple-point value),solids evaporate withoutmelting first (sublimation).

P-T diagram of pure substances.

Phase Diagram

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P-v-T surface of a substancethat contracts on freezing.

P-v-T surface of a substance thatexpands on freezing (like water).

The P-v-T surfaces present a great deal of information at once, but in athermodynamic analysis it is more convenient to work with two-dimensionaldiagrams, such as the P-v and T-v diagrams.

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Examples:Saturated liquidand saturatedvapor states ofwater on T-v andP-v diagrams.

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PROPERTY TABLES• For most substances, the relationships among thermodynamic

properties are too complex to be expressed by simple equations.• Therefore, properties are frequently presented in the form of tables.• Some thermodynamic properties can be measured easily.• Those that can’t and are calculated by using the relations between them

and measurable properties. Recall cp and cv!• The results of these measurements and calculations are presented in

tables in a convenient format.

Enthalpy—A Combination Property

The combination (u + Pv) isfrequently encountered in theanalysis of control volumes.

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Saturated Liquid and Saturated Vapor States

• Table A–4: Saturation properties of water versus temperature.• Table A–5: Saturation properties of water versus pressure.

Partial listing of Table A–4.

Enthalpy of vaporization, hfg (Latentheat of vaporization): The amount ofenergy needed to vaporize a unit massof saturated liquid at a giventemperature or pressure.

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Saturated Liquid–Vapor Mixture

The relative amounts of liquidand vapor phases in asaturated mixture are specifiedby the quality x.

A two-phase system can betreated as a homogeneousmixture for convenience.

Temperature and pressure aredependent properties for a mixture.

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Saturated Liquid–Vapor Mixture

Quality, x : The ratio of the mass of vapor to the total mass of themixture.

Quality is between 0 (sat. liquid) and 1 (sat.vapor).

The properties of the saturated liquid are the same whether it existsalone or in a mixture with saturated vapor.

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For example:

Given the quality:

The specific volume would be

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Quality is relatedto the horizontaldistances on P-vand T-vdiagrams.

The v value of asaturated

liquid–vapor mixturelies between the vf

and vg values at thespecified T or P.

Or any other thermodynamic properties…

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Example: Consider a liquid-vapor mixture on a T-v diagram.

What is quality, x?

What is the specific volume vof the mixture?

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Example: Consider a liquid-vapor mixture on a P-v diagram.

If v = 0.037565 m3/kg, thenwhat is quality x?

What is enthalpy, h?

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Superheated Vapor

In the region to the rightof the saturated vaporline (and at temperaturesabove the critical pointtemperature), asubstance exists assuperheated vapor.

Note: in this region,temperature andpressure are nowindependent properties!

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Compared to saturated vapor, superheated vapor is characterized by…

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Super heated property values can be found in Table A–6.

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Compressed liquid is characterized by…

At a given P and T, apure substance will

exist as a compressedliquid if

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A more accurate relationfor h is…

Compressed liquid properties depend much more strongly on T than p.

Thus, a compressed liquid may be approximated as a saturated liquid atthe given temperature.

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Summary

• Pure substance

• Phases of a pure substance

• Phase-change processes of pure substances

Compressed liquid, Saturated liquid, Saturated vapor,Superheated vapor

Saturation temperature and Saturation pressure

• Property diagrams for phase change processes

The T-v diagram, The P-v diagram, The P-T diagram

The P-v-T surface

• Property tables

Enthalpy

Saturated liquid, saturated vapor

Saturated liquid vapor mixture

Superheated vapor, compressed liquid