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Pure Substance Pure Substances-Homogeneous and constant chemical compositionMay exist in more than one phase but chemical composition is same in all phases.Properties of pure substances required for design and sizing of various devicesCompressible Substances: Magnetic, electrical and surface effects insignificant.Examples: Water (solid, liquid, and vapor phases) Mixture of liquid water and water vapor Carbon Dioxide (CO2), N2 Mixtures of gases, such as air, as long as there is no change of phase.Note: Mixture of liquid air and gaseous air cannot be pure substance due to difference in their compositionsVapor Liquid Solid Phase Equilibrium in a Pure SubstanceSequence of Phenomena on heating 1 kg of water in the piston/cylinder arrangement at a constant pressure of 0.1MPa and initial temperature of 20oC as a system.

0.1MPa, T=20oC , specific volume v1 0.1MPa, T=99.6oC, v2>>v1 0.1MPa, T>99.6oC, v>v2(a) 0.1MPa, T=20oC , specific volume v1 (b) 0.1MPa, T=99.6oC, v2>>v1 (c) 0.1MPa, T>99.6oC, v>v2Saturation Temperature and Saturation Pressure:The temperature at which vaporization takes place at a given pressure is called saturation temperature. This pressure is called the saturation pressure for the given temperature. Thus, for water at 99.60C the saturation is 0.1 MPa, and for water at 0.1 MPa the saturation temperature is 99.60C.

vapor-pressure curve-Plot between saturation temperature and saturation pressure for a given substance. Important DefinitionsSaturated Liquid-If a substance exists as liquid at the saturation temperature and pressure.Compressed/Subcooled liquid: Liquid at a temperature lower than the saturation temperature for a given pressureTwo Phase substance: Substance exists as part liquid and part vapor at the saturation temperature. Its quality (x) is defined as the ratio of the mass of vapor to the total mass.Saturated Vapor: If a substance exists as vapor at the saturation temperature, it is called saturated vapor. Superheated Vapor: Vapor at a temperature greater than the saturation temperature for a given pressure. Temperature Volume diagram for water showing liquid and vapor phases

Critical Point:

Its a point of inflection of zero slope in a T-V diagram

The conditions at that point are called critical temperature (Tc), critical pressure (Pc) and critical volume (vc).

Two phases never exist during a constant pressure process for P>Pc. Its a continuous substance called fluid

But, arbitrarily it is considered as compressed liquid at T < Tc and super heated vapor at T>TcAt P>Pc, liquid and gas phases never exist in equilibrium.

Critical Point:

Two phase mixtures-Quality conceptQuality of two phase mixture is mass fraction of vaporSo for saturated vapor, x=1 Saturated liquid, x=0For two phase mixture, x is between 0 and 1

Quality of two phase mixture, x = mass of vapor/(mass of liquid + mass of vapor), so for saturated vapor, x=100% and for saturated liquid, x=0Estimation of two phase properties using quality

where Estimation of two phase properties using quality

Pressure Temperature diagram for waterExperiment to understand P-T diagram

On heating 1 kg ice at -20oC, 100kPa (line EF) in a piston-cylinder arrangement, temperature increases to 0oC, at which it melts (during melting specific volume of most substances increases except for water) and the temp remains constant. This is saturated solid. After all ice is melted to liquid, on further heating temp of liquid increases.

If the initial condition of ice is -20oC and 0.26kPa (line AB), on heating, its temperature increases to -10oC when ice gets transformed directly to vapor (sublimation)

If the initial condition is -20oC, 0.6113kPa (line CD), on heating its temperature increases to 0.01oC when ice gets transformed partly to liquid and partly to vapor i.e all three phases coexist (triple point)

Though the above plot is for water, all other substances behave similarily except that their critical and triple point data shall differ.

Experiment to understand PT diagramTriple Point Data

Independent Properties of Pure Substance: The state of a compressible pure substance is defined by two independent properties.

For saturated liquid and vapor states, they have same Temperature and Pressure. Hence pressure and temperature cannot be independent properties. So pressure and specific volume or pressure and quality are required to specify a saturation state of a pure substance.

Independent Properties of Pure SubstanceThermodynamic TablesOrganisationB.1.1T Psat vf vfg vg (similarily u, h, s)

B.1.2 P Tsat --do

B.1.3 Superheated Vapor series of T as f(P)

B.1.4Compressed liquid do

B.1.5Solid + vapor T P vi, vig , vg ( other properties like u, h and s)

Thermodynamic TablesRecap

Pure substancesTsat, Psat, Vap Pressure CurveDef of Sat liquid, Sat vap, SHV, SCL/CL, Two phase mixTwo phase propertiesCritical pointThermodynamic Diagrams-T-V, P-V, P-TIndependent propertiesOrganization of Tables

Recap:Equation of StateAny equation that relates the temperature, pressure, and specific volume of a substance is called the equation of state. The simplest and convenient equation of state for substances in a gas phase is the ideal-gas equation of state. This is valid at low densities when molecules are wide apart (P.E neglected) and independent of one another. A gas tends to be close to ideal gas at low pressures and high temperatures.As the state of a substance is further removed from saturated region, it is close to ideal gas i.e in superheated region.

Ideal Gas EquationTwo forms:

Where R is kJ/Kg.K (literature), is specific volume in m3/kgWhere is is in kJ/Kmol.K (8.314), is molar specific volume in m3/kmol. The two gas constants are related by P in kPa, T in Kelvin

Where R is J/Kg.K, is specific volume in m3/kg

T - v Diagram for WaterCompressibility FactorSignifies the deviation of the actual relation from the ideal gas equation of state and it is defined as

or

It can also be expressed as

For an ideal gas Z = 1, and the deviation of Z from unity measures the deviation of the actual P-V-T relation from the ideal gas equation of state.

Compressibility Chart for NitrogenThree Observations from the Chart:

At all temperatures, Z1 (ideal gas behaviour)as , P 0

At T 300K, Z is nearly unity upto P=10MPa

At low T and high P, Z deviates significantly from 1

Compressibility diagrams of other pure substances are similar in trend.

Three Observations from the ChartGeneralized Compressibility Charts:

Since the compressibility diagrams of all pure substances are similar qualitatively and different quantitatively due to their different critical values, the compressibility chart of Z as f (reduced temp Tr = T/Tc, reduced pressure Pr =P/Pc) is same for all substances, hence called Generalized Compressibility charts.

Theorem of Corresponding States:

Substances having same Tr and Pr have same Z value and hence deviate from the ideal gas behaviour to the same extent.

Compressibility Chart based on Data for a Large Number of Gases

Lee-Kesler Simple Fluid Compressibility FactorIdeal Gas Model may be assumed if

Pvg Superheated vapor (B.4.1)From B.4.2, v of 0.05242 is lying between pressures of 500 and 600kPa at 40oC. So interpolation.

(600-500)/(0.04628-0.05636) = (P-500)/(0.05242-0.05636)P=535kPa

(u600-u500)/v600-v500 = u-u500/v-v500 (249.48-250.51)/(0.04628-0.05636)=u-250.51/0.05242-0.05636(or)600-500/u600-u500= 535-500/u-u500

u=250.2kJ/kg

Ex 2 for InterpolationQDetermine whether water at each of the following states is a compressed liquid, superheated vapor, or a mixture of saturated liquid and vapor.10 MPa, 0.003 m3/kg1 MPa, 1900C 2000C, 0.1 m3/kg 10 kPa, 100CQCalculate the specific volume of saturated steam at 2000C, if the quality of steam is 70%.

QCalculate the specific volume of saturated steam at 2000C, if the 1 m3 closed vessel contains 1:9 volumetric ratio of liquid and vapor.

Determine the mass of vapor and liquidFind qualityCompute the % vapor present by volume and also by mass, what is the difference?QFor water at 100 kPa with a quality of 10% find the volume fraction of vapor. This is a two-phase state at a given pressure: Table B.1.2: vf = 0.001043 m3/kg, vg = 1.6940 m3/kg Vol fn of vapor=Vvap/(Vvap+Vliq)=mgvg/(mgvg+mfvf)Divide with total mass and using the definition of quality=xvg/(xvg+(1-x)vf)= 0.1 1.6940 (0.1 1.694 + 0.9 0.001043) = 0.16940/17034 = 0.9945

Notice that the liquid volume is only about 0.5% of the total.QA glass jar is filled with saturated water at 500 kPa of quality 25%, and a tight lid is put on. Now it is cooled to -10oC. What is the mass fraction of solid at this temperature?

Comparison of Table, Ideal Gas and other equation of state

Specific volume calculationAmmonia at 500kPa, 40C

Table 5.2.2, v=0.2923m3/kgUsing ideal gas eqn v=RT/P=0.48819*313/500=0.3056m3/kgerror= 0.2923-0.3056/0.2923=4.5%Compressibility factor -Given Tc=405.5K, Pc=11.35MPaTr=0.772, Pr=0.044 From fig D1, Z=0.97v=ZRT/P=0.97*0.48819*313/500=0.2964 Error: 1.4% w r t Tables

Note: Table D4 gives Zf, Zg, Prsat as a f(Tr) to get vf, vg and hence two phase volume

Comparison of Table, Ideal Gas and other equation of state